'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

✬ 

Vienna, St. Stephen’s Cathedral 

✫ 

Analysis and 

visulization 

of large networks 

with Pajek 

Vladimir Batagelj 

University of Ljubljana 

Methodenforum der Fakultät für Sozialwissenschaften 

Universität Wien, 21-22. 6. 2007 

version: June 18, 2007 / 03 : 11 

✩ 

✪

V. Batagelj: Analysis and visulization of large networks with Pajek 2 

✬ 

Outline 

1 Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

6 Complexity of algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

7 Pajek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

11 Approaches to large networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

12 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

19 Clusters, clusterings, partitions, hierarchies . . . . . . . . . . . . . . . . . . . . 19 

20 Representations of properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

30 Example: Snyder and Kick World Trade . . . . . . . . . . . . . . . . . . . . . . 30 

35 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

38 Contraction of cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 

42 Subgraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 

44 Important vertices in network . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 

52 Dense groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 

60 Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

64 Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

69 Citation weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

70 k-rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

75 Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

✫ 

Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ 

❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

84 Bipartite cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

91 Directed 4-rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 

96 Pattern searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 

101 Multiplication of networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 

105 Networks from data tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 

107 EU projects on simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 

116 What else? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 

http://vlado.fmf.uni-lj.si/pub/networks/doc/tut/Vienna07.pdf 

✫ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Alexandra Schuler/ Marion Laging-Glaser: 

Analyse von Snoopy Comics 

✫ 

Networks 

A network is based on two sets – set 

of vertices (nodes), that represent 

the selected units, and set of lines 

(links), that represent ties between 

units. They determine a graph. A 

line can be directed – an arc, or 

undirected – an edge. 

Additional data about vertices or 

lines can be known – their properties 

(attributes). For example: 

name/label, type, value, . . . 

Network = Graph + Data 

The data can be measured or computed. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Networks / Formally 

A network N = (V, L, P, W) consists of: 

• a graph G = (V, L), where V is the set of vertices and L = E ∪ A is 

the set of lines; A is the set of arcs and E is the set of edges. 

n = |V|, m = |L| 

• P vertex value functions / properties: p : V → A 

• W line value functions / weights: w : L → B 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪

12 "f12" 

13 "f13" 

14 "f14" 

V. Batagelj: Analysis and visulization of large networks 15 "f15" with Pajek 3 

16 "f16" 

✬ 

17 "f17" 

18 "f18" 

19 "f19" 

✫ 

Example: 20 "f20" Wolfe Monkey Data 

inter.net inter.net sex.clu age.vec rank.per 

*Vertices 20 

1 "m01" 

2 "m02" 

3 "m03" 

4 "m04" 

5 "m05" 

6 "f06" 

7 "f07" 

8 "f08" 

9 "f09" 

10 "f10" 

11 "f11" 

12 "f12" 

13 "f13" 

14 "f14" 

15 "f15" 

16 "f16" 

17 "f17" 

18 "f18" 

19 "f19" 

20 "f20" 

*Edges 

1 2 2 

1 3 10 

1 4 4 

1 5 5 

1 6 5 

1 7 9 

1 8 7 

1 9 4 

1 10 3 

1 11 3 

1 12 7 

1 13 3 

1 14 2 

1 15 5 

1 16 1 

1 18 1 

2 3 5 

*Edges 

1 2 2 

1 3 10 

1 4 4 

1 5 5 

1 6 5 

1 7 9 

1 8 7 

1 9 4 

1 10 3 

1 11 3 

1 12 7 

1 13 3 

1 14 2 

1 15 5 

1 16 1 

1 17 4 

1 18 1 

2 3 5 

2 4 1 

2 5 3 

2 6 1 

2 7 4 

2 8 2 

2 9 6 

2 10 2 

2 11 5 

2 12 4 

2 13 3 

2 14 2 

2 15 2 

. . . 

2 16 6 

2 17 3 

2 18 1 

2 19 1 

3 4 8 

3 5 9 

3 7 11 

3 8 7 

3 9 8 

3 11 14 

3 12 17 

3 13 9 

*vertices 20 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

*vertices 20 

15 

10 

10 

8 

7 

15 

5 

11 

8 

9 

16 

10 

14 

5 

7 

11 

7 

5 

15 

4 

*vertices 20 

1 

2 

3 

4 

5 

10 

11 

6 

12 

9 

7 

8 

18 

19 

20 

13 

14 

15 

16 

17 

Important notes: 0 is not allowed as vertex number. Pajek doesn’t support Unix text files – 

lines should be ended with3 CR6 LF. 5 

Methodenforum der Fakultät 

3 10 8 

1 17 für Sozialwissenschaften, 4 

Universität Wien, 21-22. 6. 2007 ▲ 

❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Size of network 

The size of a network/graph is expressed by two numbers: number of vertices 

n = |V| and number of lines m = |L|. 

In a simple undirected graph (no parallel edges, no loops) m ≤ 1 

n(n − 1); and in 

2 

a simple directed graph (no parallel arcs) m ≤ n 2 . 

The quotient γ = m 

mmax 

is a density of graph. 

Small networks (some tens of vertices) – can be represented by a picture and 

analyzed by many algorithms (UCINET, NetMiner). 

Also middle size networks (some hundreds of vertices) can still be represented by a 

picture (!?), but some analytical procedures can’t be used. 

Till 1990 most networks were small – they were collected by researchers using 

surveys, observations, archival records, . . . The advances in IT allowed to create 

networks from the data already available in the computer(s). Large networks became 

reality. Large networks are too big to be displayed in details; special algorithms are 

needed for their analysis (Pajek ). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Large Networks 

Large network – several thousands or millions of vertices. Can be stored in 

computer’s memory – otherwise huge network. 

Usually sparse m


✬ 

✫ 

Complexity of algorithms 

From some thousands to some (tens) millions of units (vertices). 

Let us look to time complexities of some typical algorithms: 

T(n) 1.000 10.000 100.000 1.000.000 10.000.000 

LinAlg O(n) 0.00 s 0.015 s 0.17 s 2.22 s 22.2 s 

LogAlg O(n log n) 0.00 s 0.06 s 0.98 s 14.4 s 2.8 m 

SqrtAlg O(n √ n) 0.01 s 0.32 s 10.0 s 5.27 m 2.78 h 

SqrAlg O(n 2 ) 0.07 s 7.50 s 12.5 m 20.8 h 86.8 d 

CubAlg O(n 3 ) 0.10 s 1.67 m 1.16 d 3.17 y 3.17 ky 

For the interactive use on large graphs already quadratic algorithms, O(n 2 ), 

are too slow. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Pajek 

The main goals in the design of Pajek are: 

• to support abstraction by (recursive) 

decomposition of a large network into 

several smaller networks that can be 

treated further using more sophisticated 

methods; 

• to provide the user with some powerful 

visualization tools; 

• to implement a selection of efficient 

subquadratic algorithms for analysis of 

large networks. 

With Pajek we can: find clusters (components, neighbourhoods of ‘important’ vertices, 

cores, etc.) in a network, extract vertices that belong to the same clusters and show them 

separately, possibly with the parts of the context (detailed local view), shrink vertices in 

clusters and show relations among clusters (global view). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Pajek’s data types 

In Pajek analysis and visualization are performed using 6 data types: 

• network (graph), 

• partition (nominal or ordinal properties of 

vertices), 

• vector (numerical properties of vertices), 

• cluster (subset of vertices), 

• permutation (reordering of vertices, ordinal 

properties), and 

• hierarchy (general tree structure on vertices). 

Pajek supports also multi-relational, temporal 

and two-mode networks. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

. . . Pajek’s data types 

The power of Pajek is based on several transformations that support 

different transitions among these data structures. Also the menu structure 

of the main Pajek’s window is based on them. Pajek’s main window 

uses a ‘calculator’ paradigm with list-accumulator for each data type. The 

operations are performed on the currently active (selected) data and are also 

returning the results through accumulators. 

The procedures are available through the main window menus. Frequently 

used sequences of operations can be defined as macros. This allows also 

the adaptations of Pajek to groups of users from different areas (social 

networks, chemistry, genealogy, computer science, mathematics. . . ) for 

specific tasks. Pajek supports also repetitive operations on series of 

networks. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

ESNA Pajek 

An introduction to social network analysis 

with Pajek is available in the book 

ESNA (de Nooy, Mrvar, Batagelj 2005). 

Pajek– program for analysis and visualization 

of large networks is freely available, 

for noncommercial use, at its web 

site. 

http://vlado.fmf.uni-lj.si/pub/networks/pajek/ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Approaches to large networks 

In analysis of a large network (several thousands or millions of vertices, 

the network can be stored in computer memory) we can’t display it in its 

totality; also there are only few algorithms available. 

To analyze a large network we can use statistical approach or we can use 

the described decomposition approach – identify smaller (sub) networks 

that can be analyzed further using more sophisticated methods. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

Input data 

• numeric → vector 

• ordinal → permutation 

✫ 

Statistics 

• nominal → clustering (partition) 

Computed properties 

global: number of vertices, edges/arcs, components; maximum core 

number, . . . 

local: degrees, cores, indices (betweeness, hubs, authorities, . . . ) 

inspections: partition, vector, values of lines, . . . 

Associations between computed (structural) data and input (measured) data. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Degrees 

degree of vertex v, deg(v) = number 

of lines with v as end-vertex; 

indegree of vertex v, indeg(v) = 

number of lines with v as terminal 

vertex (end-vertex is both initial and 

terminal); 

outdegree of vertex v, outdeg(v) = 

number of lines with v as initial vertex. 

n = 12, m = 23, indeg(e) = 3, outdeg(e) = 5, deg(e) = 6 

� 

indeg(v) = � 

outdeg(v) = |A| + 2|E|, � 

deg(v) = 2|L| − |E0| 

v∈V 

v∈V 

v∈V 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

. . . Statistics 

The global computed properties are reported by Pajek’s commands or can 

be seen using the Info option. In repetitive commands they are stored in 

vectors. 

The local properties are computed by Pajek’s commands and stored in 

vectors or partitions. To get information about their distribution use the 

Info option. 

As an example, let us look at The Edinburgh Associative Thesaurus 

network. The EAT is a network of word association as collected from 

subjects (students). The weight on the arcs is the count of word associations. 

File/Network/Read eatRS.net 

Info/Network/General 

It has 23219 vertices and 325624 arcs (564 loops); number of lines with 

value=1 is 227481. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

. . . Statistics 

To identify the vertices with the largest degree: 

Net/Partitions/Degree/All 

Partition/Make vector 

Info/Vector +10 

The largest degrees have the vertices: 

✫ 

vertex deg label 

1 12720 1108 ME 

2 12459 1074 MAN 

3 8878 878 GOOD 

4 18122 875 SEX 

5 13793 803 NO 

6 13181 799 MONEY 

7 23136 732 YES 

8 15080 723 PEOPLE 

9 13948 720 NOTHING 

10 22973 716 WORK 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Statistics / Pajek and R 

Pajek (0.89 and higher) supports interaction with statistical program R 

and the use of other external programs as tools (menu Tools). 

In Pajek we determine the degrees of vertices and submit them to R 

info/network/general 


Partition/Make Vector 

Tools/Program R/Send to R/Current Vector 

In R we determine their distribution and plot it 

summary(v2) 

t


✬ 

✫ 

freq 

1 5 10 50 500 5000 

EAT all-degree distribution 

● 

● 

● 

● 

EAT all−degree distribution 

● 

● 

● 

● 

● ● 

● 

●●●●●●●●● 

● ●● ●● 

● 

● 

● 

●●●●●● ● ● ●●●● ●● ● 

● 

●● 

● 

●●● ● 

●●●●● 

● 

● 

● ●●● 

● 

● 

●● ● ●● ● 

● ● 

● 

● 

● 

● 

● ● 

● 

● 

● 

● 

● 

● ● 

● 

● ● 

●● ● 

● 

● 

● 

● 

● 

● ● 

● 

● 

● ● 

● ● 

● 

● 

● ●●●●● 

● 

1 5 10 50 100 500 


❙ ▲ 

▲ 

deg 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

freq 

0 2000 4000 6000 

✫ 

Random graph degree distribution, n=100000, degav=30 

● 

● 

● ● ● ● ● ● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● ● ● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

Degree distribution 

● ● 

● ● ● ● ● ● ● ● ● ● ● 

10 20 30 40 50 

deg 

1 e+00 1 e+02 1 e+04 1 e+06 

● 

● 

US Patents degree distribution 

● 

● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● 

●●●●●●●● 

●●● ●●●●●●● 

● 

●●●● 

● 

●● ●●●●● 

● ●●●● 

● 

● 

●● 

● ● 

●●● 

● 

● 

●●● 

● ●● ● 

● 

● ● 

● 

● 

● ● 

● 

● ●● 

● 

● 

● ● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● 

● ● 

● 

● 

● ●● 

● 

● 

● 

● ● ● 

● ● ●●● 

● ●●● 

● 

1 5 10 50 100 500 1000 

Real-life networks are usually not random in the Erdős/Renyi sense. The 

analysis of their distributions gave a new view about their structure – Watts 

(Small worlds), Barabási (nd/networks, Linked). 


❙ ▲ 

▲ 

freq 

deg 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Clusters, clusterings, partitions, hierarchies 

A nonempty subset C ⊆ V is called a cluster (group). A nonempty set of 

clusters C = {Ci} forms a clustering. 

Clustering C = {Ci} is a partition iff 

∪C = � 

Ci = V in i �= j ⇒ Ci ∩ Cj = ∅ 

Clustering C = {Ci} is a hierarchy iff 

i 

Ci ∩ Cj ∈ {∅, Ci, Cj} 

Hierarchy C = {Ci} is complete, iff ∪C = V; and is basic if for all 

v ∈ ∪C also {v} ∈ C. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Representations of properties 

Properties of vertices P and lines W can be measured in different scales: 

numerical, ordinal and nominal. They can be input as data or computed 

from the network. 

In Pajek numerical properties of vertices are represented by vectors, 

nominal properties by partitions or as labels of vertices. Numerical 

property can be displayed as size (width and height) of vertex (figure), as its 

coordinate; and a nominal property as color or shape of the figure, or as a 

vertex label (content, size and color). 

We can assign in Pajek numerical values to links. They can be displayed 

as value, thickness or grey level. Nominal vales can be assigned as label, 

color or line pattern (see Pajek manual, section 4.3). 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

Some comments 

While the technical graph drawing problems could ask for a single ’the 

best’ picture, the social network analysis is a part of data analysis. Its goal 

is to get insight into the structure and characteristics of a given network, but 

also how it influences related social processes. 

What is the goal: exploration of network data (layout editor), presentation 

of the obtained results (layout viewer), . . . ? 

What is a GD result: picture or layout ? 

What is the medium of the result: static picture on ’paper’, interactive 

layout, . . . ? 

What kind of user will use the result: simple, advanced, . . . ? 

Most methods are ’paper’ oriented. In larger/denser networks there is 

often too much information to be presented at once. A possible answer are 

interactive layouts where the user controls what (s)he wants to see. 

✫ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

James Moody: Display of properties – school 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Lothar Krempel 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

FAS: The scientific field of Austria 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Katy Börner: Text analysis 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Jeffrey Johnson: St Marks food web 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Big picture, V. Batagelj, AE’04 

subnetwork (n = 5952, m = 18008) of the symmetrized Edinburgh Associative Thesaurus 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

✩ 

✪ 

Big picture 

10 

13 

14 

18 

19 

1968 

1969 

20 

20th 

9 

999 

a 

a daisy 

aah 

abandon 

abate 

abatement 

abbey 

abdicate 

abel 

abide 

ablative 

able 

about 

above 

abrasive 

abroad 

abrupt 

absent 

absent-minded 

abuse 

acceleration 

accept 

accident 

accomplish 

accordance 

according 

accordion 

account 

accountant 

accounts 

accumulate 

accurate 

aces 

ache 

aches 

achieve 

achievement 

acid 

acne 

acorn 

acquaintance 

acquire 

acquired 

act 

action 

actions 

active 

actor 

actress 

actual 

actually 

adam 

add 

addition 

address 

adequate 

adhere 

adjacent 

admit 

ado 

adolescence 

adult 

adults 

advance 

advice 

aeroplane 

aesop 

afar 

affair 

affection 

affirm 

affluence 

afraid 

africa 

aft 

after 

afternoon 

afterwards 

again 

against 

age 

aged 

ageing 

ageless 

agent 

ager 

aggression 

agitate 

ago 

agony 

agree 

agriculture 

aground 

ah 

ahead 

ahoy 

aid 

aided 

ail ailing 

aim 

air 

aircraft 

airport 

airy 

ajar 

al 

alarm 

alchemy 

alcohol 

alcoholic 

alcoholism 

alderman 

ale 

alert 

ales 

algebra 

alien 

alike 

alimentary 

alive 

alkali 

all 

all right 

alley 

allotment 

allow 

allowance 

ally 

almighty 

almond 

almoner 

almost 

alone 

alphabet 

already 

also 

altar 

alter 

alternative 

although 

aluminium 

always 

am 

amaze 

amazement 

amble 

ambulance 

amen 

amends 

america 

american 

amethyst 

amiable 

ammunition 

amnesia 

amok 

among 

amount 

ample 

amputate 

amputation 

amuse 

amusement 

amusing 

anaemic 

anatomy 

anchor 

ancient 

and 

and again 

and lime 

and on 

anew 

angel 

angels 

anger 

angry 

anguish 

animal 

animals 

ankle 

annihilate 

annoy 

annoyance 

annoyed 

anonymous 

answer 

answers 

ant 

anthem 

anthill 

anthropoid 

anti 

anticipate 

antimony 

antique 

ants 

anvil 

anxiety 

anxious 

anybody 

anything 

anywhere 

apart 

apartment 

ape 

apes 

apex 

apology 

apparent 

apparition 

appear 

appears 

appendix 

appetite 

apple 

apple pie 

apples 

apricot 

april 

aquaintance 

aquiline 

arcade 

archaeology 

archaic 

architect 

architecture 

arduous 

are 

argue 

argument 

arid 

arithmetic 

ark 

arm 

armchair 

armed 

armies 

armour 

arms 

army 

around 

arrange 

arrest 

arrival 

arrive 

arrow 

arrows 

arse 

arson 

art 

arthur 

article 

articles 

articulation 

artificial 

artist 

arts 

as 

as well 

ascend 

ascending 

ash 

ash-tray 

ashtray 

ask 

asked 

asleep 

aspidistra 

ass 

assist 

assistant 

association 

assume 

aster 

astonish 

astonishment 

astray 

astronaut 

astronomy 

asylum 

at 

at all 

at last 

at once 

ate 

atheist 

athlete 

atlantic 

atlas 

atmosphere 

atom 

atomic 

attack 

attain 

attempt 

attempted 

attempts 

attic 

attractive 

au pair 

auction 

audio 

august 

aunt 

auntie 

australia 

author 

autumn 

avarice 

avenue 

average 

avoid 

avon 

awake 

away 

awful 

axe 

axminster 

aye 

azure 

b 

baa 

babies 

baby 

bach 

bachelor 

back 

backside 

backward 

backwards 

bacon 

bacteria 

bad 

bad habit 

badminton 

bag 

baggage 

bagpipes 

bait 

bake 

baked 

baker 

bakery 

baking 

bald 

bale 

ball 

ballet 

balloon 

balmy 

bamboo shoots 

ban 

band 

bandit 

bang 

bank 

banks 

banner 

bar 

bare 

bargain 

barge 

barges 

bark 

barking 

barn 

barns 

baron 

barracks 

barrel 

barrels 

barrister 

barrow 

bars 

base 

basement 

bash 

basin 

basketball 

bastard 

bat 

bath 

bathroom 

baton 

bats 

battery 

battle 

bawl 

bay 

be 

beach 

beadle 

beads 

beak 

beam 

bean 

beans 

bear 

beard 

beards 

bearing 

beast 

beat 

beater 

beatitude 

beautiful 

beauty 

because 

bed 

bedroom 

beds 

bedsit 

bedtime 

bee 

beef 

been 

beer 

bees 

beet 

beethoven 

beetle 

beetroot 

before 

beg 

began 

beggars 

begin 

beginner 

beginning 

begun 

behind 

behold 

being 

belfry 

belief 

believing 

bell 

bellow 

bells 

belly 

belong 

belonging 

below 

belt 

ben 

bench 

beneath 

beneficent 

benign 

bent 

bereavement 

berg 

berserk 

berth 

best 

better 

between 

beware 

bias bible 

bicycle 

bicycles 

bid 

bidder 

big 

bigger 

bike 

bikes 

bilge 

bill 

billion 

bills 

billy 

bin 

bind 

binder 

binding 

bird 

birds 

birmingham 

birth 

birthdays 

biscuit 

biscuits 

bishop 

bit 

bitch 

biter 

biting 

bits 

bitten 

bitter 

black 

black eye 

blackberry 

blackboard 

blackpool 

blacksmith 

blade blades 

blanco 

blanket 

blast 

blaze 

blazer 

bleat 

bleed 

bleeding 

blend 

blew 

blight 

blimey 

blinds 

bliss 

blister 

blisters 

blithe 

blob 

bloke 

blokes 

blood 

bloom 

blossom 

blouse 

blow 

blown 

blows 

blue 

bluebell 

blueberry 

bluebottle 

blues 

blunder 

blunt 

board 

boat 

boats 

bob 

bobby 

bodied 

body 

bog 

boggle 

boil 

boiled 

boiler 

boiling 

bold 

bolognese 

bolts 

bomb 

bomber 

bond 

bondage 

bone 

bones 

bonfire 

bonny 

boo 

book 

books 

boom 

boost 

boot 

boots 

booty 

booze 

boozed 

bore 

bored 

boring 

born 

borne 

borough 

borrow 

bosom 

boss 

botany 

both 

bottle 

bottles 

bottom 

bottomless 

bough 

bought 

boulder 

boulders 

bounce 

bouncer 

bound 

bountiful 

bounty 

bouquet 

bout 

bouts 

bow 

bowler 

bowling 

bows 

box 

boxer 

boxing 

boy 

boyfriend 

boys 

brace 

bracelet 

braces 

brahms 

brain 

brake 

brakes 

bran 

branch 

branches 

brass 

brat 

brave 

brawn 

bread 

breadth 

break 

breakable 

breaker 

breakers 

breakfast 

breakwater 

breast 

breath 

breathe 

breathtaking 

bred 

breed 

breeds 

breeze 

brew 

brewing 

bribe 

brick 

bricks 

bride 

bridge 

bridle 

brief 

brigade 

bright 

brightness 

brighton 

brilliant 

brim 

brine 

bring 

brisk 

britain 

british 

broad 

broadcast 

broader 

broke 

broken 

broker 

brook 

broom 

broth 

brother 

brothers 

brought 

brown 

brown ale 

brows 

bruises 

brum 

brush 

brussel 

brussels 

bubble 

bubbles 

bucket 

buckle 

bud 

buddy 

budgerigar 

budgie 

buffalo 

bugle 

bugs 

build 

building 

built 

bulb 

bulbs 

bull 

bull ring 

bullet 

bulletin bullocks 

bulls 

bumble-bee 

bumpy 

bunch 

bungalow 

bunny 

buns 

burden 

bureau 

burger 

burglar 

burial 

burn 

burning 

burrow 

burst 

bus 

busby 

buses 

bush 

bushes 

business 

busy 

but 

butcher 

butter 

buttercup 

buttercups 

butterfly 

button 

buttons 

butty 

buy 

buying 

buzz 

bye 

cab 

cabbage 

cabbage-white 

cabby 

cabin 

cable 

cache 

cactus 

cadbury’s 

cafe 

cage 

caged 

cain 

cake 

caked 

cakes 

calamity 

calcium 

calculation 

calendar 

calf 

calm 

came 

camel 

camera 

camp 

camping 

campus 

can 

canal 

canals 

canasta 

cancer 

cancerous 

candle 

candles 

candlestickmaker 

cane 

cannot 

canoe 

canon 

cans 

canterbury 

canvas 

cap 

capable 

capital 

capone 

captain 

captive 

car 

caramel 

carbonate 

cardboard 

cardiac 

cards 

care 

career 

careful 

caress 

cargo 

carnations 

carpenter 

carpentry 

carpet 

carriage 

carried 

carry 

carry on 

cars 

cart 

cartilage 

carton 

cartridge 

carver 

carving 

case 

cash 

casks 

cassock 

cast 

castaway 

caster 

casterbridge 

castle 

castles 

casualty 

cat 

catastrophy 

cater 

catfish 

cathedral 

catholic 

cats 

cattle 

cauliflower 

cause 

caution 

cavalry 

cave cavern 

ceiling 

celebrated 

celebration 

celebrity 

cell 

cellar 

cello 

celtic 

cement 

cent 

centigrade 

centimetre 

central 

centre 

cents 

century 

cereal 

cerebrum 

ceremony 

certain 

certainly 

certainty 

cha 

chaff 

chain 

chair 

chairs 

chalet 

chalk 

chance 

change 

channel 

chaos 

chap 

chapel 

char 

character 

charge 

charles 

charm 

charming 

chart 

chase 

chaste 

chastity 

chat 

chatter 

cheap 

cheat 

check 

cheddar 

cheerfulness 

cheese 

chef 

chemical 

chemist 

chemistry 

cheque 

cherish 

cherries 

cherry 

cherubs 

cheshire 

chess 

chest 

chestnut 

chew 

chewing 

chez 

chick 

chicken 

chickens 

chief 

child 

children 

chill 

chimney 

chimpanzee 

chin 

china 

chinese 

chips 

chiropody 

chisel 

chivalry 

chloride 

chocolate 

chocolates 

choice 

choir 

choke 

choose 

choosers 

chop 

chopin 

chopper 

choppy 

choral 

christ 

christianity 

christmas 

chrysalis 

chuck 

chuckle 

church 

churches 

churchyard 

churn 

cider 

cigar 

cigarette 

cigarettes 

cigars 

cinch 

cinders 

cinema 

circa 

circle 

circles 

circular 

circumference 

circumstance 

circus 

cities 

citizen 

citrus 

city 

civil 

clamber 

clanger 

clash 

class 

classes 

classical 

claw 

claws 

clean 

cleaner 

cleanliness 

cleanse 

clear 

clergy 

clergyman 

clever 

cliff 

cliffs 

climate 

climb 

climber 

climbing 

clink 

clip 

cloak 

clock 

clocks 

cloister 

close 

closed 

closeness 

closer 

clot 

cloth 

clothe 

clothes 

clothes-line 

clotted 

cloud 

clouds 

cloudy 

clown 

club 

clubs 

clutch 

clyde 

co-operation 

coagulate 

coal 

coals 

coarse 

coast 

coat 

cob 

cobweb 

coca-cola 

cocktail 

cod 

code 

coerce 

coffee 

coffer 

coffin 

coffins 

cogitate 

coif 

coin 

coins 

coke 

cold 

colder 

cole 

collapse 

collar 

colleague 

collect 

college 

collide 

colon 

colonel 

colour 

colours 

column 

coma 

comb 

combat 

come 

come back 

comes 

comfortable 

comforts 

comic 

coming 

command 

commandment 

commenced 

commerce 

commission 

common market 

commons 

communicate 

communism 

communist 

communists 

companion 

companionship 

company 

compartment 

compartments 

compel 

complain 

complete 

completely 

complex 

composition 

compound 

comprehend 

comprehensive 

comprise 

compulsory 

computer 

comrade 

concede 

concentrate 

concept 

conception 

concern 

concerto 

conclude 

conclusion 

concord 

concrete 

concur 

condition 

conditioned 

conditioning 

conducted 

conductor 

confectionery 

confess 

confession 

confide 

confinement 

confirm 

conflict 

congregate 

congregation 

coniferous 

conjunctivitis 

conjurer 

conjurors 

connect 

consciousness 

consent 

consequence 

conservative 

consider 

considerate 

consideration 

consist 

constable 

constellation 

construct 

constructed 

construction 

consulate 

consultant 

consume 

consumer 

contain 

contemplate 

contemplating 

content 

contented 

contention 

contentment 

continent 

continue 

contours 

contraband 

contraceptive 

contract 

contrary 

convalescence 

convenience 

conveniences 

convent 

convict 

coo 

cook 

cooker 

cookery 

cookies 

cool 

coon 

coons 

cop 

cops 

cor 

coral 

cord 

cordial 

corduroy 

core 

cork 

cormorant 

corn 

corned 

corner 

cornflakes 

corns 

cornwall 

coroner 

coronet 

corporal 

corps 

corpse 

corral 

correct 

correspondence 

corridors 

corrosion 

corrugated 

cortex 

cosine 

cosmology 

cost 

costly 

costume 

cosy 

cot 

cottage 

cotton 

cough 

could 

couldn’t 

council 

count 

counter 

counterpoint 

country 

county 

coup 

couple 

court 

courts 

coventry 

cover 

cow 

cowboy 

cowboys 

cower 

cows 

cowslips 

cox 

cozy 

cracker 

crackle 

cradle 

crag 

crags 

crane 

cranium 

cranny 

crap 

crash 

crate 

cravat 

craving 

crawl 

crawly 

crayon 

crazy 

cream 

creamy 

crease creases 

create 

created 

creator 

creature 

credible 

creep 

creeper 

creepy 

crescent 

crests 

crew 

crew cuts 

cricket 

cried 

crime 

criminology 

crimson 

cringe 

cripple 

crisp 

crisps 

croak 

crocus 

crook 

crooked 

crop 

cropper 

cropping 

cross 

cross-country 

crossing 

crossword 

crow 

crowd 

crowds 

crown 

crucified 

crucifix 

crucify 

cruel 

cruise 

cruiser 

crumb 

crumbly 

crumbs 

crust 

crusts 

cry 

crying 

crypt 

crystal 

cub 

cube 

cubic 

cubism 

cubs 

cuddly 

cuff 

cuisine 

cup 

curate 

cure 

curlers 

currants 

currency 

curried 

curry 

curtain 

cushion 

custard 

custody 

customs 

cut 

cutlet 

cuts 

cycle 

cylindrical 

d’etat 

d.c. 

dad 

daddy 

daffodil 

daffodils 

daft 

dagger 

daily 

dairy 

daisies 

daisy 

dale 

dam 

damn 

damp 

damsel 

dance 

dancer 

dandelion 

danger 

dangerous 

dank 

dark 

darkness 

darling 

darn 

dart 

darts 

darwin 

dash 

data 

date 

dative 

daughter 

daughters 

david 

dawdle 

day 

days 

de gaulle 

de plume 

deacon 

dead 

dead-end 

deadly 

deaf 

deafening 

deal 

dealt 

dean 

dear 

dearest 

death 

debate 

debt 

debts 

decade 

decay 

deceit 

deceive 

december 

decibel 

decimal 

deck 

decker 

decks 

declare 

decline 

decorate 

decrease 

decree 

decrepit 

dee 

deed 

deep 

deer 

defeat 

defence 

defend 

definite 

definitely 

degree 

dehydrated 

deity 

dejected 

delicate 

delight 

delilah 

delinquent 

deliver 

deltoid 

demand 

demi 

demonstrate 

den 

dense 

dental 

dentist 

dentistry 

dentists 

denude 

depart 

department 

departs 

departure 

depth 

depths 

dermis 

descend 

descending 

desert 

desire 

desist 

desk 

destiny 

destroy 

detached 

detatched 

detect 

detective 

detector 

detergent 

devalue 

devalued 

devil 

devon 

dew 

diabetic 

diagonal 

diamond 

dictionary 

did 

didn’t 

die 

died 

diesel 

diet 

different 

difficult 

difficulty 

diffraction 

dig 

digest 

digestion 

digestive 

digit 

digits 

digs 

dilute 

dim 

dime 

dimension 

din 

ding 

dingy 

dinner 

dinners 

dipper 

direct 

director 

dirt 

dirtier 

dirty 

disagree 

disappear 

disaster 

disc 

disciple 

discomfort 

discontinue 

discover 

discovered 

discovery 

discuss 

discussion 

disease 

disgrace 

disk 

dislike 

disobey 

disorder 

dispense 

displease 

dispute 

disregard 

distance 

distant 

distaste 

distress 

distribute 

district 

disturbance 

ditty 

divan 

dive 

diverse 

divide 

divine 

diving 

divorce 

dizzy 

do 

dock 

docks 

doctor 

doctor’s 

doctors 

document 

dodgems 

doer 

does 

doesn’t 

dog 

dog-collar 

dogfish 

dogs 

dole 

dolittle 

dollar 

dollars 

dolls 

dolly 

dolphin 

don’t 

donate 

donated 

done 

dong 

donkey 

donor 

door 

doors 

dose 

dot 

double 

doubles 

doubtful 

dough 

douse 

dove 

dover 

doves 

down 

downhill 

downwards 

doze 

dozen 

dozy 

drab 

drag 

dragon 

drain 

drake 

drakes 

drama 

drape 

draught 

draw 

drawbridge 

drawer 

dread 

dream 

dreaming 

dreams 

dreary 

dress 

dressing-gown 

drink 

drinker 

drinking 

drip 

dripping 

drive 

driver 

drivers 

driving 

drop 

drought 

drown 

drowning 

drug 

drugs 

drum 

drunk 

dry 

dry martini 

dubious 

duck 

duckling 

ducks 

due 

dull 

dumb 

dump 

dunce 

dung 

duodenal 

during 

dust 

dustbin 

dwarf 

dwell 

dwellings 

each 

eagle 

ear 

earlier 

early 

earn 

ears 

earth 

ease 

easel 

easier 

east 

easter 

easy 

eat 

eater 

eaters 

eating 

eats 

ebb 

economics 

economy 

ecstasy 

ed 

edam 

edge 

edifice 

edinburgh 

edition 

editor 

educate 

education 

effect 

egg 

egg-shaped 

eggs 

ego 

egypt 

eight 

eighteen 

either 

ejector 

elan 

elastic 

elated 

elbow 

elect 

electric 

elephant 

elevate 

elevator 

eleven 

elf 

elizabeth 

ellipse 

elm 

elms 

elopement 

else 

elusive 

ember 

emblem 

embrace 

emery 

emigrate 

emotion 

empire 

employment 

empty 

enamel 

encore 

encounter 

encountered 

end 

ended 

ending 

endlessness 

ends 

endure 

enemies 

enemy 

engaged 

engagement 

engine 

england 

english 

enjoyment 

enlist 

enormous 

enough 

enquire 

enquiries 

enrol 

enter 

entire 

entrance 

entry 

envelope 

envy 

epaulettes 

epidermis 

epilepsy 

epileptic 

epoch 

epsom 

er 

era 

erect 

erected 

erosion 

erotica 

errant 

error 

erupt 

especially 

essay 

essence 

essential 

esso 

estate 

estuary 

et 

eternal 

ethics 

europe 

eve 

even 

evening 

evensong 

event 

events 

ever 

ever ready 

everest 

evergreen 

everlasting 

every 

everybody 

everyone 

everything 

everywhere 

evidence 

evil 

evolution 

ewe 

ewes 

exact 

exam 

examination 

examine 

exams 

excavation 

excellent 

exception 

exceptionally 

exchange 

excise 

excitement 

exclaim 

exclamation 

exclude 

excursion 

excuse 

exhausted 

exhaustion 

exist 

existence 

exit 

expect 

expense 

expenses 

expensive 

expire 

explode 

explosion 

export 

express 

expression 

extinct 

extinguish 

extra 

extremely 

eye 

eyelid 

eyes 

fable 

fables 

fabric 

fabulous 

face 

facile 

facility 

fact 

factory 

facts 

faculty 

faeces 

fag 

fags 

fahrenheit 

fail 

failed 

failure 

fair 

faire 

fairies 

fairy 

fairy tale 

faith 

falcon 

fall 

falling 

falls 

false 

falsehood 

fame 

family 

famine 

famished 

famous 

fang 

fangs 

fantasies 

fantastic 

fantasy 

far 

farce 

fare 

farm 

farther 

farthing 

fascinating 

fascist 

fashion 

fashioned 

fast 

fastener 

faster 

fastest 

fat 

fatal 

fate 

father 

fathoms 

fatigue fatigued 

fear 

fearful 

fearless 

fears 

feasible 

feast 

feather 

feathered 

feathers 

feature 

features 

featuring 

fed 

fee 

feeble 

feed 

feel 

feeling 

feet 

fell 

fellow 

felony 

female 

feminine 

ferocious 

ferrite 

ferry 

festival 

fetch 

fetched 

fete 

fever 

few 

fewer 

fiasco 

fib 

fibre 

fiction 

fiddle 

fiddler 

field 

fields 

fiendish 

fierce 

fifteen 

fifth 

fig 

fight 

figures 

file 

filings 

fill 

filled 

fillings 

filly 

film 

films 

filter 

filth 

filthy 

fin 

final 

finality 

finally 

finals 

finance 

finch 

find 

find out 

finder 

finger 

fingers 

fingertips 

finish 

finished 

finite 

fir 

fire 

firearm 

fired 

fireside 

firework 

firs 

first 

firth 

fish 

fishes 

fishing 

fist 

fit 

fitness 

fitted 

five 

fizz 

fizzle 

fizzy 

flag 

flagpole 

flagstones 

flake 

flakes 

flame 

flames 

flat 

flats 

flatten 

flavour 

flee 

fleece 

fleet 

flesh 

flight 

fling 

flint 

flip 

flirt 

float 

flock 

flocks 

floe 

flog 

flood 

floor 

flop 

flounder 

flour 

flow 

flower 

flower-pot 

flowers 

flowing 

floyd 

flu 

flue 

fluid 

flush 

flutterby 

flux 

fly 

flying 

foal 

foam 

foe 

fog 

foggy 

foil 

fold 

folder 

foliage 

folk 

folks 

follicle 

follow 

follower 

food 

fool 

foolhardy 

foolish 

fools 

foot 

football 

for 

force 

forces 

ford 

fore 

foreign 

foreigner 

foreigners 

foremost 

foresee 

forest 

forestry 

foretell 

forget 

forgetting 

forgive 

forgot 

forgotten 

fork 

forks 

forlorn 

form 

former 

fornicate 

fornication 

forsyte 

forte 

forth 

forthwith 

fortitude 

fortnight 

fortress 

fortunate 

fortune 

forty 

forward 

forwards 

found 

foundry 

fountain 

four 

fourth 

fowl 

fox 

fracture 

fragile 

fragment 

fragrance 

frame 

france 

francs 

frank 

fray 

fred 

free 

freedom 

freeway 

freeze 

freezing 

freight 

french 

frequent 

frequently 

fret 

friar 

fried 

friend 

friendly 

friends 

fright 

frighten 

frightened 

frock 

frog 

from 

from home 

front 

frost 

froth 

frothy 

fruit 

fry’s 

frying 

fuck 

fudge 

fuel 

full 

fume 

fun 

fund 

funeral 

funnel 

funnels 

funny 

fur 

furious 

furlong 

furry 

fury 

futile 

future 

fuzz 

gagged 

gain 

gained 

gala 

galaxy 

gale 

gallery 

gallon 

gallop 

gallows 

galore 

gambling 

game 

games 

gander 

gaol 

gap 

garage 

garb 

garbage 

garden 

gardens 

garlic 

garment 

garments 

garter 

gas 

gash 

gasoline 

gasp 

gastric 

gather 

gauze 

gave 

gay 

gaze 

gazer 

gazers 

gazette 

geese 

gel 

gelding 

gender 

generation 

generous 

gent 

gentle 

gentleman 

gentlemen 

gents 

genuine 

geography 

geology 

geometry 

george 

geranium 

german 

germanium 

germs 

get 

get ready 

get set 

get-together 

ghost 

ghoul 

giant 

gibbon 

gift 

gifts 

giggle 

gill 

gin 

giraffe 

girders 

girl 

girlfriend 

girls 

give 

give out 

given 

giver 

glacial 

glacier 

glad 

glade 

gladly 

gladness 

glandular 

glare 

glass 

glasses 

gleam 

gleams 

glee 

glen 

glimmer 

glisters 

glitter 

glittering 

glitters 

globe 

gloom 

gloss 

glove 

gloves 

glow 

glucose 

glue 

glum 

gnat 

gnu 

go 

go back 

go to 

goal 

goalie 

goat 

goats 

god 

godliness 

godmother 

goes 

going 

gold 

golden 

golf 

goliath 

golly 

gone 

gong 

gonzales 

good 

good-bye 

goodbye 

goodness 

goods 

goose 

gore 

gorge 

gorilla 

gosh 

gospel 

gossip 

got 

grab 

gracious 

gradual 

graft 

grain 

grains 

gram grammar 

gramme 

grand 

grandma 

grandpa 

granite 

grant 

granted 

grape 

grapefruit 

grapes 

graph 

grasp 

grass 

grate 

grateful 

grates 

gratify 

grating 

grave 

graves 

gravity 

grease 

great 

greatest 

greed 

greek 

green 

greenhouse 

greens 

greet 

greeted 

grew 

greyhounds 

grief 

grieving 

grime 

grin 

grip 

groan 

groceries 

groin 

groom 

groove 

groovy 

grotesque 

ground 

group 

grow 

growl 

grown 

grown-up 

growth 

grub 

grumble 

guard 

guardian 

guide 

guides 

guilt 

guilty 

guiness 

gulf 

gull 

gulp 

gum 

gums 

gun 

gunpowder 

guns 

gut 

guts 

h2o 

ha 

habit 

haemoglobin 

haemorrhage 

haemorrhoids 

haggis 

hailer 

hair 

half 

halifax 

hall 

hall-mark 

halt 

halved 

ham 

hammer 

hammock 

hand 

handed 

handkerchief 

handle 

handler 

hands 

handsom 

hang 

hanger 

hanging 

happen 

happening 

happenings 

happens 

happiness 

happy 

harbours 

hard 

harden 

harder 

hardness 

hare 

hares 

harlot 

harm 

harmed 

harmony 

harness 

harold 

harpoon 

harpsichord 

harry 

hart 

harvest 

has 

has not hash 

hasn’t 

haste 

hasten 

hastings 

hasty 

hat 

hatch 

hate 

hated 

hater 

hatred 

hatter 

have 

have to 

having 

havoc 

hawthorn 

hay 

hay fever 

haystack 

hazard 

haze 

he 

head 

headache 

headgear 

headmaster 

heads 

healer 

health 

healthy 

heap 

hear 

heard 

hearer 

hearing 

hearing-aid 

hearsay 

hearse 

heart 

hearth 

heat 

heath 

heathen 

heather 

heating 

heave 

heaven 

heavens 

heavy 

hedge 

heel 

heeled 

heels 

height 

hell 

hello 

help 

helped 

helper 

hemp 

hen 

hence 

hens 

her 

herald herd 

herds 

here 

hers 

herself 

hesitation 

hexagonal 

hide 

hiding 

high 

high-speed 

higher 

highest 

highland 

hike 

hill 

hills 

hilly 

him 

himself 

hinder 

hindered 

hinge 

hinges 

hire 

hired 

his 

hiss 

history 

hit 

hitch 

hither 

hitler 

hive 

ho 

hoar 

hoarse 

hobby 

hockey 

hog 

hoist 

hold 

hole 

holiday 

holidays 

holiness 

hollow 

holly 

holst 

holster 

holy 

holy ghost 

home 

home rule 

homes 

homeward 

homicide 

homo 

homosexual 

honest 

honesty 

honey 

hong 

honk 

honours 

hood 

hoof 

hook 

hoop 

hooves 

hop 

hope 

hopes 

hopper 

hops 

horizon 

horn 

hornpipe 

horns 

horrible 

horrid 

horrific 

horror 

horse 

horses 

hose 

hospital 

hostage 

hostel 

hostile 

hot 

hothouse 

hotter 

hound 

hounds 

hour 

hours 

house 

housemaid 

houses 

how 

however 

hoyle 

hudson 

hue 

huff 

hug 

huge 

human 

humans 

humid 

humour 

hump 

hundred 

hunger hungry 

hunt 

hurdle 

hurricane 

hurry 

hurt 

hurting 

husband 

hush 

hut 

hyacinth 

hyde park 

hydrogen 

hymn 

hypothalamus 

i 

ice 

ice age 

icicle 

icing 

icy 

idea 

ideas 

identical 

idiot 

idiots 

idle 

if 

ignore 

ill 

illegitimacy 

illegitimate 

illness 

illuminations 

image 

images 

imagine 

imbecile 

imbibe 

immaterial 

immediately 

impediment 

imperative 

implement 

imply 

import 

impossible 

impressionism 

imprisonment 

improbably 

improve 

in 

in addition 

in front 

in hand 

in-law 

inanimate 

inch 

inches 

incidents 

incisor 

include 

incognito 

income 

incomplete 

incorrect 

increase 

incredible 

indeed 

indefinite article 

index 

india 

indian 

indians 

indicate 

indication 

indigestion 

indirect 

indisposed 

individual 

indolent 

industrious 

industry 

inebriated 

inebriating 

infamous 

infant 

infective 

inferior 

infernal 

infinite 

infinity 

infirmary 

infliction 

information 

inherited 

iniquity 

initially 

injection 

injure 

injured 

injury 

injustice 

ink 

ink-pot 

inland 

inmate 

inn 

inner 

innocence 

innocent 

input 

insane 

insect 

insects 

inside 

insignificant 

inspect 

inspector 

inspiration 

instant 

instantly 

instead 

insurance 

intake 

intelligent 

intentions 

interesting 

intermediate 

intestine 

intestines 

into 

invalid 

invest 

invisible 

ire 

ireland 

iris 

irish 

iron 

ironing 

irrelevant 

irritation 

is 

island 

isles 

isn’t 

isosceles 

it 

italy 

itch 

ivy 

izzy 

ja 

jack 

jacket 

jaffa 

jagged 

jail 

jailor 

jam 

jamb 

james 

jane 

jangle 

jar 

jaundice 

jaw 

jazz 

jeans 

jeep 

jeffreys 

jelly 

jersey 

jest 

jester 

jesus 

jet 

jewels 

jib 

jigsaw 

jill 

jingle 

jive 

job 

jockey 

john 

join 

joined 

joint 

joke 

jonathan 

jottings 

journal 

journalism 

joy 

joyful 

jubilation 

judge 

judgement 

judicial 

judo 

judy 

jug 

jugular 

juice 

juices 

juicy 

july 

jump 

jumper 

jumping 

jumps 

junction 

june 

jungle 

junior 

jupiter 

jury 

justice 

jutland 

juvenile 

kane 

kangaroo 

karate 

karl 

keep 

keeper 

keg 

keg bitter 

ken 

kennedy 

kennels 

kept 

kettle 

key 

key-hole 

keyboard 

keys 

khaki 

kid 

kidney 

kids 

kill 

killed 

kilt 

kin 

kind 

kinds 

king 

kingdom 

kings 

kinky 

kipper 

kippers 

kirk 

kiss 

kit 

kitchen 

kite 

kith 

kitten 

kittens 

kitty 

knee 

kneecap 

kneel 

knees 

knickers 

knife 

knight knit 

knitting 

knives 

knob 

knock 

knocker 

knocks 

knot 

know 

known 

kong 

kraut 

la 

label 

labour 

labyrinth 

lace 

laces 

lad 

ladder 

ladders 

laden 

ladies 

lady 

lag 

lager 

lagging 

lagoon 

laid 

lair 

lake 

lakes 

lamb 

lambs 

lamp 

lamps 

lampshade 

land 

landscape 

language 

lanky 

lantern 

lard 

larder 

large 

larger 

larva 

lash 

lashes 

lass 

last 

late 

lately 

later 

latest 

lather 

latter 

laugh 

laughing 

laughter 

launching 

laundrette 

laundry 

lavatory 

law 

law-court 

lawn 

lawns 

lawyer 

lay 

lazy 

lead 

leader 

leaf 

leafy 

league 

leagues 

leak 

lean 

leap 

leaping 

leaps 

lear 

learn 

learner 

learnt 

leash 

least 

leather 

leave 

leaver 

leavers 

leaves 

leaving 

lecture 

led 

ledge 

ledger 

leek 

leeks 

left 

leg 

legal 

legend 

legion 

legislate 

legs 

leisure 

lemon 

lemonade 

lemons 

lend 

length 

lens 

lenses 

lent 

lente 

leo 

less 

lessons 

let 

let go 

lethal 

letter 

letter-box 

letters 

lettuce 

level 

levi 

liberal 

liberty 

library 

licence 

lichen 

lick 

licking 

lid 

lids 

lie 

lies 

lieutenant 

life 

life-boat 

lift 

lifting 

ligament 

light 

lighter 

lightning 

lights 

like 

likely 

lily 

limb 

limbs 

lime 

lime juice 

limit 

limited 

limp 

line 

liner 

liners 

lines 

lining 

link 

links 

lino 

lion 

lion-tamer 

lioness 

lions 

lip 

lips 

lipstick 

liquid 

liquor 

list 

listen 

listened 

listener 

literature 

litre 

little 

live 

liver 

livery 

living 

liz 

lizard 

lo 

load 

loaded 

loaf 

loan 

loath 

loathe 

loaves 

lobe 

local 

location 

loch 

lock 

locket 

locks 

locomotive 

locus 

locution 

lodge 

lodging 

lodgings 

loft 

lofty 

log 

logs 

lollipop 

lomond 

london 

lone 

loneliness 

lonely 

long 

long time 

longer 

longing 

loo 

look 

look for 

looked 

looking 

loom 

loose 

loot 

lord 

lorry 

lose 

loser 

loss 

lost 

loth lotion 

lots 

lotus 

loud 

love 

loved 

loveliness 

lovely 

lover 

lovers 

low 

lower 

lowest 

luck 

lucky 

ludwig 

luggage 

lump 

lumps 

lunatic 

lung 

lung cancer 

lungs 

lust 

lying 

macaroni 

machine 

mackerel 

mackintosh 

mad 

madam 

made 

magazine 

magic 

magician 

magistrate 

magistrates 

maid 

maiden 

mail 

mainland 

maisonettes 

majesty 

major 

majority 

make 

maker 

malady 

male 

mallet 

malt 

man 

manchester 

mane 

manhole 

maniac 

manner 

manners 

manor 

mansion 

mantel 

mantis 

manufacture 

manufacturer 

manure 

many 

mao 

map 

maple 

march 

mare 

margarine 

marge 

mark 

market 

marmalade 

marriage 

married 

marrow 

marry 

mars 

mart 

martial 

martin 

martini 

martyr 

marvellous 

marx 

masculine 

mask 

masochism 

mason 

mass 

mass production 

masses 

massive 

mast 

master 

masts 

masturbate 

masturbating 

masturbation 

mat 

match 

matchbox 

matches 

mate 

matelot 

material 

mates 

maths 

mating 

matrimony 

matron 

matt 

matter 

mattress 

maturity 

mauve 

maximum 

may 

maybe 

mayor 

mayoress 

maze 

me 

meadow 

meadows 

meal 

meals 

mean 

meander 

meaning 

means 

measles 

measure 

measures 

meat 

media 

medic 

medicine 

meditate 

meditation 

meek 

meet 

meeting 

melancholy 

mellow 

melody 

melt 

member 

memoir 

memory 

men 

mend 

menstrual 

menstruation 

mentioned 

menu 

mercenary 

merchandise 

merchant 

merci 

merry 

mersey 

mesh 

messing 

met 

metal 

meter 

methedrine 

method 

methodist 

meths 

methylated 

metre 

metres 

metric 

mexico 

mice 

micro 

mid-way 

middle 

middle-aged 

midlands 

midst 

migraine 

mild 

mile 

mileage 

miles 

milk 

milk bottle 

milking 

milkmaid 

milky way 

milligan 

million 

millionaire 

mince 

mind 

mine 

miner 

mineral 

miners 

mines 

mini-skirt 

minimum 

minister 

mink 

minor 

minority 

minster 

mint 

minus 

minute 

minutes 

mire 

mirror 

mirth 

misdeed 

miser 

miserable 

miserly 

miss 

mist 

mistake 

mistress 

mists 

misuse 

mitre 

mitten 

mix 

mixer 

moan 

mob 

mobile 

mod 

mode 

modern 

moisture 

mole 

molehill 

moment 

monarch 

monarchy 

monastery 

money 

monger 

monk 

monkey 

monkeys 

monks 

monotonous 

month 

months 

moo 

moon 

moorland 

moped 

morals 

morbid 

more 

morning 

morose 

morrow 

morse 

mortality 

mortar 

mortgage 

mosaic 

mosquito 

moss 

most 

moth 

mother 

motion 

motive 

motor 

motors 

mould 

mound 

mount 

mountain 

mountaineering 

mountains 

mourn 

mournful 

mourning 

mouse 

mousse 

mouth 

movement 

movies 

mower 

mozart 

much 

muck 

mucky 

mud 

mule 

multiply 

mum 

mummy 

murder 

murmur 

muscle 

mushroom 

mushrooms 

music 

muslin 

must 

mutiny 

mutton 

my 

myself 

myth 

mythology 

nail 

nails 

naked 

name 

nanny 

nap 

napalm 

nape 

napkin 

nappies 

napping 

nappy 

narcissus 

narrate 

narrow 

narrows 

nasty 

nation 

national 

nationality 

natural 

naturally 

nausea 

nauseating 

nauseous 

naval 

navigation 

navy 

nazi 

near 

nearby 

nearer 

nearest 

nearly 

neat 

neater 

neath 

necessary 

necessities 

necessity 

neck 

necklace 

need 

needed 

needle 

needles 

needs 

needy 

negative 

negatively 

negress 

negro 

negroes 

neigh 

neighbour 

neighbours 

neither 

nelson 

neon 

ness 

nest 

net 

netball 

netting 

neurology 

neuter 

never 

nevertheless 

new 

newcastle 

news 

newsagent 

newspaper 

newt 

newton 

newyork 

next 

next door 

next to 

niagara 

nibble 

nice 

nick 

nickel 

nigger 

nigh 

night 

nightmare 

nightmares 

nights 

nil 

nimble 

nine 

nineteen 

ninety 

ninth 

nip 

nippy 

nisi 

nit 

no 

no see 

noah 

nobody 

noise 

noiseless 

noises 

noisy 

nom 

non-violence 

nonsense 

nook 

noon 

nor 

north 

northern 

nose 

nostril 

nostrils 

nosy 

not 

not at all 

not me 

not nice 

not out 

not quite 

notes 

nothing 

nothingness 

notice 

notion 

notorious 

nought 

noun 

nourishment 

nous 

nova 

novel 

novels 

november 

now 

nowhere 

nuclear 

nude 

nuisance 

number 

numbers 

numerous 

nun 

nurse 

nursery 

nursery school 

nurses 

nut 

nuts 

nylon 

o’clock 

o.k. 

oak 

oar 

oars 

oath 

oats 

obese 

obey 

object 

objection 

objects 

obligatory 

oblong 

observe 

observed 

obstinate 

obtain 

obtained 

obvious 

occasionally 

occupation 

occupied 

occur 

occurence 

occurs 

ocean 

oceanography 

octaves 

octopus 

odd 

odds 

odontology 

odour 

oesophagus 

of 

of a kind 

of cake 

of course 

of fact 

off 

offend 

offer 

office 

offside 

offspring 

often 

oh 

oh la la 

oil 

old 

old age 

olive 

omelette 

omit 

on 

once 

once upon a time 

one 

ones 

oneself 

onion 

onions 

only 

onward 

onyx 

ooh 

oops 

open 

opener 

operation 

opinion 

opportunity 

oppose 

opposed 

opposing 

opposite 

optics 

optimism 

option 

or 

or not 

or not to be 

or nothing 

oral 

orange 

oranges 

oration 

orator 

orb 

orbit 

orchard 

orchestra 

order 

ore 

organ 

organic 

orifice 

origin 

ornament 

orphan 

orthopaedic 

osborne 

osprey 

ostrich 

other 

others 

ouch 

ought 

ounce 

ounces 

our 

ours 

ourselves 

out 

outboard 

outdated 

outer 

outing 

output 

outside 

over 

overdraft 

overruled 

overtake 

owe 

owed 

owing 

own 

owned 

owner 

ox 

oxo 

oxygen 

oz 

pacific 

pack 

package 

packet 

paddle 

paddy 

padlock 

pagan 

page 

pages 

paid 

pail 

pain 

painful 

pains 

paint 

painting 

pair 

pairs 

pakistani 

pal 

palate 

pale 

palm 

palms 

pan 

panda 

pane 

pang 

pangs 

panning 

panorama 

panoramic 

pans 

pansies 

pansy 

panther 

pantry 

pants 

paper 

papers 

paradise 

parallel 

parcel 

parched 

parent 

parents 

paris 

parish 

park 

parker 

parking 

parrot 

parson 

part 

particle 

particularly 

partridge 

party 

pass 

passed 

passion 

passive 

past 

paste 

pastry 

pasture 

pastures 

paternal 

path 

paths 

pathway 

patience 

patient 

patients 

patriotism 

pattern 

patterson 

pauper 

pause 

pavement 

paving 

paw 

paws 

pax 

pay 

payment 

pea 

peace 

peaceful 

peaches 

peak 

pear 

pears 

peas 

pebble 

pebbles 

peck 

peculiar 

pedal 

peel 

peeler 

peeling 

peer 

peg 

pegs 

pelmet 

pen 

pence 

pencil 

peninsula 

pennies 

penniless 

penny 

pension 

pensions 

penthouse 

penultimate 

people 

pepper 

peppery 

peptic 

per cent 

perambulate 

perceive 

perceived 

perfect 

perforation 

perform 

performance 

perfume 

perhaps 

period 

perjury 

permission 

permit 

perpetual 

persevere 

persian 

person 

personal 

personality 

personally 

persons 

perspex 

perspire 

pessimism 

pest 

pests 

pet 

petal 

petals 

petite 

petrel 

petrol 

petroleum 

pets 

pew 

phallus 

pheasant 

phoney 

photosynthesis 

phrase 

physician 

physics 

piano 

pick 

picking 

pickle 

pickles 

picture 

pictures 

pidgeon 

pie 

piece 

pieces 

pied 

pier 

pig 

pigeon 

piggy bank 

pile 

piles 

pilfer 

pilfering 

pilgrim 

pill 

pillow 

pillow-case 

pillows 

pillowslip 

pills 

pilot 

pimple 

pin 

pin-stripe 

pinch 

pine 

pineapple 

ping 

pink 

pins 

pint 

pints 

pious 

pip 

pipe 

piper 

piping 

pips 

pissed 

pistol 

piston 

pit 

pitcher 

pitt 

pity 

placard 

place 

placed 

placid 

plaice 

plaintive 

plan 

plane 

planet 

planetarium 

planets 

plank 

planks 

plankton 

planning 

plant 

plants 

plasma 

plaster 

plastic 

plated 

platform 

play 

player 

players 

playground 

playing 

plays 

plaything 

pleasant 

please 

pleased 

pleasure 

pleat pleats 

pledge 

plenty 

plot 

plough 

plug 

plum 

plump 

plunge 

plus 

ply 

pocket 

pod 

poem poet 

poetry 

point 

pointed 

poison 

poisonous 

poke 

poker 

polar bear 

pole 

pole vault 

police 

policeman 

policy 

polite 

politician 

poll 

pollen 

polly 

polo 

polythene 

pomp 

pond 

ponder 

pong 

pony 

poodle 

pool 

poor 

poorly 

pop 

pop group 

pope 

popeye 

poplar 

poppies 

pops 

population 

porcelain 

pores 

pork 

porpoise 

porridge 

port 

portion 

portrait 

ports 

position 

positive 

positively 

possess 

possessed 

possessing 

possibility 

possible 

possibly 

post 

postcard 

posted 

poster 

postman 

pot 

potato 

potatoes 

pots 

pottage 

pouch 

pound 

pounds 

poverty 

pow 

powder 

power 

powerful 

pox 

practice 

praise 

pram 

prawn 

pray 

prayer 

praying 

precarious 

precipice 

precise 

predicate 

prefect 

prefer 

pregnant 

prejudice 

premium 

prepared 

prescription 

present 

presented 

presents 

preserve 

preserved 

president 

press 

presume 

pretender 

pretty 

prevent 

previous 

preying 

price 

prick 

prickly 

pride 

priest 

priestess 

primary 

prime 

prince 

princess 

print 

printing 

prison 

prisoner 

prisoners 

private 

private eye 

prize 

probable 

probably 

problem 

proceed 

procure 

prodigy 

produced 

producer 

profession 

professor 

proffer 

profile 

profit 

profound 

programme 

progress 

promenade 

promise 

pronoun 

proof 

proper 

props 

prose 

prosper 

prosperity 

prosperous 

protein 

protest 

protestant 

provide 

provost 

prow 

pub 

pubic 

public 

pudding 

puff 

puke 

pull 

pullover 

pulp 

pulse 

pump 

punch 

puncher 

punishment 

pup 

pupil 

pupils 

puppet 

puppies 

puppy 

purchase 

pure 

purple 

purse 

pursue 

push 

pusher 

puss 

pussy 

put 

putty 

puzzle 

pyjamas 

pyramid 

quack 

quacks 

quadruped 

quaint 

quake 

quality quantity 

quarantine 

quarrel 

quarter 

quartered 

quartet 

quarto 

queen 

queens 

queer 

quench 

quenched 

query 

quest 

question 

questions 

queue 

quick 

quickly 

quid 

quiescent 

quiet 

quietly 

quilt 

quinine 

quo 

rabbit 

rabbits 

rabble 

race 

rack 

racket 

racquet 

radio 

radish 

raffle 

rage 

rags 

rail 

railroad 

rails 

railway 

railways 

rain 

rainbow 

rained 

raining 

raise 

raising 

raisins 

rally 

ram 

ramble 

ran 

rang 

range 

rangers 

rant 

rapid 

rapidly 

rare 

rarely 

rash 

rasp 

raspberry 

rat 

rather 

rats 

rattle 

rave 

raw 

ray 

rayon 

rays 

razor 

reach 

reaction 

reactor 

read 

reader 

reading 

ready 

reagents 

real 

really 

reap 

rear 

reason 

recall 

receipt 

receive 

received 

recently 

recipe 

recital 

recline 

recognise 

recognize 

recollect 

reconsider 

record 

recorder 

recount 

rectangle 

rector 

red 

reddish 

reef 

reel 

reeling 

refectory 

referee 

reference 

refill 

reflect 

reflection 

reflections 

reflex 

refund 

refuse 

refused 

regal 

regard 

regiment 

regret 

regulation 

regulations 

reign 

relate 

relay 

release 

religion 

remain 

remainder 

remaining 

remedy 

remember 

remembered 

remembering 

remittance 

remove 

render 

repair 

repay 

repeat 

repetition 

replenished 

reply 

reports 

repose 

reproduce 

reptile 

republic 

request 

require 

rescue 

reservoir 

residence 

residing 

resort 

respond 

response 

rest 

restaurant 

result 

results 

resurrection 

retail 

retain 

retained 

retaliate 

retard 

retreat 

return 

reveal 

revenue 

reverend 

reverie 

revolve 

reward 

rhodesia 

rhyme rhymes 

rhythm 

ribbon 

ribbons 

rice 

rich 

riches 

ridden 

ride 

rider 

ridge 

ridiculous 

riding 

rifle 

rifleman 

rifles 

rigging 

right 

rights 

rigid 

ring 

rink 

rip 

ripe 

ripped 

ripple 

ripples 

rise 

rising 

risk 

river 

rivulet 

road 

road works 

roads 

roam 

roar 

roars 

roast 

rob 

robber 

robbers 

robe 

robin 

robust 

rock 

rocker 

rocket 

rocking 

rocks 

rocky 

rod 

rode 

rodent 

rodents 

roe 

rolling 

rolls 

roman 

romantic 

rome 

romper 

roof 

roofs 

room 

root 

rope 

rose 

roses 

rot 

rotten 

rough 

round 

route 

rover 

row 

rowan 

roy 

royal 

royalty 

royce 

rubbish 

rug 

rugby 

rugger 

ruin 

ruins 

rule 

rules 

rum 

rummy 

run 

rung 

rungs 

runner 

running 

rush 

russia 

rust 

sacked 

sacred 

sad 

saddle 

sadism 

safe 

safety 

saga 

said 

sail 

sailing 

sailor 

sailors 

saint 

salad 

salary 

sale 

saline 

saliva 

sallow 

saloon 

salt 

salt water 

salts 

salty 

salvation 

same 

samson 

sanction 

sand 

sandal 

sandals 

sandy 

sane 

sank 

sap 

sapiens 

sarcasm 

sari 

sat 

satan 

satellite 

satiate 

satin 

satisfy 

saturn 

sauce 

saucer 

sausage 

save 

saver 

saves 

saving 

savoir 

saw 

sawdust 

say 

scaffolding 

scales 

scalpel 

scape 

scarce 

scare 

scared 

scarf 

scarlet 

scent 

sceptre 

scheme 

school 

schoolroom 

schooner 

science 

scissor 

scissors 

scones 

scooters 

score 

scotch 

scotia 

scotland 

scout 

scouts 

scrambled 

scrap 

scrape 

scratch 

scrawl 

scream 

screech 

screw screwdriver 

screws 

scribble 

scripture 

sculpture 

scuttle 

scythe 

sea 

seagull 

seaman 

search 

searching 

seascape 

seasoning 

seat 

seatbelt 

seats 

second 

seconds 

secretary 

sect 

section 

secure 

see 

seeing 

seek 

seeker 

seem 

seems 

seen 

segment 

seldom 

select 

selection 

self 

sell 

seller 

selling 

semi 

semi-detached 

semibreves 

sender 

senior 

sensation 

sense 

senseless 

sent 

sentence 

sentry 

separate 

sequence 

serenade 

serene 

serf 

sergeant 

series 

servant servility 

set 

setter 

settle 

seven 

seventh 

sever 

several 

severe 

severn 

sew 

sewing 

sex 

shade 

shadows 

shaft 

shaggy 

shake 

shaker 

shakes 

shakespeare 

shall 

shallow 

shame 

shampoo 

shanties 

shanty 

shape 

shares 

shark 

sharp 

sharpen 

sharpener 

shatter 

shave 

shaving 

she 

shear 

shearing 

shears 

sheath 

shed 

sheep 

sheepskin 

sheet 

sheets 

shelf 

shell 

shepherd 

shepherds 

shilling 

shillings 

shimmer 

shin 

shine 

shiner 

shines 

shining 

ship 

shipment 

ships 

shirt 

shirts 

shit 

shiver 

shock 

shod 

shoe 

shoes 

shoot 

shooter 

shooters 

shooting 

shop 

shopping 

shore 

short 

shorter 

shorts 

shot 

shotgun 

should 

shoulder 

shoulders 

shout 

shouting 

shove 

shovel 

show 

shower 

showing 

shrews 

shrub 

shrubs 

shrug 

shrunken 

shudder 

shush 

shut 

shutter 

shy 

sick 

sickle 

sickness 

sidewalk 

sight 

sighted 

sign 

signal 

signalman 

signature 

signpost 

silence 

silencer 

silent 

silica 

silk 

silky 

sill 

sills 

silly 

silly bitch 

silver 

similar similarity 

simon 

simple 

simplicity 

simultaneous 

sin 

since 

sine 

sing 

singer 

singing 

single 

sink 

sip 

siphon 

sipping 

sir 

sister 

sisters 

sit 

site 

sits 

sitter 

sitting 

six 

sixpence 

sixteen 

sixth 

size 

skate 

skates 

skating 

skeleton 

sketch 

ski 

skiing 

skin 

skinny 

skip 

skipping 

skirt 

skull 

sky 

sky-line 

slabs 

slack 

slake 

slaked 

slams 

slash 

slate 

slaughter 

slave 

slay 

sledge 

sleep 

sleepiness 

sleeping 

sleeping bag 

sleepy 

slept 

slice 

slick 

slide 

slim 

slime 

slip 

slipper 

slippers 

slippy 

slope 

sloshed 

slothful 

slow 

slow down 

slower 

slowest 

slowly 

sludge 

slug 

sluggish 

slumber 

slumbers 

slush 

sly 

smack 

small 

smartie 

smash 

smashed 

smell 

smelling 

smile 

smith’s 

smog 

smoke 

smokes 

smoking 

smooth 

smuggle 

smut 

snack 

snail 

snake 

snakes 

snap 

snarl 

snatch 

sneak 

sneeze 

sniff 

snip 

snipe 

snob 

snog 

snooker 

snooty 

snooze 

snore 

snoring 

snort 

snow 

snowdon 

snub 

snuff 

snug 

so 

soak 

soap 

soaring 

sob 

sober 

soccer 

social 

societies 

sock 

socks 

sod 

soda 

sodium 

soft 

soften 

softer 

softly 

softness 

soil 

soiled 

soiree 

solar 

solar system 

sold 

solder 

soldier 

soldiers 

sole 

solicitor 

solid 

solitary 

solitude 

solution 

solve 

solved 

solving 

sombre 

somebody 

somerset 

something 

sometime 

sometimes 

somewhere 

son 

sonata 

song 

sons 

soon 

sooner 

soot 

sore 

sorrow 

sorry 

sort 

sorts 

sought 

soul 

sound 

sounds 

soup 

sour 

source 

south 

southern 

sow 

spa 

space 

spacious 

spade 

spades 

spaghetti 

span 

spanner 

spare 

spark 

sparkle 

sparrow 

spasm 

spawn 

speak 

speaker 

speaking 

spear 

spectacles 

speech 

speed 

speedy 

spelling 

spend 

spending 

spent 

spew 

sphere 

spherical 

spice 

spider 

spiders 

spike 

spinach 

spindly 

spine 

spinning 

spinster 

spiral 

spire 

spires 

spirit 

spirits 

spit 

spitfire 

splash 

splinter 

spoil 

spoilt 

spoke 

spoken 

spooky 

spoon 

spoonful 

sport 

spot 

spotless 

spots 

spotted 

spouse 

sprain 

spread 

spree 

spring 

springs 

sprint 

sprinted 

sprinter 

sprout 

sprouts 

spud 

spuds 

sputnik 

squadron 

squalor 

square 

squares 

squash 

squaw 

squeak 

squelch 

squint 

squirm 

sssh 

stab 

stable 

stack 

stage 

stags 

stains 

stair 

staircase 

stairs 

stale 

stalk 

stall 

stallion 

stamen 

stamp 

stand 

stands 

stanza 

star 

starched 

stare 

stark 

starling 

starlings 

starring 

stars 

start 

started 

starve 

starved 

starving 

state 

stated 

states 

statesman 

station 

stationery 

stations 

statistics 

statue 

stature 

status 

stay 

staying 

steady 

steak 

steal 

stealing 

steam 

steel 

steep 

steeple 

stem 

stench 

steps 

sterling 

stethoscope 

stew 

steward 

stick 

sticks 

sticky 

stiff 

stifling 

still 

sting 

stingy 

stink 

stir 

stitch 

stoat 

stock 

stocking 

stockings 

stocks 

stodge 

stodgy 

stole 

stomach 

stone 

stoned 

stones 

stool 

stop 

stopped 

stopper 

storage 

store 

stories 

stork 

storm 

stormy 

story 

straight 

strain 

strand 

strange 

stranger 

strap 

strategy 

straw 

strawberries 

strawberry 

stream 

street 

streets 

strength 

stress 

stretch 

strike 

string 

strip 

striped 

stripes 

strips 

strive 

stroganoff 

stroke 

stroll 

strolled 

strong 

struck 

structure 

strudel 

struggle 

stub 

stubble 

stubborn 

stud 

studies 

study 

studying 

stuff 

stump 

stupendous 

stupid 

subject 

subtract 

subtraction 

suburb 

succeed 

success 

succour 

succulent 

such 

suds 

sues 

suet 

suffer 

sufferer 

suffering 

suffice 

sufficient 

sugar 

sugar lumps 

sugars 

suggestion 

suicide 

suit 

suite 

sum 

summer 

summit 

sums 

sun 

sun-tan 

sunday 

sunny 

sunrise 

sunset 

superficial 

superior 

supply 

sure 

surely 

surface 

surgeon 

surgery 

surmise 

surprise 

suspend 

swallow 

swear 

sweat 

sweater 

swede 

sweep 

sweet 

sweetness 

sweets 

sweety 

swift 

swiftly 

swim 

swimming 

switch 

switzerland 

swoop 

sword 

swotting 

symbol 

symphony 

synthetic syringe 

syrup 

system 

table 

tables 

tablet 

tablets 

tack 

tackled 

tacks 

tadpole 

tag 

tail 

tailor 

tails 

take 

take place 

taken 

taker 

tale 

tales 

talk 

talked 

talking 

tall 

talon 

talons 

tame 

tamer 

taming 

tan 

tang 

tangerine 

tankard 

tanker 

tanks 

tanned 

tantrum 

tap 

tape 

taps 

tar 

target 

tarmac 

tart 

tartan 

tarts 

tarzan 

task 

taste 

taste-bud 

tasty 

taught 

tax 

taxi 

taylor 

tea 

tea-cup 

teach 

teacher 

teacup 

teak 

tear 

tears 

tease 

technology 

ted 

teen 

teeth 

telegram 

television 

tell 

teller 

temper 

temperature 

tempest 

tempo 

ten 

tenderness 

tennis 

tent 

tenth 

terminally 

terrain 

terrible 

terribly 

terrified 

terrify terror 

test 

tested 

tests 

text 

text book 

textile 

thames 

than 

thank 

thank you thankful 

thanks 

that 

thatch 

the 

theatre 

theatres 

thee 

theft 

their 

theirs 

them 

theme 

themselves 

then 

therapy 

there 

therefore 

thermodynamics 

thermometer 

these 

they 

thick 

thicker 

thicket 

thief 

thieve 

thieves 

thigh 

thin 

thine 

thing 

things 

think 

thinking 

thinner 

third 

thirst 

thirsty 

thirty 

this 

thistle 

thither 

thong 

thorn 

thoroughly 

those 

thou 

thought 

thoughts 

thousand 

thread 

three 

three-legged 

thrift 

thrill 

throat 

throb 

throbbing 

throne 

throw 

throwing 

thrush 

thrust 

thumb 

thumbs 

thump 

thunder 

thus 

thyself 

tick ticket 

tickle 

tide 

tidier 

tidings 

tidy 

tie 

tie-pin 

tied 

ties 

tiger 

tigers 

tight 

tights 

tigress 

tile 

tiles 

till 

tim 

timber 

time 

timer 

times 

timid 

timing 

tin 

tinker 

tinned 

tins 

tinsel 

tiny 

tip 

tired 

tiredness 

tissue 

tit 

title 

to 

to be 

to-day 

toad 

toadstool 

toadstools 

toast 

tobacco 

tock 

today 

toe 

toenail 

toenails 

toes 

toffee 

toga 

together 

togs 

toil 

toilet 

token 

tomato 

tomatoes 

tomb 

tomorrow 

ton 

tongs 

tongue 

tonic 

too 

tool 

toot 

tooth 

toothache 

toothbrush 

top 

topic 

topical 

topper 

tops 

torch 

torn 

tornado 

tortoise 

torture 

tory 

tot 

total 

totally 

totter 

touch 

towel 

tower 

towers 

town 

towns 

toy 

toys 

tractor 

trade 

trafalgar 

traffic 

traffic light 

train 

trains 

trams 

tranquil 

tranquillity 

transform 

transfusion 

transition 

transmit 

transplant 

transplants 

transport 

trap 

tray 

treacle 

treasure 

treble 

tree 

trees 

trek 

tremble 

trench 

trews 

triad 

trial 

triangle 

tribulation 

trick 

trickle 

tricky 

tricolour 

tried 

tries 

trigger 

trim 

trinity 

trio 

trip 

triplet 

triste 

triumph 

trivial 

trodden 

trooper 

troops 

tropic 

trot 

trotted 

trotter 

trotting 

troubled 

trouser 

trousers 

trove 

truck 

true 

truly 

trumpet 

trunk 

truth 

try 

tse tung 

tub 

tube 

tuck 

tug 

tulip 

tumble 

tumbler 

tummy 

tumour 

tune 

tuner 

tunnel 

turban 

turkish 

turn 

turning 

turnip 

turtle 

twain 

twelve 

twentieth 

twenty 

twice 

twig 

twin 

twins 

twist 

twit 

two 

twos 

type 

tyrant 

tyre 

u 

udder 

ugliness 

ugly 

ulcer 

um 

umbilical 

umbrella 

umpire 

unbound 

uncertain 

uncle 

unclean 

uncommon 

under 

underground 

underlay 

understand 

unearth 

unemployed 

uneven 

unexpected 

unfair 

unfinished 

unforgivable 

unhappiness 

unhappy 

unharmed 

unhealthy 

unicorn 

uniform 

unimportant 

union jack 

unit 

unite 

united 

unity 

universe 

university 

unjust 

unkind 

unknown 

unladen 

unlike 

unlikely 

unload 

unlucky 

unmarried 

unnatural 

unpleasant 

unpleasantness 

unprepared 

unready 

unreal 

unsafe 

unsure 

until 

untrue 

untruth 

unusual 

unwell 

up 

uphill 

upon a time 

upper 

upright 

upwards 

urban 

us 

useless 

usually 

utensils 

vacant 

vacation 

vacations 

vacuum 

vale 

valiant 

valid 

valley 

value 

van 

vanilla 

vanish 

vanity 

variety 

various 

vase 

vast 

veal 

vegetarian 

vehicle 

vein 

velocity 

vendor 

venetian 

venice 

ventricle 

venus 

verb 

verdict 

verse 

very 

vessel 

vessels 

vest 

vicar 

vicarage 

vietnam 

view 

vigour 

village 

ville 

vine 

vinegar 

vines 

vintage 

viola 

violin 

violins 

virgin 

virile 

visage 

visible 

vision 

vista 

visual 

vital 

vitamin c 

vivid 

vocation 

vodka 

void 

volcano 

volume 

vote 

wag 

wage 

wages 

waggon 

wagon 

wail 

wait 

waiting 

wake 

waking 

wales 

walk 

walked 

walking 

wall 

wallpaper 

wand 

wander 

wane 

want 

wanted 

wants 

war 

ward 

warden 

warder 

wardrobe 

wards 

ware 

warehouse 

warm 

warmer 

warmth 

warning 

warrant 

wary 

was 

wash 

washer 

washing 

washing up 

washington 

wasp 

waste 

watch 

watchman 

water 

water wings 

wave 

waves 

waving 

wavy 

wax 

way 

ways 

we 

weak 

weakness 

wealth 

wealthy 

weapon 

wear 

weary 

weasel 

weather 

weave 

weaver 

web 

wed 

wedding 

wee 

weeding 

weeds 

week 

weeks 

weep 

weight 

weights 

weighty 

weird 

welcome 

weld 

welfare 

well 

well mannered 

went 

wept 

were 

west 

westminster 

wet 

whale 

what 

what’s 

wheat 

wheel 

wheel chair 

wheels 

when 

where 

whether 

while 

whilst 

whimper 

whine 

whip 

whisk 

whiskey 

whisky 

whisper 

whistle 

white 

white collar 

who 

whole 

wholesale 

wholesome 

whom 

whore 

why 

wick 

wicked 

wide 

wider 

width 

wife 

wig 

wild 

wilderness 

will 

william willing 

willingly 

willow 

willows 

wilson 

win 

wind 

wind-screen 

window 

window pane 

windows 

windsor 

wine 

wing 

wings 

wink 

winner 

winter 

wipe 

wiper 

wire 

wireless 

wish 

wishers 

wit 

witch 

with 

with the wind 

within 

without 

wits 

wizard 

wog 

wogs 

wolf 

woman 

womb 

women 

wonderful 

woo 

wood 

wooden 

woods 

wool 

woolly 

word 

words 

wordsworth 

work 

worker 

working 

works 

world 

worlds 

worm 

worried 

worry 

worse 

worship 

worst 

worth 

would 

wound 

wounded 

woven 

wow 

wrap 

wrath 

wreck 

wriggle 

wriggling 

wrist 

write 

writer 

writing 

wrong 

wrongs 

y 

yacht 

yachts 

yank 

yard 

yards 

yarn 

yawn 

year 

yearn 

years 

yell 

yellow 

yes 

yesterday 

yield 

yolk 

york 

you 

young 

your 

yours 

yourself 

youth 

z 

zebra 

zero 

zip 

zoo 

zoology 


Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ▲ 

❙ ▲ 

● ▲ 

❙ ▲ ▲ 

☛ ✖


✬ 

✫ 

Temporal networks / September 11 

Pictures in SVG: 66 days. (SVG viwer) 

Steve Corman with collaborators 

from Arizona State 

University transformed, using 

his Centering Resonance Analysis 

(CRA), daily Reuters news 

(66 days) about September 

11th into a temporal network of 

words coappearance. This network 

was a challange network 

for Viszards 2002 session. 

Every year (from 2002) we have at the Sunbelt conference a Viszards 

session presenting solutions of Viszards group to a visualizations of 

selected network or type of networks. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Example: Snyder and Kick World Trade 

The data are available as a Pajek’s project file 

SaKtrade.paj 

The network consists of trade relations (118 vertices, 515 arcs, 2116 edges). 

The source of the data is the paper: Snyder, David and Edward Kick 

(1979). The World System and World Trade: An Empirical Exploration of 

Conceptual Conflicts, Sociological Quaterly, 20,1, 23-36. 

The project file contains also the (sub)continents partition: 

1 - Europe, 2 - North America, 3 - Latin America, 4 - South America, 5 - 

Asia, 6 - Africa, 7 - Oceania. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

kod 

Draw / Partition 

yem 

alb 

par 

lib 

mat 

bol 

nic 

gua 

zai 

nau 

hai 

hon 

mon 

syr 

tri 

sri 

saf 

uru tai rum 

vnr 

arg 

pol 

usr lux spa nor 

ins isr 

mex 

pan 

usa 

cze 

fra net 

eth 

gre 

jap 

can 

ita 

col 

ege 

bra 

swe gui bur ind 

vnd nep por 

uki 

sau pak 

wge 

chi 

den 

cha 

yug 

bel 

swi 

dom phi 

irn egy 

cyp 

aus 

alg 

aut 

lebhun 

ire 

irq fin 

ven per nig 

kuw 

ice 

som 

cub 

mla 

brm sud 

tun 

cos 

ken 

kmr 

sie 

upv 

gab 

bul liy mli 

jor 

chd 

tha nze 

tur 

uga 

els maa 

con 

mor kor 

cam 

gha afg rwa 

sen 

ecu 

ivo 

jam nir 

upv 

mat 

cub cyp 

ice 

som 

eth rum 

mli 

bul 

lib 

cze 

sie 

usr hun ege uru 

pol gre 

yug 

per 

gha 

chi 

mor 

ire braarg 

coltri 

can aus 

por fin 

ivo nig 

mex 

bol 

spa swi 

den swe 

chd 

nor 

ita 

uga 

saf 

fra 

ven 

gua ecu 

ken uki wgenet 

sen bel lux usa 

pan 

dom 

tog 

nir maa 

nic cos 

zai 

cam 

par 

con 

els jam 

hon 

dah 

gab 

gui 

hai 

rwa 

nau 

bur 

car 

alg 

afg 

yem 

tun liy syr 

leb 

jor tur sud 

kuw 

sau sri 

egy irq pak 

cha irn 

ind 

aut 

mla 

brm 

nze 

kmr 

isr 

jap 

tai 

tha phi 

vnr 

ins kor 

kod 

vnd 

nep 

dah 

car 

lao 

Draw/Draw Partition 

Layout/Energy/Kamada-Kawai/Free 

Layout/Energy/Fruchterman Reingold/2D 

tog 


❙ ▲ 

▲ 

alb 

mon 

lao 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Zoom in 

Using right button on the mouse select 

the zoom area. 

To restore the standard view select 

Redraw. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

rwa 

gui 

kod 

dah 

nep 

lao 

tog 

yem 

nau 

vnd 

hai 

chd 

els 

hon 

con 

upv 

car 

nir 

✫ 

cos 

bol 

mon 

cam 

kmr 

Fruchterman Reingold / factor = 9 

pan dom 

jamkor 

vnr 

gua zai 

ecu 

nic 

brm 

sen uga 

sie 

mat 

mli maa 

afg alb 

jap 

ins 

ven 

lux 

bel 

usa 

uki net 

wge 

fra 

lib 

par 

ita 

cha 

gha 

aut 

can 

nig 

ivo 

swi 

yug 

jor 

tha 

ind 

chicol 

phi tri 

eth 

spa 

mex 

swe 

nor 

cze 

ken 

den 

egy 

usr 

liy 

tun 

aus 

per mla 

bur 

irn 

ege 

saf 

gab 

tai 

nze 

isr 

fin arg 

pak 

pol 

leb 

bul 

rum 

syr 

som 

bra 

por 

cyp 

sud 

cub 

mor 

ice 

sau uru 

ire 

irq gre 

kuw 

tur 

sri hun 

alg 

Layout/Energy/Fruchterman Reingold/3D 

3D picture / King 

rwa 

gui 

dah 

nau 

vnd 

hai 

els 

hon 

upv 

car 

nir 

cos 

bol 

mon 

pan dom 

jamkor 

vnr 

gua zai 

ecu 

nic 

sen uga 

sie 

mat 

mli maa 

afg alb 

ven 

lux 

bel 

usa 

uki net 

wge 


❙ ▲ 

▲ 

kod 

nep 

lao 

tog 

yem 

chd 

con 

cam 

kmr 

brm 

jap 

ins 

fra 

lib 

par 

ita 

cha 

gha 

aut 

can 

nig 

ivo 

swi 

yug 

jor 

tha 

ind 

chicol 

phi tri 

eth 

spa 

mex 

swe 

nor 

cze 

ken 

den 

egy 

usr 

liy 

tun 

aus 

per mla 

bur 

irn 

ege 

saf 

gab 

tai 

nze 

isr 

fin arg 

pak 

pol 

leb 

bul 

rum 

syr 

som 

bra 

por 

cyp 

sud 

cub 

mor 

ice 

sau uru 

ire 

irq gre 

kuw 

tur 

sri hun 

alg 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Pajek - shadow [0.00,1.00] 

usa 

can 

cub 

hai 

dom 

jam 

tri 

mex 

gua 

hon 

els 

nic 

cos 

pan 

col 

ven 

ecu 

per 

bra 

bol 

par 

chi 

arg 

uru 

uki 

ire 

net 

bel 

lux 

fra 

swi 

spa 

por 

wge 

ege 

pol 

aus 

hun 

cze 

ita 

mat 

alb 

yug 

gre 

cyp 

bul 

rum 

usr 

fin 

swe 

nor 

den 

ice 

mli 

sen 

dah 

nau 

nir 

ivo 

gui 

upv 

lib 

sie 

gha 

tog 

cam 

nig 

gab 

car 

chd 

con 

zai 

uga 

ken 

bur 

rwa 

som 

eth 

saf 

maa 

mor 

alg 

tun 

liy 

sud 

irn 

tur 

irq 

egy 

syr 

leb 

jor 

isr 

sau 

yem 

kuw 

afg 

cha 

mon 

tai 

kod 

kor 

jap 

ind 

pak 

brm 

sri 

nep 

tha 

kmr 

lao 

vnd 

vnr 

mla 

phi 

ins 

aut 

nze 

Matrix representation 

usa 

can 

cub 

hai 

dom 

jam 

tri 

mex 

gua 

hon 

els 

nic 

cos 

pan 

col 

ven 

ecu 

per 

bra 

bol 

par 

chi 

arg 

uru 

uki 

ire 

net 

bel 

lux 

fra 

swi 

spa 

por 

wge 

ege 

pol 

aus 

hun 

cze 

ita 

mat 

alb 

yug 

gre 

cyp 

bul 

rum 

usr 

fin 

swe 

nor 

den 

ice 

mli 

sen 

dah 

nau 

nir 

ivo 

gui 

upv 

lib 

sie 

gha 

tog 

cam 

nig 

gab 

car 

chd 

con 

zai 

uga 

ken 

bur 

rwa 

som 

eth 

saf 

maa 

mor 

alg 

tun 

liy 

sud 

irn 

tur 

irq 

egy 

syr 

leb 

jor 

isr 

sau 

yem 

kuw 

afg 

cha 

mon 

tai 

kod 

kor 

jap 

ind 

pak 

brm 

sri 

nep 

tha 

kmr 

lao 

vnd 

vnr 

mla 

phi 

ins 

aut 

nze 

Partition/Make Hierarchy [Yes][No] 

Hierarchy/Make Permutation 

File/Network/Export Matrix to EPS/Using Permutation [SaKmatrix.EPS][No] 

GsView: Media/User Defined ... [1300 pt][1300 pt] 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Clustering 

Better network matrix reorderings can be obtained using clustering: 

Cluster/Create Complete Cluster [118] 

Operations/Dissimilarity*/d5 [1][SaKdendro.EPS] 

Hierarchy/Make Permutation 

[select network SaK.net] 

File/Network/Export Matrix to EPS/Using Permutation [SaKmatrix.EPS][No] 

or blockmodeling. 

P. Doreian, V. Batagelj, A. Ferligoj: 

Generalized Blockmodeling, 

CUP, 2004. Amazon. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

✩ 

✪ 

Clustering 

Pajek - Ward [0.00,135.13] 

cyp 

ice 

tun 

cub 

liy 

mor 

alg 

nig 

uga 

ken 

eth 

brm 

tha 

sud 

sri 

gha 

gre 

tur 

egy 

bul 

rum 

syr 

leb 

irn 

irq 

pak 

ire 

aut 

hun 

isr 

sau 

kuw 

aus 

fin 

por 

bra 

arg 

pol 

cze 

usr 

ege 

yug 

ind 

cha 

uki 

fra 

wge 

jap 

net 

ita 

usa 

bel 

lux 

swe 

den 

swi 

can 

nor 

spa 

car 

chd 

nau 

tog 

dah 

nir 

gab 

sie 

con 

hai 

gui 

mat 

bol 

par 

cam 

maa 

yem 

kod 

lao 

mon 

nep 

bur 

rwa 

vnd 

som 

afg 

mli 

upv 

alb 

kmr 

jor 

kor 

vnr 

phi 

nze 

tai 

mla 

ins 

saf 

mex 

col 

uru 

per 

chi 

ven 

ecu 

lib 

dom 

zai 

jam 

tri 

pan 

sen 

ivo 

els 

cos 

gua 

hon 

nic 


cyp 

ice 

tun 

cub 

liy 

mor 

alg 

nig 

uga 

ken 

eth 

brm 

tha 

sud 

sri 

gha 

gre 

tur 

egy 

bul 

rum 

syr 

leb 

irn 

irq 

pak 

ire 

aut 

hun 

isr 

sau 

kuw 

aus 

fin 

por 

bra 

arg 

pol 

cze 

usr 

ege 

yug 

ind 

cha 

uki 

fra 

wge 

jap 

net 

ita 

usa 

bel 

lux 

swe 

den 

swi 

can 

nor 

spa 

car 

chd 

nau 

tog 

dah 

nir 

gab 

sie 

con 

hai 

gui 

mat 

bol 

par 

cam 

maa 

yem 

kod 

lao 

mon 

nep 

bur 

rwa 

vnd 

som 

afg 

mli 

upv 

alb 

kmr 

jor 

kor 

vnr 

phi 

nze 

tai 

mla 

ins 

saf 

mex 

col 

uru 

per 

chi 

ven 

ecu 

lib 

dom 

zai 

jam 

tri 

pan 

sen 

ivo 

els 

cos 

gua 

hon 

nic 

cyp 

ice 

tun 

cub 

liy 

mor 

alg 

nig 

uga 

ken 

eth 

brm 

tha 

sud 

sri 

gha 

gre 

tur 

egy 

bul 

rum 

syr 

leb 

irn 

irq 

pak 

ire 

aut 

hun 

isr 

sau 

kuw 

aus 

fin 

por 

bra 

arg 

pol 

cze 

usr 

ege 

yug 

ind 

cha 

uki 

fra 

wge 

jap 

net 

ita 

usa 

bel 

lux 

swe 

den 

swi 

can 

nor 

spa 

car 

chd 

nau 

tog 

dah 

nir 

gab 

sie 

con 

hai 

gui 

mat 

bol 

par 

cam 

maa 

yem 

kod 

lao 

mon 

nep 

bur 

rwa 

vnd 

som 

afg 

mli 

upv 

alb 

kmr 

jor 

kor 

vnr 

phi 

nze 

tai 

mla 

ins 

saf 

mex 

col 

uru 

per 

chi 

ven 

ecu 

lib 

dom 

zai 

jam 

tri 

pan 

sen 

ivo 

els 

cos 

gua 

hon 

nic 

Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ▲ 

❙ ▲ 

● ▲ 

❙ ▲ ▲ 

☛ ✖


✬ 

The order of clusters in a hierarchy 

is not fixed and can be 

changed. 

✫ 

Reordering clustering 


We see the typical center–periphery structure. 

uki 

fra 

wge 

jap 

net 

ita 

usa 

bel 

lux 

swe 

den 

swi 

can 

nor 

spa 

irn 

irq 

pak 

ire 

aut 

hun 

isr 

sau 

kuw 

aus 

fin 

por 

bra 

arg 

pol 

cze 

usr 

ege 

yug 

ind 

cha 

gre 

tur 

egy 

bul 

rum 

syr 

leb 

cyp 

ice 

tun 

cub 

liy 

mor 

alg 

nig 

uga 

ken 

eth 

brm 

tha 

sud 

sri 

gha 

kor 

vnr 

phi 

nze 

tai 

mla 

ins 

saf 

mex 

col 

uru 

per 

chi 

ven 

ecu 

lib 

dom 

zai 

jam 

tri 

pan 

sen 

ivo 

els 

cos 

gua 

hon 

nic 

car 

chd 

nau 

tog 

dah 

nir 

gab 

sie 

con 

hai 

gui 

mat 

bol 

par 

cam 

maa 

yem 

kod 

lao 

mon 

nep 

bur 

rwa 

vnd 

som 

afg 

mli 

upv 

alb 

kmr 

jor 

uki 

fra 

wge 

jap 

net 

ita 

usa 

bel 

lux 

swe 

den 

swi 

can 

nor 

spa 

irn 

irq 

pak 

ire 

aut 

hun 

isr 

sau 

kuw 

aus 

fin 

por 

bra 

arg 

pol 

cze 

usr 

ege 

yug 

ind 

cha 

gre 

tur 

egy 

bul 

rum 

syr 

leb 

cyp 

ice 

tun 

cub 

liy 

mor 

alg 

nig 

uga 

ken 

eth 

brm 

tha 

sud 

sri 

gha 

kor 

vnr 

phi 

nze 

tai 

mla 

ins 

saf 

mex 

col 

uru 

per 

chi 

ven 

ecu 

lib 

dom 

zai 

jam 

tri 

pan 

sen 

ivo 

els 

cos 

gua 

hon 

nic 

car 

chd 

nau 

tog 

dah 

nir 

gab 

sie 

con 

hai 

gui 

mat 

bol 

par 

cam 

maa 

yem 

kod 

lao 

mon 

nep 

bur 

rwa 

vnd 

som 

afg 

mli 

upv 

alb 

kmr 

jor 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Contraction of cluster 

Contraction of cluster C is called a graph G/C, in which all vertices of the 

cluster C are replaced by a single vertex, say c. More precisely: 

G/C = (V ′ , L ′ ), where V ′ = (V \ C) ∪ {c} and L ′ consists of lines 

from L that have both end-vertices in V \ C. Beside these it contains also 

a ’star’ with the center c and: arc (v, c), if ∃p ∈ L, u ∈ C : p(v, u); 

or arc (c, v), if ∃p ∈ L, u ∈ C : p(u, v). There is a loop (c, c) in c if 

∃p ∈ L, u, v ∈ C : p(u, v). 

In a network over graph G we have also to specify how are determined the 

values/weights in the shrunk part of the network. Usually as the sum or 

maksimum/minimum of the original values. 

Operations/Shrink Network/Partition 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 


usa 

can 

cub 

hai 

dom 

jam 

tri 

mex 

gua 

hon 

els 

nic 

cos 

pan 

col 

ven 

ecu 

per 

bra 

bol 

par 

chi 

arg 

uru 

uki 

ire 

net 

bel 

lux 

fra 

swi 

spa 

por 

wge 

ege 

pol 

aus 

hun 

cze 

ita 

mat 

alb 

yug 

gre 

cyp 

bul 

rum 

usr 

fin 

swe 

nor 

den 

ice 

mli 

sen 

dah 

nau 

nir 

ivo 

gui 

upv 

lib 

sie 

gha 

tog 

cam 

nig 

gab 

car 

chd 

con 

zai 

uga 

ken 

bur 

rwa 

som 

eth 

saf 

maa 

mor 

alg 

tun 

liy 

sud 

egy 

irn 

tur 

irq 

syr 

leb 

jor 

isr 

sau 

yem 

kuw 

afg 

cha 

mon 

tai 

kod 

kor 

jap 

ind 

pak 

brm 

sri 

nep 

tha 

kmr 

lao 

vnd 

vnr 

mla 

phi 

ins 

aut 

nze 

✫ 

Contracted clusters – international trade 

usa 

can 

cub 

hai 

dom 

jam 

tri 

mex 

gua 

hon 

els 

nic 

cos 

pan 

col 

ven 

ecu 

per 

bra 

bol 

par 

chi 

arg 

uru 

uki 

ire 

net 

bel 

lux 

fra 

swi 

spa 

por 

wge 

ege 

pol 

aus 

hun 

cze 

ita 

mat 

alb 

yug 

gre 

cyp 

bul 

rum 

usr 

fin 

swe 

nor 

den 

ice 

mli 

sen 

dah 

nau 

nir 

ivo 

gui 

upv 

lib 

sie 

gha 

tog 

cam 

nig 

gab 

car 

chd 

con 

zai 

uga 

ken 

bur 

rwa 

som 

eth 

saf 

maa 

mor 

alg 

tun 

liy 

sud 

egy 

irn 

tur 

irq 

syr 

leb 

jor 

isr 

sau 

yem 

kuw 

afg 

cha 

mon 

tai 

kod 

kor 

jap 

ind 

pak 

brm 

sri 

nep 

tha 

kmr 

lao 

vnd 

vnr 

mla 

phi 

ins 

aut 

nze 

Asia 

Europe 

Australia 

S. America 

Snyder and Kick’s international trade. Matrix display of dense networks. 

w(Ci, Cj) = n(Ci, Cj) 

n(Ci) · n(Cj) 

N. America 


❙ ▲ 

▲ 

L. America 

Africa 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Computing the weights 

File / Pajek Project File / Read [SaKtrade.paj] 

Net / Transform / Remove / Loops [No] 

Net / Transform / Edges -> Arcs [No] 

Operations / Shrink Network / Partition [1][0] 

1 2 3 4 5 6 7 

--------------------------------------------- 

#usa 1. 2 30 13 56 42 45 4 

#cub 2. 30 74 25 196 20 37 12 

#per 3. 12 28 33 124 16 36 5 

#uki 4. 55 217 130 695 427 483 41 

#mli 5. 42 8 14 406 122 117 11 

#irn 6. 43 37 43 444 142 307 30 

#aut 7. 4 4 5 39 9 30 2 

Partition / Make Permutation 

[select partition (Sub)continents] 

Operations / Functional Composition / Partition*Permutation 

Partition / Count 

Partition / Make Vector 

Operations / Vector / Put loops 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

. . . Computing the weights 

1 2 3 4 5 6 7 

-------------------------------------------- 

#usa 1. 4 30 13 56 42 45 4 

#cub 2. 30 89 25 196 20 37 12 

#per 3. 12 28 40 124 16 36 5 

#uki 4. 55 217 130 723 427 483 41 

#mli 5. 42 8 14 406 155 117 11 

#irn 6. 43 37 43 444 142 337 30 

#aut 7. 4 4 5 39 9 30 4 

count 2 15 7 29 33 30 2 

Vector / Create Identity Vector [7] 

[select as second vector From partition ...] 

Vectors / Divide First by Second 

Operations / Vector / Vector # Network / input 

Operations / Vector / Vector # Network / output 

[edit partition - rename vertices] 

1 2 3 4 5 6 7 

--------------------------------------------- 

N.Am 1. 1.00 1.00 0.93 0.97 0.64 0.75 1.00 

L.Am 2. 1.00 0.40 0.24 0.45 0.04 0.08 0.40 

S.Am 3. 0.86 0.27 0.82 0.61 0.07 0.17 0.36 

Euro 4. 0.95 0.50 0.64 0.86 0.45 0.56 0.71 

Afri 5. 0.64 0.02 0.06 0.42 0.14 0.12 0.17 

Asia 6. 0.72 0.08 0.20 0.51 0.14 0.37 0.50 

Ocea 7. 1.00 0.13 0.36 0.67 0.14 0.50 1.00 

In Pajek sequences of 

commands can be combined 

into a macro command 

using 

Macro / Record 

and 

Macro / Recording... 

The macro can be activated 

by 

Macro / Play 

The sequence for computing 

the weights 

w(Ci, Cj) is saved in the 

macro weights. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Subgraph 

A subgraph H = (V ′ , L ′ ) of a given graph G = (V, L) is a graph which set of lines 

is a subset of set of lines of G, L ′ ⊆ L, its vertex set is a subset of set of vertices of 

G, V ′ ⊆ V, and it contains all end-vertices of L ′ . 

A subgraph can be induced by a given subset of vertices or lines. It is a spanning 

subgraph iff V ′ = V. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Cut-out – induced subgraph: Snyder and Kick – Africa 

lib 

upv 

car 

gha 

tog 

mli 

sud 

eth 

ivo 

tun 

egy 

nir 

nig 

som 

Operations/Extract from Network/Partition [6] 


❙ ▲ 

▲ 

mor 

sie 

liy 

dah 

bur 

gab 

maa 

ken 

sen 

alg 

rwa 

chd 

cam 

saf 

zai 

uga 

con 

gui 

nau 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

gua 

els 

jam 

hon 

hai dom 

nic 

Cut-out: Snyder and Kick 

Latin America : South America 

cos 

ecu 

col 

mex 

pan 

ven 

tri 

cub 

Operations/Extract from Network/Partition [3,4] Pajek 

Operations/Transform/Remove lines/Inside clusters [3,4] 

The vertices can be manually put on a rectangular grid produced by 

[Draw] Move/Grid 


❙ ▲ 

▲ 

per 

bra 

chi 

arg 

uru 

par 

bol 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Important vertices in network 

It seems that the most important distinction between different vertex indices 

is based on the view/decision whether the network is considered directed or 

undirected. This gives us two main types of indices: 

• directed case: measures of importance; with two subgroups: measures 

of influence, based on out-going arcs; and measures of support, based 

on incoming arcs; 

• undirected case: measures of centrality, based on all lines. 

For undirected networks all three types of measures coincide. 

If we change the direction of all arcs (replace the relation with its inverse 

relation) the measure of influence becomes a measure of support, and vice 

versa. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

. . . Important vertices in network 

The real meaning of measure of importance depends on the relation 

described by a network. For example the most ’important’ person for the 

relation ’ doesn’t like to work with ’ is in fact the least popular person. 

Removal of an important vertex from a network produces a substantial 

change in structure/functioning of the network. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Closeness 

Most indices are based on the distance d(u, v) between vertices in a network 

N = (V, L). Two such indices are 

radius r(v) = maxu∈V d(v, u) 

total closeness S(v) = � 

u∈V d(v, u) 

These two indices are measures of influence – to get measures of support 

we have to replace in definitions d(u, v) with d(v, u). 

If the network is not strongly connected rmax and Smax equal ∞. Sabidussi 

(1966) introduced a related measure 1/S(v); or in its normalized form 

closeness cl(v) = 

� 

u∈V 

n − 1 

d(v, u) 

D = maxu,v∈V d(v, u) is called the diameter of network. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Betweeness 

Important are also the vertices that can control the information flow in the 

network. If we assume that this flow uses only the shortest paths (geodesics) 

we get a measure of betweeness (Anthonisse 1971, Freeman 1977) 

b(v) = 

1 

(n − 1)(n − 2) 

� 

u,t∈V:g u,t >0 

u�=v,t�=v,u�=t 

For computation of geodesic matrix see Brandes. 

✫ 

gu,t(v) 

where gu,t is the number of geodesics from u to t; and gu,t(v) is the number 

of those among them that pass through vertex v. 

gu,t 

If we know matrices [du,v] and [gu,v] we can determine also gu,v(t) by: 

⎧ 

⎨ gu,t · gt,v du,t + dt,v = du,v 

gu,v(t) = 

⎩ 0 otherwise 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Hubs and authorities 

To each vertex v of a network N = (V, L) we assign two values: quality of 

its content (authority) xv and quality of its references (hub) yv. 

A good authority is selected by good hubs; and good hub points to good 

authorities (see Klienberg). 

xv = � 

yu and yv = � 

u:(u,v)∈L 

u:(v,u)∈L 

Let W be a matrix of network N and x and y authority and hub vectors. 

Then we can write these two relations as x = W T y and y = Wx. 

We start with y = [1, 1, . . . , 1] and then compute new vectors x and 

y. After each step we normalize both vectors. We repeat this until they 

stabilize. 

We can show that this procedure converges. The limit vector x 

✫ 

∗ is the 

principal eigen vector of matrix WT W; and y∗ of matrix WWT . 


❙ ▲ 

▲ 

xu 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

. . . Hubs and authorities 

Similar procedures are used in search engines on the web to evaluate the 

importance of web pages. 

PageRank, PageRank / Google, HITS / AltaVista, SALSA, teorija. 

Examples: Krebs, Krempl. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Clustering coefficient 

Let G = (V, E) be simple undirected graph. Clustering in vertex v is 

usually measured as a quotient between the number of lines in subgraph 

G 1 (v) = G(N 1 (v)) induced by the neighbors of vertex v and the number of 

lines in the complete graph on these vertices: 

C(v) = 

⎧ 

⎪⎨ 

⎪⎩ 

2|L(G 1 (v))| 

deg(v)(deg(v) − 1) 

deg(v) > 1 

0 otherwise 

We can consider also the size of vertex neighborhood by the following 

correction 

C1(v) = deg(v) 

∆ C(v) 

where ∆ is the maximum degree in graph G. This measure attains its largest 

value in vertices that belong to an isolated clique of size ∆. 

✫ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Dense groups 

Several notions were proposed in attempts to formally describe dense 

groups in graphs. 

Clique of order k is a maximal complete subgraph (isomorphic to Kk), 

k ≥ 3. 

s-plexes, LS sets, lambda sets, cores, . . . 

For all of them, except for cores, it turned out that they are difficult to 

detemine. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Cores and generalized cores 

The notion of core was introduced 

by Seidman in 1983. Let G = 

(V, E) be a graph. A subgraph H = 

(W, E|W ) induced by the set W is 

a k-core or a core of order k iff 

∀v ∈ W : deg H(v) ≥ k, and H is 

a maximal subgraph with this property. 

The core of maximum order is 

also called the main core. 

The core number of vertex v is the highest order of a core that contains 

this vertex. The degree deg(v) can be: in-degree, out-degree, in-degree + 

out-degree, etc., determining different types of cores. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Properties of cores 

From the figure, representing 0, 1, 2 and 3 core, we can see the following 

properties of cores: 

• The cores are nested: i < j =⇒ Hj ⊆ Hi 

• Cores are not necessarily connected subgraphs. 

An efficient algorithm for determining the cores hierarchy is based on the 

following property: 

If from a given graph G = (V, E) we recursively delete all vertices, 

and edges incident with them, of degree less than k, the remaining 

graph is the k-core. 

For details see the paper. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

6-core of Krebs Internet industries 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Generalized cores 

The notion of core can be generalized to networks. Let N = (V, E, w) 

be a network, where G = (V, E) is a graph and w : E → R is a function 

assigning values to edges. A vertex property function on N, or a pfunction 

for short, is a function p(v, U), v ∈ V, U ⊆ V with real values. 

Let NU (v) = N(v) ∩ U. Besides degrees, here are some examples of 

p-functions: 

pS(v, U) = � 

w(v, u), where w : E → R + 0 

u∈NU (v) 

pM (v, U) = max w(v, u), where w : E → R 

u∈NU (v) 

pk(v, U) = number of cycles of length k through vertex v in (U, E|U) 

The subgraph H = (C, E|C) induced by the set C ⊆ V is a p-core at level 

t ∈ R iff ∀v ∈ C : t ≤ p(v, C) and C is a maximal such set. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

For details see the paper. 

✫ 

Generalized cores algorithm 

The function p is monotone iff it has the property 

C1 ⊂ C2 ⇒ ∀v ∈ V : (p(v, C1) ≤ p(v, C2)) 

The degrees and the functions pS, pM and pk are monotone. For a monotone 

function the p-core at level t can be determined, as in the ordinary case, by 

successively deleting vertices with value of p lower than t; and the cores on 

different levels are nested 

t1 < t2 ⇒ Ht2 

⊆ Ht1 

The p-function is local iff p(v, U) = p(v, NU (v)) . 

The degrees, pS and pM are local; but pk is not local for k ≥ 4. For a local 

p-function an O(m max(∆, log n)) algorithm for determining the p-core 

levels exists, assuming that p(v, NC(v)) can be computed in O(deg C(v)). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

B.Chazelle 

R.Seidel 

B.Aronov 

L.Guibas 

H.Edelsbrunner 

R.Pollack 

J.Pach 

M.Bern 

D.Dobkin 

E.Welzl 

pS-core at level 46 of Geombib network 

D.Eppstein 

M.Sharir 

J.Matousek 

S.Suri 

J.Hershberger 

C.Yap 

E.Arkin 

J.Mitchell 

P.Agarwal 

D.Halperin 

J.Snoeyink 

M.Overmars 

O.Schwarzkopf 

C.Icking 

M.vanKreveld 

M.deBerg 

R.Klein 

J.O’Rourke 

M.Goodrich 

G.Toussaint 

P.Bose 

I.Tollis 

F.Preparata 

M.Teillaud 

A.Garg 

G.diBattista 

R.Tamassia 

J.Boissonnat 

O.Devillers 

J.Czyzowicz 

M.Yvinec 

G.Liotta 

L.Vismara 


❙ ▲ 

▲ 

J.Vitter 

J.Urrutia 

M.Smid 

P.Gupta 

R.Janardan 

J.Majhi 

J.Schwerdt 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Cores and generalized cores / Pajek commands 

File/Network/Read [Geom.net] 

Net/Partitions/Core/All 

Info/Partition 

Operations/Extract from Network/Partition [13-*] 

Draw/Draw-Partition 

Layout/Energy/Kamada-Kawai 

Options/Values of lines/Similarities 



Draw 


Options/Values of lines/Forget 


[select Geom.net] 

Net/Vector/PCore/Sum/All 

Info/Vector 

Vector/Make Partition/by Intervals/Selected Thresholds [45] 



Draw 

Options/Values of lines/Similarities 

Layout/Energy/Fruchterman-Reingold 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Connectivity 

Weak and strong connectivity are equivalence relations. 

Equivalence classes induce weak/strong components. 

Vertex u is reachable from vertex v iff 

there exists a walk with initial vertex v 

and terminal vertex u. 

Vertex v is weakly connected with vertex 

u iff there exists a semiwalk with v 

and u as its end-vertices. 

Vertex v is strongly connected with vertex 

u iff they are mutually reachable. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Weak components 

Reordering the vertices of network 

such that the vertices from the same 

class of weak partition are put together 

we get a matrix representation 

consisting of diagonal blocks – 

weak components. 

Most problems can be solved separately 

on each component and afterward 

these solutions combined into 

final solution. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Reduction (condensation) 

If we shrink every strong component of a given graph into a vertex, delete 

all loops and identify parallel arcs the obtained reduced graph is acyclic. 

For every acyclic graph an ordering / level function i : V → N exists s.t. 

(u, v) ∈ A ⇒ i(u) < i(v). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Reduction – Example 

Net / Components / Strong [1] 

Operations / Shrink Network / Partition [1][0] 

Net / Transform / Remove / Loops [yes] 

Net / Partitions / Depth / Acyclic 


Permutation / Inverse 

select partition [Strong Components] 

Operations / Functional Composition / Partition*Permutation 


select [original network] 

File / Network / Export Matrix to EPS / Using Permutation 

a 

k 

f 

b 

d 

h 

j 

c 

e 

l 

i 

g 

k 

f 

#a 

#e 

g 

i 



❙ ▲ 

▲ 

i 

e 

h 

j 

l 

a 

b 

c 

d 

g 

f 

k 

i 

e 

h 

j 

l 

a 

b 

c 

d 

g 

f 

k 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Cuts 

The standard approach to find interesting groups inside a network was based 

on properties/weights – they can be measured or computed from network 

structure (for example Kleinberg’s hubs and authorities). 

The vertex-cut of a network N = (V, L, p), p : V → R, at selected level t 

is a subnetwork N(t) = (V ′ , L(V ′ ), p), determined by the set 

V ′ = {v ∈ V : p(v) ≥ t} 

and L(V ′ ) is the set of lines from L that have both endpoints in V ′ . 

The line-cut of a network N = (V, L, w), w : V → R, at selected level t is 

a subnetwork N(t) = (V(L ′ ), L ′ , w), determined by the set 

L ′ = {e ∈ L : w(e) ≥ t} 

and V(L ′ ) is the set of all endpoints of the lines from L ′ . 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Vertex-cut: Krebs Internet Industries, core=6 


Yahoo! 

AT&T 

Motorola 

AOL 

Lucent 

Ariba 

EMC 

Oracle Peoplesoft 

Sun 

FoundryNetworks 

EDS 

divine WebMethods 

IBM 

E.piphany 

HP 

Siebel BMCSoftware 

Cisco 

Novell 

ExodusComm 

KPNQwest 

Intel 

Vignette 

RealNetworks 

Akamai 

Compaq 

Inktomi 

CacheFlow 

Dell 

Loudcloud 

MSFT 

CommerceOne 

Each vertex represents a company that competes in the Internet industry, 1998 do 2001. n = 219, m = 631. red – content, blue – infrastructure, 

green – commerce. Two companies are linked with an edge if they have announced a joint venture, strategic alliance or other partnership. 


❙ ▲ 

▲ 

CIBER 

RedHat 

UPS 

SAP 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪ 

Pajek


✬ 

✫ 

Line-cut: Krebs Internet Industries, w3 ≥ 5 


TerraLycos 

Intel 

AT&T 


AOL 

IBM 

Motorola 

AOL 

Sun 


HP 

KPNQwest 


Akamai 

Cisco 

TerraLycos 


Sun 

Oracle 

Compaq 

Inktomi 

Inktomi 

HP 

IBM 

Intel 

Dell 

Oracle 

MSFT 

Ariba 

AT&T 

Cisco 

E.piphany 


❙ ▲ 

▲ 

CIBER 

CIBER 

E.piphany 

KPMG 

MSFT 

KPMG 

Akamai 

Ariba Motorola 

▲ 

● ❙ ▲ 

▲ 


Compaq 

Dell 

KPNQwest 


☛ ✖ 

✩ 

✪


✬ 

Vertex-cut: 

✫ 

Cuts / Pajek commands 

File/Pajek Project File/Read [Krebs.paj] 

Net/Partitions/Core/All 


Draw/Draw-Partition-Vector 



[select Types ... as First partition] 

[select All core ... as Second partition] 

Partitions/Extract Second from First [6] 



Line-cut: 

[select Krebs ... network] 

Net/Count/3-Rings/Undirected 

Info/Network/Line Values 

Net/Transform/Remove/Lines with Values/lower than [5] 



Operations/Extract from Network/Partition [1-*] 

[select Types ... as First partition] 

[select All Degree ... as Second partition] 

Partitions/Extract Second from First [1-*] 




❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

We look at the components of N(t). 

✫ 

Simple analysis using cuts 

Their number and sizes depend on t. Usually there are many small 

components. Often we consider only components of size at least k and 

not exceeding K. The components of size smaller than k are discarded as 

’noninteresting’; and the components of size larger than K are cut again at 

some higher level. 

The values of thresholds t, k and K are determined by inspecting the 

distribution of vertex/arc-values and the distribution of component sizes 

and considering additional knowledge on the nature of network or goals of 

analysis. 

We developed some new and efficiently computable properties/weights. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

BROWN-TH-1988-V242-P724 

TREVES-A-1991-V2-P371 

BROWN-TH-1990-V13-P475 

HASSELMO-ME-1993-V16-P218 


GLUCK-MA-1997-V48-P481 

ASHBY-FG-1999-V6-P363 

KOHONEN-T-1976-V22-P159 

POGGIO-T-1975-V19-P201 


WOOD-CC-1978-V85-P582 

SUTTON-RS-1981-V88-P135 

Citation weights 


ANDERSON-JA-1977-V84-P413 

COOPER-LN-1979-V33-P9 

BIENENSTOCK-EL-1982-V2-P32 

ANDERSON-JA-1983-V13-P799 

CARPENTER-GA-1987-V37-P54 

GROSSBERG-S-1987-V11-P23 

GROSSBERG-S-1988-V1-P17 

SEJNOWSKI-TJ-1988-V241-P1299 

BARKAI-E-1994-V72-P659 




PFAFFELHUBER-E-1975-V18-P217 

PALM-G-1980-V36-P19 

KNAPP-AG-1984-V10-P616 

MCCLELLAND-JL-1985-V114-P159 

AMARI-SI-1977-V26-P175 

HOPFIELD-JJ-1982-V79-P2554 

HECHTNIELSEN-R-1987-V26-P1892 




AMARI-S-1980-V42-P339 


The citation network analysis 

started in 1964 with the paper of 

Garfield et al. In 1989 Hummon 

and Doreian proposed three 

indices – weights of arcs that are 

proportional to the number of 

different source-sink paths passing 

through the arc. We developed 

algorithms to efficiently compute 

these indices. 

Main subnetwork (arc cut at level 

0.007) of the SOM (selforganizing 

maps) citation network (4470 vertices, 

12731 arcs). 

See paper. 


❙ ▲ 

▲ 


▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

k-rings 

A k-ring is a simple closed chain of length k. Using k-rings we can define 

a weight of edges as 

wk(e) = # of different k-rings containing the edge e ∈ E 

Since for a complete graph Kr, r ≥ k ≥ 3 we have 

wk(Kr) = (r − 2)!/(r − k)!, the edges belonging to 

cliques have large weights. Therefore these weights 

can be used to identify the dense parts of a network. 

For example: all r-cliques of a network belong to r−2edge 

cut for the weight w3. 

We can assign to a given graph a triangular network in 

which every line of the original graph gets as its weight 

the number of triangles that contain it. The triangular 

weights provide us, combined with islands, with a very 

efficient way to identify dense parts of a graph. 

✫ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Triangular connectivity 

Related to triangular network is the notion of triangular connectivity 

that can be used to operationalize the notion of strong ties. 

These notions can be generalized to short cycle connectivity (see paper). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Edge-cut at level 16 of triangular network of Erdős 

collaboration graph 

WORMALD, NICHOLAS C. 

MCKAY, BRENDAN D. 

KLEITMAN, DANIEL J. 

SAKS, MICHAEL E. 

CHUNG, FAN RONG K. 

ARONOV, BORIS 

LINIAL, NATHAN PACH, JANOS 

POLLACK, RICHARD M. 

HENNING, MICHAEL A. 

FRANKL, PETER 

SPENCER, JOEL H. 

ALON, NOGA 

OELLERMANN, ORTRUD R. 

LOVASZ, LASZLO 

KOMLOS, JANOS 

GODDARD, WAYNE D. 

FUREDI, ZOLTAN 

TUZA, ZSOLT 

ALAVI, YOUSEF 

BABAI, LASZLO 

SZEMEREDI, ENDRE 

CHARTRAND, GARY 

BOLLOBAS, BELA 

HARARY, FRANK 

AJTAI, MIKLOS 

KUBICKI, GRZEGORZ 

SCHWENK, ALLEN JOHN 

LEHEL, JENO 

GYARFAS, ANDRAS 

HEDETNIEMI, STEPHEN T. 

CHEN, GUANTAO 

FAUDREE, RALPH J. 

JACOBSON, MICHAEL S. 

LASKAR, RENU C. 

RODL, VOJTECH 

NESETRIL, JAROSLAV 

SCHELP, RICHARD H. 

GRAHAM, RONALD L. 

MAGIDOR, MENACHEM 

MULLIN, RONALD C. 

COLBOURN, CHARLES J. 

PHELPS, KEVIN T. 

SHELAH, SAHARON 

ROSA, ALEXANDER 

STINSON, DOUGLAS ROBERT 

without Erdős, 

n = 6926, 

m = 11343 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Directed 3-rings 

In directed networks there are two types of 3-rings: 

cyclic transitive 

The 3-rings weights were implemented in Pajek in May 2002. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Edge-cut at level 11 of transitive network of ODLIS 

dictionary graph 

charge 

call number 

suggestion box 

fixed location 

blanket order 

vendor 

American Library Directory 

transaction log 

entry 

catalog 

bibliographic record 

invoice 

publisher 

library 

American Library Association /ALA/ 

librarian 

dust jacket 

half-title 

book size 

homepage 

round table 

library binding 

new book 

binding 

periodical 

publishing 

cover 

Books in Print /BIP/ 

condition 

Oak Knoll 

publication 

review 

series 

Library Literature 

book 

front matter 

page 

collation 

folio 

issue 

imprint 

bibliography 

endpaper 

frequency 

colophon 

journal layout 

International Standard Book Number /ISBN/ 

published price 

dummy 

edition 

text 

serial 

parts of a book 

title page 

plate 

printing 

table of contents /TOC/ 

fiction 

copyright 


❙ ▲ 

▲ 

work 

abstract 

editor 

title 

index 

▲ 

● ❙ ▲ 

▲ 


☛ ✖ 

✩ 

✪


✬ 

See details. 

✫ 

Islands 

If we represent a given or computed value of vertices / lines as a height of 

vertices / lines and we immerse the network into a water up to selected level 

we get islands. Varying the level we get different islands. Islands are very 

general and efficient approach to determine the ’important’ subnetworks in 

a given network. 

We developed very efficient algorithms to determine the islands hierarchy 

and to list all the islands of selected sizes. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

call 

phone 

cell 

help 

plea 

louisiana 

air_force 

car 

arab 

base 

barksdale 

smoke 

man 

air 

✫ 

attendant 

airline 

flight 

arabic-language 

dept 

fire 

rental 

suspect 

space 

contain 

case 

offutt 

nebraska 

scare 

plaugher 

chief 

edward 

united_airlines 

passenger 

american_airlines 

Islands - Reuters terror news 

aid 

chemical 

bin_laden 

inhale 

firefighter 

jet 

fbi 

dissident taliban 

necessary 

afghanistan airport 

anthrax 

trace 

skin 

police 

officer 

knife-wielding 

agent 

world 

commercial 

official 

airliner 

hijacker 

support 

hijack 

country 

thursday force 

pakistan 

special 

terrorism 

war 

united_states 

embassy 

jonn 

specialist 

edmund 

mighty 

110-story 

twin 

pentagon 

plane deadly 

attack 

world_trade_ctr 

the_worst 

business 

wednesday 

week 

strike 

east 

act military 

headquarters 

terrorist 

apparent 

action 

cheyenne 

north 

tower 

washington 

tuesday 

morning 

africa 

wyoming 

florida 

south 

city 

late 

new_york 

news 

terror 

anti-american 

group 

responsibility 

mayor 

pfc 

mayor_giuliani 

conference 

american 

team 

exchange 

landmark 

debris 

miss 

people 

effort 

train 

manual 

rescue 

postal 

pilot 

member 

worker 

service 

uniform 

power 

stock 

emergency 

state 

nuclear 

market 

plant 

weapon 

financial 

district 

center 

saudi 

saudi-born 

pakistani 

organization 

large 

newspaper 

buildng 

boston 

herald 

leader 

thousand 

toll 

death 

congressional 

Using CRA S. Corman 

and K. Dooley produced 

the Reuters terror news 

network that is based on 

all stories released during 

66 consecutive days by 

the news agency Reuters 

concerning the September 

11 attack on the US. The 

vertices of a network are 

words (terms); there is an 

edge between two words 

iff they appear in the same 

text unit. The weight of an 

edge is its frequency. It has 

n = 13332 vertices and 

m = 243447 edges. 


❙ ▲ 

▲ 


▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Islands – US patents 

As an example, let us look at Nber network of US Patents. It has 3774768 

vertices and 16522438 arcs (1 loop). We computed SPC weights in it and 

determined all (2,90)-islands. The reduced network has 470137 vertices, 

307472 arcs and for different k: C2 =187610, C5 =8859,C30 =101, 

C50 =30 islands. Rolex 

[1] 0 139793 29670 9288 3966 1827 997 578 362 250 

[11] 190 125 104 71 47 37 36 33 21 23 

[21] 17 16 8 7 13 10 10 5 5 5 

[31] 12 3 7 3 3 3 2 6 6 2 

[41] 1 3 4 1 5 2 1 1 1 1 

[51] 2 3 3 2 0 0 0 0 0 1 

[61] 0 0 0 0 1 0 0 2 0 0 

[71] 0 0 1 1 0 0 0 1 0 0 

[81] 2 0 0 0 0 1 2 0 0 7 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

freq 

1 100 10000 

● 

● 

Island Theme size size distribution 

● 

● 

● 

● 

● 

● 

● 

● 

● ● 

● 

● ●●● 

●● ●● 

● ● 

●● 

● 

● ● 

●●● 

●● 

● 

● 

●●●● 

● 

● ● 

● ● 

● ●● 

● 

● 

● ● 

● 

● 

● ● 

●● ● 

2 5 10 20 50 100 


❙ ▲ 

▲ 

size 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Main path and main island of Patents 

5855814 

5683624 

5543077 

5374374 

5308538 

5171469 

5122295 

4877547 

4797228 

4710315 

4659502 

4550981 

4526704 

4472293 

4422951 

4386007 

4340498 

4302352 

4229315 

4149413 

4082428 

4011173 

3960752 

3872140 3881806 

2544659 3675987 3731986 3795436 

3891307 

4387039 

4387038 

4154697 

4349452 

4202791 

4419263 4422951 

4368135 

4195916 

4340498 

4293434 4290905 4361494 

4302352 4330426 

4149413 

4113647 4130502 4032470 4083797 4082428 4118335 

4013582 4029595 4077260 4017416 

4415470 

4455443 

4400293 

4229315 4261652 

3975286 4011173 4000084 

3954653 3947375 

3960752 

4198130 

4456712 

5124824 5171469 5283677 

4957349 

4630896 

5016988 5122295 

5016989 

4583826 

4510069 

4558151 

4877547 

4770503 4795579 4797228 

4709030 4719032 

4695131 4710315 4713197 4704227 

4659502 

4526704 

4621901 

4550981 

4502974 

4460770 4480117 4472293 4472592 

4820839 4832462 

4752414 

4514044 

4721367 

4657695 

4386007 

4357078 

3876286 

3697150 3636168 3767289 3666948 3322485 3773747 3796479 3795436 2682562 3691755 


❙ ▲ 

▲ 

5555116 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Table 1: Patents on the liquid-crystal display 

patent date author(s) and title 

2544659 Mar 13, 1951 Dreyer. Dichroic light-polarizing sheet and the like and the 

formation and use thereof 

2682562 Jun 29, 1954 Wender, et al. Reduction of aromatic carbinols 

3322485 May 30, 1967 Williams. Electro-optical elements utilazing an organic 

nematic compound 

3636168 Jan 18, 1972 Josephson. Preparation of polynuclear aromatic compounds 

3666948 May 30, 1972 Mechlowitz, et al. Liquid crystal termal imaging system 

having an undisturbed image on a disturbed background 

3675987 Jul 11, 1972 Rafuse. Liquid crystal compositions and devices 

3691755 Sep 19, 1972 Girard. Clock with digital display 

3697150 Oct 10, 1972 Wysochi. Electro-optic systems in which an electrophoreticlike 

or dipolar material is dispersed throughout a liquid 

crystal to reduce the turn-off time 

3731986 May 8, 1973 Fergason. Display devices utilizing liquid crystal light 

modulation 

3767289 Oct 23, 1973 Aviram, et al. Class of stable trans-stilbene compounds, 

some displaying nematic mesophases at or near room 

temperature and others in a range up to 100 ◦ C 

3773747 Nov 20, 1973 Steinstrasser. Substituted azoxy benzene compounds 

3795436 Mar 5, 1974 Boller, et al. Nematogenic material which exhibit the Kerr 

effect at isotropic temperatures 

3796479 Mar 12, 1974 Helfrich, et al. Electro-optical light-modulation cell 

utilizing a nematogenic material which exhibits the Kerr 

effect at isotropic temperatures 

3872140 Mar 18, 1975 Klanderman, et al. Liquid crystalline compositions and 

method 

3876286 Apr 8, 1975 Deutscher, et al. Use of nematic liquid crystalline substances 

3881806 May 6, 1975 Suzuki. Electro-optical display device 

3891307 Jun 24, 1975 Tsukamoto, et al. Phase control of the voltages applied to 

opposite electrodes for a cholesteric to nematic phase 

transition display 

3947375 Mar 30, 1976 Gray, et al. Liquid crystal materials and devices 

3954653 May 4, 1976 Yamazaki. Liquid crystal composition having high dielectric 

anisotropy and display device incorporating same 

3960752 Jun 1, 1976 Klanderman, et al. Liquid crystal compositions 

3975286 Aug 17, 1976 Oh. Low voltage actuated field effect liquid crystals 

compositions and method of synthesis 

4000084 Dec 28, 1976 Hsieh, et al. Liquid crystal mixtures for electro-optical 

display devices 

4011173 Mar 8, 1977 Steinstrasser. Modified nematic mixtures with 

positive dielectric anisotropy 

4013582 Mar 22, 1977 Gavrilovic. Liquid crystal compounds and electro-optic 

devices incorporating them 

4017416 Apr 12, 1977 Inukai, et al. P-cyanophenyl 4-alkyl-4’-biphenylcarboxylate, 

method for preparing same and liquid crystal compositions 

using same 

4029595 Jun 14, 1977 Ross, et al. Novel liquid crystal compounds and electro-optic 

devices incorporating them 

4032470 Jun 28, 1977 Bloom, et al. Electro-optic device 

4077260 Mar 7, 1978 Gray, et al. Optically active cyano-biphenyl compounds and 

liquid crystal materials containing them 

4082428 Apr 4, 1978 Hsu. Liquid crystal composition and method 

Liquid crystal display 



4083797 Apr 11, 1978 Oh. Nematic liquid crystal compositions 

4113647 Sep 12, 1978 Coates, et al. Liquid crystalline materials 

4118335 Oct 3, 1978 Krause, et al. Liquid crystalline materials of reduced viscosity 

4130502 Dec 19, 1978 Eidenschink, et al. Liquid crystalline cyclohexane derivatives 

4149413 Apr 17, 1979 Gray, et al. Optically active liquid crystal mixtures and 

liquid crystal devices containing them 

4154697 May 15, 1979 Eidenschink, et al. Liquid crystalline hexahydroterphenyl 

derivatives 

4195916 Apr 1, 1980 Coates, et al. Liquid crystal compounds 

4198130 Apr 15, 1980 Boller, et al. Liquid crystal mixtures 

4202791 May 13, 1980 Sato, et al. Nematic liquid crystalline materials 

4229315 Oct 21, 1980 Krause, et al. Liquid crystalline cyclohexane derivatives 

4261652 Apr 14, 1981 Gray, et al. Liquid crystal compounds and materials and 

devices containing them 

4290905 Sep 22, 1981 Kanbe. Ester compound 

4293434 Oct 6, 1981 Deutscher, et al. Liquid crystal compounds 

4302352 Nov 24, 1981 Eidenschink, et al. Fluorophenylcyclohexanes, the preparation 

thereof and their use as components of liquid crystal dielectrics 

4330426 May 18, 1982 Eidenschink, et al. Cyclohexylbiphenyls, their preparation and 

use in dielectrics and electrooptical display elements 

4340498 Jul 20, 1982 Sugimori. Halogenated ester derivatives 

4349452 Sep 14, 1982 Osman, et al. Cyclohexylcyclohexanoates 

4357078 Nov 2, 1982 Carr, et al. Liquid crystal compounds containing an alicyclic 

ring and exhibiting a low dielectric anisotropy and liquid 

crystal materials and devices incorporating such compounds 

4361494 Nov 30, 1982 Osman, et al. Anisotropic cyclohexyl cyclohexylmethyl ethers 

4368135 Jan 11, 1983 Osman. Anisotropic compounds with negative or positive 

DC-anisotropy and low optical anisotropy 

4386007 May 31, 1983 Krause, et al. Liquid crystalline naphthalene derivatives 

4387038 Jun 7, 1983 Fukui, et al. 4-(Trans-4’-alkylcyclohexyl) benzoic acid 

4’”-cyano-4”-biphenylyl esters 

4387039 Jun 7, 1983 Sugimori, et al. Trans-4-(trans-4’-alkylcyclohexyl)-cyclohexane 

carboxylic acid 4’”-cyanobiphenyl ester 

4400293 Aug 23, 1983 Romer, et al. Liquid crystalline cyclohexylphenyl derivatives 

4415470 Nov 15, 1983 Eidenschink, et al. Liquid crystalline fluorine-containing 

cyclohexylbiphenyls and dielectrics and electro-optical display 

elements based thereon 

4419263 Dec 6, 1983 Praefcke, et al. Liquid crystalline cyclohexylcarbonitrile 

derivatives 

4422951 Dec 27, 1983 Sugimori, et al. Liquid crystal benzene derivatives 

4455443 Jun 19, 1984 Takatsu, et al. Nematic halogen Compound 

4456712 Jun 26, 1984 Christie, et al. Bismaleimide triazine composition 

4460770 Jul 17, 1984 Petrzilka, et al. Liquid crystal mixture 

4472293 Sep 18, 1984 Sugimori, et al. High temperature liquid crystal substances of 

four rings and liquid crystal compositions containing the same 

4472592 Sep 18, 1984 Takatsu, et al. Nematic liquid crystalline compounds 

4480117 Oct 30, 1984 Takatsu, et al. Nematic liquid crystalline compounds 

4502974 Mar 5, 1985 Sugimori, et al. High temperature liquid-crystalline ester 

compounds 

4510069 Apr 9, 1985 Eidenschink, et al. Cyclohexane derivatives 



4514044 Apr 30, 1985 Gunjima, et al. 1-(Trans-4-alkylcyclohexyl)-2-(trans-4’-(p-sub 

stituted phenyl) cyclohexyl)ethane and liquid crystal mixture 

4526704 Jul 2, 1985 Petrzilka, et al. Multiring liquid crystal esters 

4550981 Nov 5, 1985 Petrzilka, et al. Liquid crystalline esters and mixtures 

4558151 Dec 10, 1985 Takatsu, et al. Nematic liquid crystalline compounds 

4583826 Apr 22, 1986 Petrzilka, et al. Phenylethanes 

4621901 Nov 11, 1986 Petrzilka, et al. Novel liquid crystal mixtures 

4630896 Dec 23, 1986 Petrzilka, et al. Benzonitriles 

4657695 Apr 14, 1987 Saito, et al. Substituted pyridazines 

4659502 Apr 21, 1987 Fearon, et al. Ethane derivatives 

4695131 Sep 22, 1987 Balkwill, et al. Disubstituted ethanes and their use in liquid 

crystal materials and devices 

4704227 Nov 3, 1987 Krause, et al. Liquid crystal compounds 

4709030 Nov 24, 1987 Petrzilka, et al. Novel liquid crystal mixtures 

4710315 Dec 1, 1987 Schad, et al. Anisotropic compounds and liquid crystal 

mixtures therewith 

4713197 Dec 15, 1987 Eidenschink, et al. Nitrogen-containing heterocyclic compounds 

4719032 Jan 12, 1988 Wachtler, et al. Cyclohexane derivatives 

4721367 Jan 26, 1988 Yoshinaga, et al. Liquid crystal device 

4752414 Jun 21, 1988 Eidenschink, et al. Nitrogen-containing heterocyclic compounds 

4770503 Sep 13, 1988 Buchecker, et al. Liquid crystalline compounds 

4795579 Jan 3, 1989 Vauchier, et al. 2,2’-difluoro-4-alkoxy-4’-hydroxydiphenyls and 

their derivatives, their production process and 

their use in liquid crystal display devices 

4797228 Jan 10, 1989 Goto, et al. Cyclohexane derivative and liquid crystal 

composition containing same 

4820839 Apr 11, 1989 Krause, et al. Nitrogen-containing heterocyclic esters 

4832462 May 23, 1989 Clark, et al. Liquid crystal devices 

4877547 Oct 31, 1989 Weber, et al. Liquid crystal display element 

4957349 Sep 18, 1990 Clerc, et al. Active matrix screen for the color display of 

television pictures, control system and process for producing 

said screen 

5016988 May 21, 1991 Iimura. Liquid crystal display device with a birefringent 

compensator 

5016989 May 21, 1991 Okada. Liquid crystal element with improved contrast and 

brightness 

5122295 Jun 16, 1992 Weber, et al. Matrix liquid crystal display 

5124824 Jun 23, 1992 Kozaki, et al. Liquid crystal display device comprising a 

retardation compensation layer having a maximum principal 

refractive index in the thickness direction 

5171469 Dec 15, 1992 Hittich, et al. Liquid-crystal matrix display 

5283677 Feb 1, 1994 Sagawa, et al. Liquid crystal display with ground regions 

between terminal groups 

5308538 May 3, 1994 Weber, et al. Supertwist liquid-crystal display 

5374374 Dec 20, 1994 Weber, et al. Supertwist liquid-crystal display 

5543077 Aug 6, 1996 Rieger, et al. Nematic liquid-crystal composition 

5555116 Sep 10, 1996 Ishikawa, et al. Liquid crystal display having adjacent 

electrode terminals set equal in length 

5683624 Nov 4, 1997 Sekiguchi, et al. Liquid crystal composition 

5855814 Jan 5, 1999 Matsui, et al. Liquid crystal compositions and liquid crystal 

display elements 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Islands – The Edinburgh Associative Thesaurus 

n = 23219, m = 325624, transitivity weight 

WHY 

NEVERTHELESS 

SCIENTIFIC 

YET 

NOTWITHSTANDING 

BUT 

THEREFORE 

ANYWAY 

TEACHING 

ENGINEERING 

LECTURES 

HOMEWORK 

SCIENCE 

RESEARCH 

JUST 

NOW 

AS 

MEANWHILE 

LECTURER 

WORK 

LEARNING 

STUDY 

STUDYING 

HAPPEN 

AGAIN 

SCHOOL 

SOMETIME 

MATHS 

ACTIVITY 

ALREADY 

HAPPENED 

OFTEN 

SOON 

TEACHER 

EDUCATION 

TRAINING 

LESSONS 

PROBABLY 

COINS 

BELIEVE 

NOT 

COULD 

MONIES 

NO 

PAYMENT 

PAY 

INCREASE 

DEFICIT THRIFT 

INHUMAN 

RESPONSIBLE 

PROFESSION 

PAID 

MONEY 

MORE MONEY 

OFFER 

PROVIDE 

REFUSE 

PLEASE 

BOSS 

RECEIPT 

REPAY 

CHAIRMAN 

ADORABLE 

STOLE 

UNPAID 

THRIFTY 

DEALER 

LOOT 

PROPERTY 

ELEGANCE 

MYSTERIOUS NICE 

CHARM 

BELOVED 

LOVE 

KINDNESS 

POWERFUL 


❙ ▲ 

▲ 

MAN 

FLIRT 

HAIRY 

GIRL 

SHAPELY 

ATTRACTIVE 

BEAUTIFUL 

LOVELY 

DELIGHTFUL 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Islands / Pajek commands 

File/Network/Read [eatRS.net] 

Net/Partitions/Islands/Generate Network with Islands [On] 

Net/Partitions/Islands/Line Weights Simple [2 50] 

Partition/Canonical Partition - Decreasing Frequencies 


Operations/Extract from Network/Partition [1-38] 

Draw/Draw-Partition-Vector 

Layout/Energy/Kamada-Kawai/Free 

[manually distribute components over the available space] 

Options/Transform/Fit area 

The procedure for ’triangular islands’ is similar 

File/Network/Read [eatRS.net] 

Net/Count/3-Rings/Directed/Transitive 

Net/Partitions/Islands/Generate Network with Islands [On] 

Net/Partitions/Islands/Line Weights Simple [2 50] 

... 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Internet Movie Database http://www.imdb.com/ 

12th Annual Graph Drawing Contest, 2005. The IMDB network is bipartite (2-mode) and has 

1324748 = 428440 + 896308 vertices and 3792390 arcs. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Bipartite cores 

The subset of vertices C ⊆ V is a (p, q)-core in a bipartite (2-mode) 

network N = (V1, V2; L), V = V1 ∪ V2 iff 

a. in the induced subnetwork K = (C1, C2; L(C)), C1 = C ∩ V1, C2 = 

C ∩ V2 it holds ∀v ∈ C1 : deg K(v) ≥ p and ∀v ∈ C2 : deg K(v) ≥ q ; 

b. C is the maximal subset of V satisfying condition a. 

Properties of bipartite cores: 

• C(0, 0) = V 

• K(p, q) is not always connected 

• (p1 ≤ p2) ∧ (q1 ≤ q2) ⇒ C(p1, q1) ⊆ C(p2, q2) 

• C = {C(p, q) : p, q ∈ N}. If all nonempty elements of C are different 

it is a lattice. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Algorithm for bipartite cores 

To determine a (p, q)-core the procedure similar to the ordinary core 

procedure can be used: 

repeat 

remove from the first set all vertices of degree less than p, 

and from the second set all vertices of degree less than q 

until no vertex was deleted 

It can be implemented to run in O(m) time. 

Interesting (p, q)-cores? Table of cores’ characteristics n1 = |C1(p, q)|, 

n2 = |C2(p, q)| and k – number of components in K(p, q): 

• n1 + n2 ≤ selected threshold 

• big jumps from C(p − 1, q) and C(p, q − 1) to C(p, q). 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Table (p, q : n1, n2) for Internet Movie Database 

1 1590: 1590 1 | 22 24: 1854 1153 | 43 14: 29 83 

2 516: 788 3 | 23 23: 47 56 | 44 14: 29 83 

3 212: 1705 18 | 24 23: 34 39 | 45 13: 30 95 

4 151: 4330 154 | 25 22: 42 53 | 46 13: 29 94 

5 131: 4282 209 | 26 22: 31 38 | 47 12: 29 101 

6 115: 3635 223 | 27 22: 31 38 | 48 12: 28 100 

7 101: 3224 244 | 28 20: 36 53 | 49 12: 26 95 

8 88: 2860 263 | 29 20: 35 52 | 50 11: 27 111 

9 77: 3467 393 | 30 19: 35 59 | 51 11: 26 110 

10 69: 3150 428 | 31 19: 35 59 | 52 11: 16 79 

11 63: 2442 382 | 32 19: 34 57 | 53 10: 35 162 

12 56: 2479 454 | 33 18: 34 62 | 54 10: 35 162 

13 50: 3330 716 | 34 18: 34 62 | 55 10: 34 162 

14 46: 2460 596 | 35 18: 33 61 | 56 10: 34 162 

15 42: 2663 739 | 36 17: 33 65 | 57 9: 35 187 

16 39: 2173 678 | 37 16: 33 75 | 58 9: 33 180 

17 35: 2791 995 | 38 16: 30 73 | 59 9: 33 180 

18 32: 2684 1080 | 39 16: 29 70 | 60 9: 32 178 

19 30: 2395 1063 | 40 15: 29 77 | 61 9: 31 177 

20 28: 2216 1087 | 41 15: 28 76 | 62 9: 31 177 

21 26: 1988 1087 | 42 15: 28 76 | 63 8: 31 202 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Survivor Series 

Royal Rumble 

✫ 

(247,2)-core and (27,22)-core 

Zhukov, Boris (I) 

Wright, Charles (II) 

Wilson, Al (III) 

Wight, Paul 

Wickens, Brian 

White, Leon 

Warrior 

Warrington, Chaz 

Ware, David (II) 

Waltman, Sean 

Walker, P.J. 

von Erich, Kerry 

Vaziri, Kazrow 

Van Dam, Rob 

Valentine, Greg 

Vailahi, Sione 

Tunney, Jack 

Traylor, Raymond 

Tenta, John 

Taylor, Terry (IV) 

Taylor, Scott (IX) 

Tanaka, Pat 

Tajiri, Yoshihiro 

Szopinski, Terry 

Storm, Lance 

Steiner, Scott 

Steiner, Rick (I) 

Solis, Mercid 

Snow, Al 

Smith, Davey Boy 

Slaughter, Sgt. 

Simmons, Ron (I) 

Shinzaki, Kensuke 

Shamrock, Ken 

Senerca, Pete 

Scaggs, Charles 

Savage, Randy 

Saturn, Perry 

Sags, Jerry 

Ruth, Glen 

Runnels, Dustin 

Rude, Rick 

Rougeau, Raymond 

Rougeau Jr., Jacques 

Rotunda, Mike 

Ross, Jim (III) 

Rock, The 

Roberts, Jake (II) 

Rivera, Juan (II) 

Rhodes, Dusty (I) 

Reso, Jason 

Reiher, Jim 

Reed, Bruce (II) 

Race, Harley 

Prichard, Tom 

Powers, Jim (IV) 

Poffo, Lanny 

Plotcheck, Michael 

Piper, Roddy 

Pfohl, Lawrence 

Pettengill, Todd 

Peruzovic, Josip 

Palumbo, Chuck (I) 

Page, Dallas 

Ottman, Fred 

Orton, Randy 

Okerlund, Gene 

Nowinski, Chris 

Norris, Tony (I) 

Nord, John 

Neidhart, Jim 

Nash, Kevin (I) 

Muraco, Don 

Morris, Jim (VII) 

Morley, Sean 

Morgan, Matt (III) 

Mooney, Sean (I) 

Moody, William (I) 

Miller, Butch 

Mero, Marc 

McMahon, Vince 

McMahon, Shane 

Matthews, Darren (II) 

Martin, Andrew (II) 

Martel, Rick 

Marella, Robert 

Marella, Joseph A. 

Manna, Michael 

Lothario, Jose 

Long, Teddy 

LoMonaco, Mark 

Lockwood, Michael 

Levy, Scott (III) 

Levesque, Paul Michael 

Lesnar, Brock 

Leslie, Ed 

Leinhardt, Rodney 

Layfield, John 

Lawler, Jerry 

Lawler, Brian (II) 

Laurinaitis, Joe 

Laughlin, Tom (IV) 

Lauer, David (II) 

Knobs, Brian 

Knight, Dennis (II) 

Killings, Ron 

Kelly, Kevin (VIII) 

Keirn, Steve 

Jones, Michael (XVI) 

Johnson, Ken (X) 

Jericho, Chris 

Jarrett, Jeff (I) 

Jannetty, Marty 

James, Brian (II) 

Jacobs, Glen 

Jackson, Tiger 

Hyson, Matt 

Hughes, Devon 

Huffman, Booker 

Howard, Robert William 

Howard, Jamie 

Houston, Sam 

Horowitz, Barry 

Horn, Bobby 

Hollie, Dan 

Hogan, Hulk 

Hickenbottom, Michael 

Heyman, Paul 

Hernandez, Ray 

Henry, Mark (I) 

Hennig, Curt 

Helms, Shane 

Hegstrand, Michael 

Heenan, Bobby 

Hebner, Earl 

Hebner, Dave 

Heath, David (I) 

Hayes, Lord Alfred 

Hart, Stu 

Hart, Owen 

Hart, Jimmy (I) 

Hart, Bret 

Harris, Ron (IV) 

Harris, Don (VII) 

Harris, Brian (IX) 

Hardy, Matt 

Hardy, Jeff (I) 

Hall, Scott (I) 

Guttierrez, Oscar 

Gunn, Billy (II) 

Guerrero, Eddie 

Guerrero Jr., Chavo 

Gray, George (VI) 

Goldberg, Bill (I) 

Gill, Duane 

Gasparino, Peter 

Garea, Tony 

Funaki, Sho 

Fujiwara, Harry 

Frazier Jr., Nelson 

Foley, Mick 

Flair, Ric 

Finkel, Howard 

Fifita, Uliuli 

Fatu, Eddie 

Farris, Roy 

Eudy, Sid 

Enos, Mike (I) 

Eaton, Mark (II) 

Eadie, Bill 

Duggan, Jim (II) 

Douglas, Shane 

DiBiase, Ted 

DeMott, William 

Davis, Danny (III) 

Darsow, Barry 

Cornette, James E. 

Copeland, Adam (I) 

Constantino, Rico 

Connor, A.C. 

Cole, Michael (V) 

Coage, Allen 

Coachman, Jonathan 

Clemont, Pierre 

Clarke, Bryan 

Chavis, Chris 

Centopani, Paul 

Cena, John (I) 

Canterbury, Mark 

Candido, Chris 

Calaway, Mark 

Bundy, King Kong 

Buchanan, Barry (II) 

Brunzell, Jim 

Brisco, Gerald 

Bresciano, Adolph 

Bloom, Wayne 

Bloom, Matt (I) 

Blood, Richard 

Blanchard, Tully 

Blair, Brian (I) 

Blackman, Steve (I) 

Bischoff, Eric 

Bigelow, Scott ’Bam Bam’ 

Benoit, Chris (I) 

Batista, Dave 

Bass, Ron (II) 

Barnes, Roger (II) 

Backlund, Bob 

Austin, Steve (IV) 

Apollo, Phil 

Anoai, Solofatu 

Anoai, Sam 

Anoai, Rodney 

Anoai, Matt 

Anoai, Arthur 

Angle, Kurt 

AndrØ the Giant 

Anderson, Arn 

Albano, Lou 

Al-Kassi, Adnan 

Ahrndt, Jason 

Adams, Brian (VI) 

Young, Mae (I) 

Wright, Juanita 

Wilson, Torrie 

Vachon, Angelle 

Stratus, Trish 

Runnels, Terri 

Robin, Rockin’ 

Psaltis, Dawn Marie 

Moretti, Lisa 

Moore, Jacqueline (VI) 

Moore, Carlene (II) 

Mero, Rena 

McMichael, Debra 

McMahon, Stephanie 

Martin, Judy (II) 

Martel, Sherri 

Laurer, Joanie 

Keibler, Stacy 

Kai, Leilani 

Hulette, Elizabeth 

Guenard, Nidia 

Garca, LiliÆn 

Ellison, Lillian 

Dumas, Amy 

’WWF Smackdown!’ 

’WWE Velocity’ 

’Sunday Night Heat’ 

’Raw Is War’ 

WWF Vengeance 

WWF Unforgiven 

WWF Rebellion 

WWF No Way Out 

WWF No Mercy 

WWF Judgment Day 

WWF Insurrextion 

WWF Backlash 

WWE Wrestlemania XX 

WWE Wrestlemania X-8 

WWE Vengeance 

WWE Unforgiven 

WWE SmackDown! Vs. Raw 

WWE No Way Out 

WWE No Mercy 

WWE Judgment Day 

WWE Armageddon 

Wrestlemania X-Seven 

Wrestlemania X-8 

Wrestlemania 2000 

Survivor Series 

Summerslam 

Royal Rumble 

No Way Out 

King of the Ring 

Invasion 

Fully Loaded 


❙ ▲ 

▲ 

Taylor, Scott (IX) 

Van Dam, Rob 

Matthews, Darren (II) 

LoMonaco, Mark 

Hughes, Devon 

Huffman, Booker 

Heyman, Paul 

Hebner, Earl 

McMahon, Stephanie 

Keibler, Stacy 

Wight, Paul 

Simmons, Ron (I) 

Senerca, Pete 

Ross, Jim (III) 

Rock, The 

Reso, Jason 

McMahon, Vince 

McMahon, Shane 

Martin, Andrew (II) 

Levesque, Paul Michael 

Layfield, John 

Lawler, Jerry 

Jericho, Chris 

Jacobs, Glen 

Hardy, Matt 

Hardy, Jeff (I) 

Gunn, Billy (II) 

Guerrero, Eddie 

Copeland, Adam (I) 

Cole, Michael (V) 

Calaway, Mark 

Bloom, Matt (I) 

Benoit, Chris (I) 

Austin, Steve (IV) 

Anoai, Solofatu 

Angle, Kurt 

Stratus, Trish 

Dumas, Amy 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Hot Tight Asses 6 


Hot Sweet Honey 

Hot Shots 

Hot Nights at the Blue Note Cafe 

Hot In the City 

Hospitality Sweet 

Hooter Heaven 

Honey Buns 

Hollywood Starlets 

Hollywood Exposed 2 

Holly Does Hollywood 

Holiday for Angels 

Hindlick Maneuver, The 

Hienie’s Heroes 

Hidden Obsessions 

Hershe Highway 4 

Herman’s Bed 

Heads and Tails 

Head Games 

Head Clinic 

Hawaii Vice Part III: Beyond the Badge 

Hawaii Vice 6 

Hawaii Vice 5 

Hawaii Vice 2 

Harlequin Affair 

Hard to Handle 

Hard Rider 

Hard as a Rock 

Happy Endings 

Guilty by Seduction 

Greatest American Blonde 

Grand Opening 

Graduation from F.U. 

Gorgeous 

Good Girls Do 

Going Pro 

Goin’ Down Slow 

Goddess of Love 

Gluteus to the Maximus 

Glen or Glenda? 

Glamour Girl 5 

Give Me Your Soul... 

Girls’ Club, The 

Girls Who Love to Suck 

Girls of the Double D 9 



Girls of the A Team, The 

Girls of Paradise 

Girls of Cell Block F 

Girl with the Heart-Shaped Tattoo, The 

Ginger’s Private Party 

Ginger’s Greatest Boy/Girl Hits 

Ginger Then and Now 

Ginger Snacks 

Ginger On the Rocks 

Ginger Lynn: The Movie 

Ginger Lynn Non-Stop 

Ginger Lynn and Co. 

Ginger in Ecstasy 

Ginger Effect, The 

Ghost Town 

Gettin’ Ready 

Gang Bangs II 

Gang Bangs 

Gang Bang Wild Style 2 

Gang Bang Nymphette 

Gang Bang Jizz Queens 

Gang Bang Jizz Jammers 

Gang Bang Girl 22 





Gang Bang Face Bath 4 



Gang Bang Face Bath 

Gang Bang Cummers 

Games Couples Play 

Future Voyeur 

Full Throttle Girls 1: Boredom Pulled the Trigger 

Full Nest 

Full Moon Fever 

Friends and Lovers: The Sequel 

Fresh Meat 

French Doll 

Forbidden Cravings 

Forbidden Bodies 

For Your Thighs Only 

For the Money 1 

Fluffer, The 

Flesh Shopping Network 

Flashback 

First Annual XRCO Adult Film Awards 

Firm Offer 

Firefoxes 

Fire in the Hole 

Fine Art of Cunnilingus, The 

Film Buff 

Filet-o-Breast 

Femmes Ørotiques, Les 

Femme Vanessa, La 

Fast Girls 

Farmer’s Daughter 2 

Fantasy Inc. 

Fame Is a Whore On Butt Row 

Eyewitness Nudes 

Extreme Sex 4: The Experiment 

Extreme Sex 2: The Dungeon 

Extreme Sex 1: The Club 

Exhibitionist, The 

Executive Suites 

Every Woman Has a Fantasy 3 

Eternity 

Eternal Lust 2 

Escort to Ecstasy 

Erotic Starlets 12: Crystal Lee 

Erotic Newcummers 4 

Erotic Explosions 2 

Entertainment L.A. Style 

Encore 

Enchantress 

Edge of Heat 2 

Edge of Heat 

Ecstasy 

Easy Way, The 

Earth Girls Are Sleazy 

E. TV 

DØj Vu 

Dreams of Candace Hart 

Dreams in the Forbidden Zone 

Dream Machine, The 

Dream Lust 

Dragon Lady 4: Tales from the Bed 3, The 

Double Penetrations 7 



Double Penetration 5 



Double Penetration 

Dirty Prancing 

Dirty Pictures 

Dirty Movies 

Dirty Looks 

Dirty Dreams 

Dickman and Throbbin 

Diamond in the Rough 

Diamond Collection Double X 74 

Diamond Collection Double X 10 

Diamond Collection 79 




Dial F for Fantasy 

Dial a Nurse 

Dial A for Anal 

Devil Made Her Do It, The 

Devil in Miss Jones 5: The Inferno, The 

Devil in Miss Jones 4: The Final Outrage 

Devil in Miss Jones 3: A New Beginning, The 

Desktop Dolls 

DeRenzy Tapes 

Delinquents On Butt Row 

Deeper, Harder, Faster 

Deep Throat Girls 

Deep Obsession 

Deep Inside Victoria Paris 

Deep Inside Vanessa del Rio 

Deep Inside Traci 

Deep Inside Shanna McCullough 

Deep Inside Samantha Strong 

Deep Inside Racquel Darrian 

Deep Inside P.J. Sparxx 

Deep Inside Nina Hartley 

Deep Inside Missy 

Deep Inside Kelly O’Dell 

Deep Inside Ginger Lynn 

Deep Inside Brittany O’Connell 

Deep Inside Barbii 

Deep Inside Ariana 

Deep In Angel’s Ass 

Deep Cover 

Deep Cheeks 3 

Decadence 

Debutante, The 

Dear Bridgette 

Darker Side of Shayla, The 

Darker Side of Shayla 2, The 

Curse of the Catwoman 

Cumshot Revue 5 



Cumming of Ass 

Cumback Pussy 9: Your Ass Is Mine! 

Cumback Pussy 8 

Cumback Pussy 6 

Cumback Pussy 4 Get Some 

Cum for Me Carol 

Cream of Cumback Pussy 

Crazed 

Covergirl 

Country Girl 

Coming on Strong 

Coming of Age 

Come Hither, Cum Ginger 

Club Head 

Club Ginger 

Club DV8 2 

Cherry Cheeks 

Cheerleader Academy 

Cheeks 2: The Bitter End 

Cheek to Cheek 2: The Newest Cheeks on the Block 

Checkmate 

Charmed and Dangerous 

Chameleon, The 

Certifiably Anal 

Centerfolds 

Caught In the Middle 

Caught in the Act 

Caught From Behind 9 



Caught From Behind 2: The Sequel 


Cat Alley 

Car Wash Angels 

Captain Butt’s Beach 

Canned Heat 

California Native 

Cajun Heat 

Butts of Steel 

Butties 

Butt Sisters, The 

Busted 

Burning Desire 

Burgundy Blues 

Bun for the Money 

Bun Busters 

British Are Coming, The 

Bringing Up the Rear 

Bride, The 

Breaking It 

Brazilian Connection, The 

Brat Force 

Bottoms Up! Series 8 

Bottom Line, The 

Bottom Dweller Part Deux, The 

Bottom Dweller 5: In Search of... 

Booty Mistress 

Booty Ho 3 

Boobs Butts and Bloopers 1 

Boiling Point 

Boiling Desires 

Body of Innocence 

Body Music 

Bod Squad, The 

Blowin’ the Whistle 

Bloopers 2 

Bloopers 

Blondes Who Blow 

Blondage 

Blame It On Ginger 

Black Valley Girls 2 

Black Valley Girls 

Black Throat 

Black Stockings 

Billionaire Girls Club 

Bigger They Come 

Big Pink, The 

Big Melons 4 

Big Melons 31 

Big Melons 26 

Big Mellons 25 

Beyond Thunderbone 

Beyond Reality: Mischief in the Making 

Between the Cheeks 3 

Between the Cheeks 2 

Between the Cheeks 

Best Rears of Our Lives, The 

Best of the Vivid Girls #30 

Best of the Dark Bros., Vol. 2, The 

Best of the Dark Bros., The 

Best of Talk Dirty, Vol. 1, The 

Best of Shane 1 

Best of Loose Ends 

Best of Double Penetration 

Best of Diamond Collection 11 

Best of Christy Canyon 

Best of Caught from Behind 2 

Best of Caught from Behind 

Best of Amber Lynn 

Beefeaters 

Beaverly Hills Cop 

Beaver and Buttcheeks 

Beat Goes On, The 

Bazooka County 3 

Battle of the Titans 

Battle of the Superstars 

Bare Market 

Bare Elegance 

Barbii Unleashed 

Barbara Dare’s Bad 

Ball Street 

Badgirls 2: Strip Search 

Bad 

Backroad to Paradise 

Backing in 3 

Backfield in Motion 

Backdoor to Hollywood 11 

Backdoor Summer II 

Backdoor Brides Part 2 

Backdoor Brides 

Backdoor Bonanza 9 

Backdoor Bonanza 13 

Back to Nature 

Back Doors, The 

Bachelor Party 

Baby Face 2 

Babe Watch 

Aussie Exchange Girls 

Asspiring Actresses 

Ass Openers 8 

Ass Openers 6 

Ass Openers 4 

Ass Openers 3 

Ass Openers 10 

Ass Openers 1 

Ass Lovers Special 

Ass Busters Inc. 

Ass Backwards 

Art of Desire 

Aroused 

Army Brat 2 

Arizona Gold 

Anything Goes 

Another Rear View 

Animal in Me 

Angels of Mercy 

Angelica 

Angel Rising 

Angel Puss 

Analizer, The 

Anal Trashy Ass 

Anal Thunder 2 

Anal Taboo 

Anal Sweetheart 

Anal Sluts and Sweethearts 

Anal Secrets 

Anal Riders 106 

Anal Queen 

Anal Princess 

Anal Mystique 

Anal Lover 

Anal Justice 

Anal Innocence 2 

Anal Inferno 

Anal Hounds and Bitches 

Anal Hellraiser 2 

Anal Encounters 2 

Anal Encounters 1 

Anal Ecstasy 

Anal Delights 3 

Anal Deep Rider 

Anal Crack Master 

Anal Climax 3 

Anal Attitude 

Anal Anarchy 

Anal Adventures of Suzy Super Slut 

American Pie 

American Beauty 

Amber Lynn: The Totally Awesome 

Amazing Tails 5 





All the Best, Barbara 

Alice in Hollyweird 

Al Terego’s Double Anal Alternatives 

Aja 

After Midnight 

Afro Erotica 15 

Adventures of Tracy Dick: The Case of the Missing Stiff 

Adventures of Billy Blues, The 

Adult 45 

Above the Knee 

A-List, The 

A Is for Asia 

4F Dating Service 

40 Something 

1-800-934-Boob 

(2,516)-Hard core 

North, Peter (I) 

Wallice, Marc 

Byron, Tom 

Ribald Tales of Canterbury 

Return to Sex 5th Avenue 

Reincarnation of Don Juan 

Red Vibe Diaries 2: Dark Desires 

Rear Ended Roommates 

Rear Busters 

Raunch V 

Raunch 6 

Rapture 

Rambone the Destroyer 

Rainwoman 6 

Rainwoman 4 

Rainbird 

Radio-active 

Radio K-KUM 

Rachel Ryan RR 

Queen of Hearts 3 

Pussypoppers 

Pussyman Takes Hollywood 

Pussyman 2: The Prize 

Pussyman 

Psychic, The 

Prom Girls 

Project: Ginger 

Private Teacher 

Private Affairs: Vol 6 

Private Affairs: Vol 2 

Pretty As You Feel 

Precious Peaks 

Pouring It On 

Possessions 

Portrait of Dorian 

Pornomania 1 

Porn on the 4th of July 

Poonies, The 

Pleasure Seekers 

Pleasure Party 

Pleasure Hunt Part II 

Plaything 2 

Plaything 

Playing with a Full Dick 

Play It Again... Samantha! 

Pink Pussycat, The 

Piece of Heaven 

Physical II 

Photo Flesh 

Perverted Passions 

Perverted 1 

Perks 

Perfect Fit 

Peggy Sue 

Passionate Heiress 

Passionate Angels 

Passenger 69 

Passages 2 

Passages 1 

Party Doll A Go-Go, Part 1 

Party Doll A Go-Go 2 

Party Doll 

Paradise Lost 

Paler Shade of Blue, A 

Overtime: Oral Hijinx 

Oval Office, The 

Outrageous Orgies 5 

Outlaw, The 

Out of Love 

Orgies 

Oral Majority 9 






Oral Majority 

Open Up Traci 

Only the Very Best On Video 

Only the Best of the 80’s 

One Night Stand 

On the Loose 

On Golden Blonde 

Office Girls 

Obsession 

Nurse Nancy 

Nurse Fantasies 

Norma Jeane Anal Legend 

Nobody’s Looking 

No Tell Motel 

Nightbreed 

Night Temptress 

Night Tales 

Night Deposit 

New Wave Hookers 4 

New Wave Hookers 2 

New Wave Hookers 

Never Say Never 

Naughty Thoughts 

Naughty 90’s 

Nasty Nymphos 3 

Nasty Lovers 

Naked Truth, The 

Naked Ambition 

Naked and Nasty 

Mystic Pieces 

Mystery of the Golden Lotus 

Muff ’n’ Jeff 

Motel Sex 

More Than Friends 

Moonstroked 

Model Wife 

Miscreants 

Mirage 2 

Mirage 

Mind Shadows 2 

Mind Shadows 

Midslumber’s Night Dream 

Midnight Pink 

Midnight Hour, The 

Megasex 

Matter of Size, A 

Masque 

Mark of Zara 

Marilyn Whips Wallstreet 

Manbait 2 

Manbait 

Man Who Loves Women, The 

Make My Wife, Please 

Make My Night 

Make Me Want It 

Magic Shower, The 

Lust in the Fast Lane 

Lust College 

Lust Bug, The 

Lust at the Top 

Luscious Lucy in Love 

Lucky Break 

Lovin’ USA 

Lovers, The 

Love Lessons 

Love Ghost 

Love Bites 

Loose Morals 

Loose Ends III 

Loose Ends II 

Loose Ends 

Loads of Fun 4 

Little Romance 

Like a Virgin 

Life and Loves of Nikki Charm 

Let’s Play Doctor 

Legend of Barbi-Q and Little Fawn, The 

Laying the Ghost 

Latin Lust 

Last Temptation, The 

Lascivious Ladies of Dr. Lipo, The 

Laid Off 

Lady in Red, The 

KSEX 106.9 

Kiss, The 

Kiss My Asp 

Kinky Vision 2 

Kinky Couples 

Kinky 

Keyhole Video #114: Christy Canyon Special 

Kascha and Friends 

Just Another Pretty Face 

Juicy Sex Scandals 

Juicy Lucy 

Jezebel 

Jaded Love 

It’s My Body 

Interactive 

Insatiable 

Inferno 

Indecent Itch 

Indecent Exposures 

Inches for Keisha 

In Search of the Golden Bone 

Immaculate Erection 

Images of Desire 

I Want It All 

I Touch Myself 

I Like to Be Watched 

I Dream of Christy 

Hunger, The 

House On Chasey Lane 

House of the Rising Sun 

House of Sleeping Beauties 2 

House of Sleeping Beauties 

House of Blue Dreams 

Hottest Ticket 

Hothouse Rose Part 1 

Hotel Sodom 

Hotel Paradise 

Hotel Fantasy 

Hot Wired 



Young Nurses In Lust 

Young Girls in Tight Jeans 

Young and Naughty 

Year of the Sex Dragon, The 

XTV 2 

XTV 1 

X-rated Bloopers and Outtakes 

X-rated Blondes 

X Dreams 

Wrapped Up 

WPINK-TV 3 

Woman in Pink, The 

Within and Without You 

With Love from Susan 

With Love from Ginger 

Witching Hour, The 

Wire Desire 

Wings of Passion 

Willing Women 

Wild Women 61: Rachel Ryan 

Wild Women 32: Summer Rose 

Wild Women 11: Tanya Foxx 

Wild Weekend 

Wild in the Wilderness 

Wild Buck 

Wild Bananas On Butt Row 

Wild and Wicked 3 

Wicked Whispers 

Wicked Ways #2 

Wicked One 

Wicked As She Seems 

Whore, The 

Whore of the Worlds 

Whore House 

Who Killed Holly Hollywood? 

White Bunbusters 

Whispered Lies 

Where the Sun Never Shines 

What Gets Me Hot! 

Wet Dreams Reel Fantasies 

West Coast Girls 

We Love to Tease 

Way They Were, The 

Wacky World of X-Rated Bloopers 

Voyeur, The 

Voyeur’s Favorite Blowjobs and Anals 8, The 

Voodoo Lust: The Possession 

Visions of Desire 

Virgin Dreams 

Video Tramp 

Victoria and Company 

Vegas: Snake Eyes 

Vagina Town 

Up Your Ass 5 

Up ’n Coming 

Unforgivable 

Unchain My Heart 

Unbelievable Orgies 

Turnabout 

True Legends of Adult Cinema: The Modern Video Era 

True Legends of Adult Cinema: The Erotic 80’s 

Trashy Lady 

Tracie Lords 

Toys 4 Us 2 

Touch of Mischief 

Touch Me 

Torrid Without a Cause 

Top It Off 

Top 25 Adult Stars of All Time, The 

Too Good to Be True 

Tomboy 

To the Rear 

Tits Ahoy 

Tip of the Tongue 

Tight Squeeze 

Tight Ends in Motion 

Thrill Street Blues 

Three-way Lust 

Three by Three 

Those Lynn Girls 

This Is Your Sex Life 

Texas Crude 

Terms of Endowment 

Terminal Case of Love 

Temptation Eyes 

Teasers 

Tease, The 

Tawnee Be Good 

Taste of Victoria Paris 

Taste of Tawnee, A 

Taste of Ariel 

Tarnished Knight 

Talk Dirty to Me, Part III 

Talk Dirty to Me 9 

Takin’ It to the Limit 

Take My Wife, Please! 

Take Me 

Tailspin 1 

Tails of Perversity 3 

Tails of Perversity 2 

Tails of Perversity 

Tailiens 2 

Tailiens 

Tailhouse Rock 

Tailgunners 

Swedish Erotica 74 



Surfside Sex 

Superstars of Sex: Racquel Darrian 

Super Tramp 

Super Groupie 

Sunny After Dark 

Summer Break 

Sugarpussy Jeans 

Suburban Swingers 2 

Street Walkers 

Strange Sex in Strange Places 

Stiff Competition 2 

Stiff Competition 

Starting Over 

Starr 

Star, The 

Star Cuts 4: Ginger Lynn 

Star Cuts 39: Trinity Loren 

Star Cuts 37: Buffy Davis 

Star 85 

Splendor in the Ass 

Splash Shots 

Spies 

Spermbusters 

Spellbound 

Spectacular Orgasms 

Sorority Pink 2: The Initiation 

Sophisticated Lady 

Sodomania: The Baddest of the Best 

Sodomania: Slop Shots 1 

Sodomania 18 

Sodomania 13 

Snatched 

Smart Ass, The 

Smart Ass Returns, The 

Slumber Party 

Sloppy Seconds 

Slip of the Tongue 

Slip Into Ginger and Amber 

Slightly Used 

Sleeping with Everybody 

Slave to Love 

Sky Foxes 

Skin Games 

Sister Dearest 

Sindy Does Anal Again 

Simply Kia 

Simply Blue 

Shot From Behind 

Sheila’s Deep Desires 

Shayla’s Gang 

Shaved Pink 

Shane’s World 

Sexy Secrets N 1 

Sexy and 18 

Sexual Fantasies 

Sextectives 

Sexpertease 

Sex Toys 

Sex Stories 

Sex Sluts in the Slammer 

Sex Shoot 

Sex Plays 

Sex Maniacs 

Sex Fifth Avenue 

Sex Busters 

Sex Beat 

Sex Appraisals 

Sex Academy 2: The Art of Talking Dirty 

Sex 3: After Seven 

Sensual Exposure 

Seeing Red 

Seducers, The 

Secret of Her Suckcess 

Secret Life of Nina Hartley, The 

Secret Fantasies 4 

Secret Fantasies 3 

Screaming Rage 

Scarlet Woman, The 

Scarlet Bride, The 

Savanah Unleased 

Satyr 

Satin Seduction 

Sabotage 

Ruthless Affairs 

Royals: Ginger Lynn 

Roll-x Girls 

Rocky Porno Video Show, The 

Rising, The 

Rise of the Roman Empress 2 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

IMDB cores / Pajek commands 

See How to deal with very large networks? 

Options/Read-Write/Read-Save vertices labels [Off] 

Read/Network [IMDB.net] 1:40 

Info/Memory 

Net/Partitions/Core/2-Mode Review 

Net/Partitions/Core/2-Mode [27 22] 


Operations/Extract from Network/Partition [Yes 1] 

Net/Partitions/2-Mode 

Net/Transform/Add/Vertices Labels from File [IMDB.nam] 


Layers/in y direction 

Options/Transform/Rotate 2D [90] 

Different result (because of multiple lines) 

Net/Components/Weak [2] 


Net/Transform/Remove/Multiple lines/Single line 

Net/Partitions/Core/2-Mode [27 22] 

Operations/Extract from Network/Partition [Yes 1] 



❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

4-rings and analysis of 2-mode networks 

In bipartite (2-mode) network there are no 3-rings. The densest substructures 

are complete bipartite subgraphs Kp,q. They contain many 4-rings. 

� �� 

p q 

w4(Kp,q) = 

2 2 

The 4-rings weights were implemented in 

Pajek only recently, in August 2005. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

There are 4 types of directed 4-rings: 

✫ 

Directed 4-rings 

cyclic transitive genealogical diamond 

In the case of transitive rings Pajek provides a special weight counting on 

how many transitive rings the arc is a shortcut. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Simple line islands in IMDB for w4 

We obtained 12465 simple line islands on 56086 vertices. Here is their size 

distribution. 

Size Freq Size Freq Size Freq Size Freq 

-------------------------------------------------------- 

2 5512 20 19 38 4 59 2 

3 1978 21 18 39 3 61 1 

4 1639 22 15 40 2 64 1 

5 968 23 9 42 2 67 1 

6 666 24 13 43 3 70 1 

7 394 25 12 45 3 73 1 

8 257 26 6 46 4 76 1 

9 209 27 6 47 5 82 1 

10 148 28 5 48 1 86 1 

11 118 29 6 49 2 106 1 

12 87 30 3 50 2 122 1 

13 55 31 6 51 1 135 1 

14 62 32 5 52 2 144 1 

15 46 33 3 53 1 163 1 

16 39 34 1 54 2 269 1 

17 27 35 5 55 1 301 1 

18 28 36 4 57 1 332 2 

19 29 37 7 58 1 673 1 

-------------------------------------------------------- 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

Stratford, Tracy 

✫ 

Example: Islands for w4 / Charlie Brown and Adult 

Hauer, Brent 

Robbins, Peter (I) 

Shea, Christopher (I) Charlie Brown and Snoopy Show 

Altieri, Ann 

Reilly, Earl ’Rocky’ 

Charlie Brown Celebration 

Ornstein, Geoffrey 

You Don’t Look 40, Charlie Brown 

He’s Your Dog, Charlie Brown 

Making of ’A Charlie Brown Christmas’ 

You’re In Love, Charlie Brown 

It’s the Great Pumpkin, Charlie Brown 

Charlie Brown’s All Stars! 

Life Is a Circus, Charlie Brown 

Charlie Brown Christmas 

Race for Your Life, Charlie Brown 

Mendelson, Karen 

Dryer, Sally 

Boy Named Charlie Brown 

Momberger, Hilary 

Brando, Kevin 

Melendez, Bill 

Kesten, Brad 

There’s No Time for Love, Charlie Brown Charlie Brown Thanksgiving 

It’s the Easter Beagle, Charlie Brown 

Be My Valentine, Charlie Brown 

It’s Magic, Charlie Brown 

It’s a Mystery, Charlie Brown 

It’s an Adventure, Charlie Brown 

It’s Flashbeagle, Charlie Brown 

Play It Again, Charlie Brown 

Is This Goodbye, Charlie Brown? 

You’re Not Elected, Charlie Brown 

Snoopy Come Home 

Shea, Stephen 

Schoenberg, Jeremy 

You’re a Good Sport, Charlie Brown 


Boy, T.T. 

North, Peter (I) 

Byron, Tom 

Wallice, Marc 


❙ ▲ 

▲ 

Morgan, Jonathan (I) 

Davis, Mark (V) 

Voyeur, Vince 

Dough, Jon 

Sanders, Alex (I) 

Michaels, Sean 

Horner, Mike 

Drake, Steve (I) 

Silvera, Joey 

West, Randy (I) 

Jeremy, Ron 

Savage, Herschel 

Thomas, Paul (I) 

✩ 


● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✪


✬ 

Example: Island for w4 / Polizeiruf 110 and Starkes Team 

✫ 

’Affre Semmeling, Die’ 

Maranow, Maja 

Starkes Team - Erbarmungslos, Ein 

Starkes Team - Mrderisches Wiedersehen, Ein 

Starkes Team - Roter Schnee, Ein 

Martens, Florian 

Lansink, Leonard 

Bademsoy, Tayfun 

Starkes Team - Der Verdacht, Ein 

Lerche, Arnfried 

Starkes Team, Ein 

Starkes Team - Eins zu Eins, Ein 

Starkes Team - Kollege Mrder, Ein 

Starkes Team - Sicherheitsstufe 1, Ein 

Starkes Team - Das Bombenspiel, Ein 

Starkes Team - Blutsbande, Ein 

Starkes Team - Tdliche Rache, Ein 

Starkes Team - Der Mann, den ich hasse, Ein 

Starkes Team - Kindertrume, Ein 

Starkes Team - Auge um Auge, Ein 

Schwarz, Jaecki 

Starkes Team - Lug und Trug, Ein 

Starkes Team - Der letzte Kampf, Ein 

Starkes Team - Kleine Fische, groe Fische, Ein 

Starkes Team - Der Todfeind, Ein 

Starkes Team - Mordlust, Ein 

Starkes Team - Das groe Schweigen, 

Winkler, 

Ein 

Wolfgang 

Starkes Team - Der schne Tod, Ein 

Starkes Team - Trume und Lgen, Ein 

Starkes Team - Bankraub, Ein 

Starkes Team - Verraten und verkauft, Ein 

Starkes Team - Braunauge, Ein 

Starkes Team - Im Visier des Mrders, Ein 

Starkes Team - Die Natter, Ein 

Polizeiruf 110 - Ein Bild von einem Mrder 

Polizeiruf 110 - Kopf in der Schlinge 

Polizeiruf 110 - Zerstrte Trume 

Polizeiruf 110 - Angst um Tessa Blow 

Polizeiruf 110 - Rosentod 

Polizeiruf 110 - Doktorspiele 

Polizeiruf 110 - Jugendwahn 

Polizeiruf 110 - Heikalte Liebe 

Polizeiruf 110 - Todsicher 

Polizeiruf 110 - Der Spieler 

Polizeiruf 110 - Mordsfreunde 

Polizeiruf 110 - Kurschatten 

Polizeiruf 110 - Tote erben nicht 

Polizeiruf 110 - Der Pferdemrder 

Polizeiruf 110 - Henkersmahlzeit 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 


✩ 

✪


✬ 

✫ 

5-rings 

In the future we intend to implement in Pajek also weights w5. Again 

there are only 4 types of directed 5-rings. 

cyclic transitive ???? ???? 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Pattern searching 

If a selected pattern determined by a given graph does not occur frequently 

in a sparse network the straightforward backtracking algorithm applied for 

pattern searching finds all appearences of the pattern very fast even in the 

case of very large networks. Pattern searching was successfully applied to 

searching for patterns of atoms in molecula (carbon rings) and searching for 

relinking marriages in genealogies. 

Michael/Zrieva/ 

Francischa/Georgio/ 

Damianus/Georgio/ 

Legnussa/Babalio/ 

Nicolinus/Gondola/ 

Franussa/Bona/ 

Marin/Gondola/ 

Magdalena/Grede/ 

Junius/Georgio/ 

Anucla/Zrieva/ 

Nicola/Ragnina/ 

Nicoleta/Zrieva/ 

Junius/Zrieva/ 

Margarita/Bona/ 

Sarachin/Bona/ 

Nicoletta/Gondola/ 

Marinus/Bona/ 

Phylippa/Mence/ 

Marinus/Zrieva/ 

Maria/Ragnina/ 

Lorenzo/Ragnina/ 

Slavussa/Mence/ 

Three connected relinking marriages in the 

genealogy (represented as a p-graph) of ragusan 

noble families. A solid arc indicates 

the is a son of relation, and a dotted arc 

indicates the is a daughter of relation. 

In all three patterns a brother and a sister 

from one family found their partners in the 

same other family. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

m-grandmother 

sister-in-law 

brother 

daughter-in-law 

grandson 

m-grandfather 

mother 

father 

I wife 

Ore-graph 

f-grandfather f-grandmother 

stepmother 

son son-in-law daughter 

sister 

In Ore-graph every person is repre- 

sented by a vertex, marriages, rela- 

tion is a spouse of , are repre- 

sented with edges and relations is 

a mother of and is a father 

of as arcs pointing from parents 

to their children. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

father & stepmother 

✫ 

son & daughter-in-law 

sister 

grandson 

I & wife 

father & mother 

p-graph 

son-in-law & daughter 

brother & sister-in-law 

f-grandfather & f-grandmother m-grandfather & m-grandmother 

In p-graph vertices represent indi- 

viduals or couples. In the case that 

a person is not married yet (s)he is 

represented by a vertex, otherwise 

person is represented with the part- 

ner in a common vertex. There are 

only arcs in p-graphs – they point 

from children to their parents, rep- 

resenting the relations FiC is a 

daughter of and MiC is a son 

of ; where FiC ≡ female in the 

couple; and MiC ≡ male in the 

couple. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

A5.1 

A6.1 

A2 

A4.1 

B6.1 

✫ 

A5.2 

A6.2 

B6.2 

B4 

A3 

Relinking patterns in p-graphs 

A4.2 

B5 

A6.3 

B6.3 

C6 

B6.4 

All possible relinking marriages in p- 

graphs with 2 to 6 vertices. Patterns are 

labeled as follows: 

• first character – number of first 

vertices: A – single, B – two, C 

– three. 

• second character: number of ver- 

tices in pattern (2, 3, 4, 5, or 6). 

• last character: identifier (if the two 

first characters are identical). 

Patterns denoted by A are exactly the 

blood marriages. In every pattern the 

number of first vertices equals to the 

number of last vertices. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Frequencies normalized with number of couples in 

p-graph × 1000. 

pattern Loka Silba Ragusa Turcs Royal 

A2 0.07 0.00 0.00 0.00 0.00 

A3 0.07 0.00 0.00 0.00 2.64 

A4.1 0.85 2.26 1.50 159.71 18.45 

B4 3.82 11.28 10.49 98.28 6.15 

A4.2 0.00 0.00 0.00 0.00 0.00 

A5.1 0.64 3.16 2.00 36.86 11.42 

A5.2 0.00 0.00 0.00 0.00 0.00 

B5 1.34 4.96 23.48 46.68 7.03 

A6.1 1.98 12.63 1.00 169.53 11.42 

A6.2 0.00 0.90 0.00 0.00 0.88 

A6.3 0.00 0.00 0.00 0.00 0.00 

C6 0.71 5.41 9.49 36.86 4.39 

B6.1 0.00 0.45 1.00 0.00 0.00 

B6.2 1.91 17.59 31.47 130.22 10.54 

B6.3 3.32 13.53 40.96 113.02 11.42 

B6.4 0.00 0.00 2.50 7.37 0.00 

Sum 14.70 72.17 123.88 798.53 84.36 

Most of the relinking marriages happened in the genealogy of Turkish nomads; the second is 

Ragusa while in other genealogies they are much less frequent. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Multiplication of networks 

To a simple two-mode network N = (I, J, E, w); where I and J are sets 

of vertices, E is a set of edges linking I and J, and w : E → R (or some 

other semiring) is a weight; we can assign a network matrix W = [wi,j] 

with elements: wi,j = w(i, j) for (i, j) ∈ E and wi,j = 0 otherwise. 

Given a pair of compatible networks NA = (I, K, EA, wA) and NB = 

(K, J, EB, wB) with corresponding matrices AI×K and BK×J we call a 

product of networks NA and NB a network NC = (I, J, EC, wC), where 

EC = {(i, j) : i ∈ I, j ∈ J, ci,j �= 0} and wC(i, j) = ci,j for (i, j) ∈ EC. 

The product matrix C = [ci,j]I×J = A ∗ B is defined in the standard way 

ci,j = � 

k∈K 

ai,k · bk,j 

In the case when I = K = J we are dealing with ordinary one-mode 

networks (with square matrices). 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

Fast sparse matrix multiplication 

The standard matrix multiplication has the complexity O(|I| · |K| · |J|) – it 

is (usually) too slow to be used for large networks. 

For sparse large networks we can multiply faster considering only nonzero 

elements: 

for k in K do 

for i in NA(k) do 

for j in NB(k) do 

if ∃ci,j then ci,j := ci,j + ai,k ∗ bk,j 

else new ci,j := ai,k ∗ bk,j 

NA(k): neighbors of vertex k in network A 

NB(k): neighbors of vertex k in network B 

In general the multiplication of large sparse networks is a ’dangerous’ 

operation since the result can ’explode’ – it is not sparse. 

✫ 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Complexity of fast sparse matrix multiplication 

Let A and B be matrices of networks NA = (I, K, EA, wA) and NB = 

(K, J , EB, wB). 

Assume that the body of the loops can be computed in the constant time c. 

Then we can prove: 

If at least one of the sparse networks NA and NB has small maximal degree 

on K then also the resulting product network NC is sparse. 

And after more detailed complexity analysis: 

Let dmin(k) = min(deg A(k), deg B(k)), ∆min = maxk∈K dmin(k), 

dmax(k) = max(deg A(k), deg B(k)), K(d) = {k ∈ K : dmax(k) ≥ d}, 

d ∗ = argmin d(|K(d)| ≤ d) and K ∗ = K(d ∗ ). 

If for the sparse networks NA and NB the quantities ∆min and d ∗ are small 

then also the resulting product network NC is sparse. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

2-mode network analysis by conversion to 1-mode network 

Often we transform a 2-mode network into an ordinary (1-mode) network 

N1 = (U, E1, w1) or/and N2 = (V, E2, w2), where E1 and w1 are 

determined by the matrix A (1) = AA T , a (1) 

uv = � 

z∈V auz · a T zv. Evidently 

a (1) 

uv = a (1) 

vu . There is an edge {u, v} ∈ E1 in N1 iff N(u) ∩ N(v) �= ∅. Its 

weight is w1(u, v) = a (1) 

uv . 

The network N2 is determined in a similar way by the matrix A (2) = A T A. 

The networks N1 and N2 are analyzed using standard methods. 

✫ 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Networks from data tables 

A data table T is a set of records T = {Tk : k ∈ K}, where K is the set of 

keys. A record has the form Tk = (k, q1(k), q2(k), . . . , qr(k)) where qi(k) 

is the value of the property (attribute) qi for the key k. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

. . . Networks from data tables 

Suppose that the property q has the range Q. If Q is finite (it can always be 

transformed in such set by partitioning the set Q and recoding the values) 

we can assign to the property q a two-mode network K ×q = (K, Q, E, w) 

where (k, v) ∈ E iff q(k) = v, and w(k, v) = 1. 

Also, for properties qi and qj we can define a two-mode network qi ×qj = 

(Qi, Qj, E, w) where (u, v) ∈ E iff ∃k ∈ K : (qi(k) = u ∧ qj(k) = v), 

and w(u, v) = card({k ∈ K : (qi(k) = u ∧ qj(k) = v)}). 

We define [qi × qj] T = qj × qi. 

It holds qi × qj = [K × qi] T ∗ [K × qj] = [qi × K] ∗ [K × qj]. 

We can join a pair of properties qi and qj also with respect to the third 

property qs: we get a two-mode network [qi×qj]/qs = [qi×qs]∗[qs×qj]. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

EU projects on simulation 

For the meeting The Age of Simulation at Ars Electronica in Linz, January 

2006 a dataset of EU projects on simulation was collected by FAS research, 

Vienna and stored in the form of Excel table (RuthDELmain.csv). 

The rows are the projects participants (idents) and colomns correspond to 

different their properties. We produced from this table three two-mode 

networks using Jürgen Pfeffer’s Text2Pajek program: 

• project.net – idents × projects = P 

• country.net – idents × countries = C 

• institution.net – idents × institutions = U 

|idents| = 8869, |projects| = 933, |institutions| = 3438, 

|countries| = 60. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

EU projects – network multiplication 

Since all three networks have the common set (idents) we can derive from 

them using network multiplication several interesting networks: 

• ProjInst.net – projects × institutions W = P T ⋆ U 

• Countries.net – countries × countries S = C T ⋆ C 

• Institutions.net – institutions × institutions Q = W T ⋆ W 

• . . . 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

EU projects – deleted projects 

Some projects (27) from original data set have to be deleted – in the final 

data set RuthDELmain they were marked as deleted. When producing 

two-mode networks we could first physicaly delete them. Instead of this, 

we used another approach: we produced the cluster CD of deleted idents 

and from it a two-mode matrix D (idents × idents; not implemented yet 

in Pajek). Matrix D is a ’diagonal’ matrix with value 1 for idents not 

belonging to CD and 0 otherwise. Using matrix D we can determine the 

network ProjInst.net by W = P T ⋆ D ⋆ U – the deleted idents don’t 

contribute to the network. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

Analysis of ProjInst.net 

For identifying important parts of ProjInst.net we first computed the 

4-rings weights and in the obtained network we determined the line islands 

Net/Count/4-rings/Undirected 

Net/Partitions/Islands/Line Weights[Simple [2,200] 

We obtain 101 islands. We extracted 18 islands of the size at least 5. There 

are two most important islands: aviation companies and car companies. 

In labels we used a new option \n. 

For analysis of two-mode networks we can use also (p, q)−cores. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

BICC GENERAL CABLE 

25525 

PSI FUR PRODUKTE UND 

SYS.E DER INFORMATIONSTECH. 

29817 

BARCO NV 

COLOPLAST A/S 

FRAUENHOFER INST. FUER 

PRODUKTIONSTECH. UND AUTOMATISIERUNG 

LMS UMWELTSYS.E, DIPL. ING. DR. HERBERT BACK 

TESSITURA LUIGI SANTI SPA 

INST. FUER TEXTIL UND 

VERFAHRENSTECH. DENKENDORF 

KBC MANUFAKTUR, KOECHLIN, 

BAUMGARTNER UND CIE. AG 

MSO CONCEPT INNOVATION + SOFTWARE 

TRUMPF-BLUSEN-KLEIDER 

WALTER GIRNER UND CO. KG 

7210-PR/163 

Analysis of ProjInst.net 

IST-2000-29207 

MTU AERO ENGINES 

EADS DE 

AIRBUS UK LIMITED 

BAE SYSTEMS 

EUROCOPTER S. 

28283 

EA TECH. LTD 

506503 

MECALOG SARL 

506257 

INST. NAT. DE RECHERCHE 

SUR LES TRANSPORTS ET LEUR SCURIT 

AIRBUS DEUTSCHLAND 

502917 

SNECMA MOTEURS SA 

INST. SUPERIOR TECNICO 

C. R. FIAT S.C.P.A. 

NAT. TEC. UNIV. 502909 OF ATHENS NL ORG. FOR APPLIED 

SCIENTIFIC RESEARCH - TNO 

502842 

AIRBUS FRANCE SAS 

ALENIA AERONAUTICA SPA 

BARTENBACH 

501084 

G4RD-CT-2002-00836 

G4MA-CT-2002-00022 

STICHTING NATIONAAL LUCHT 

POLYMAGE SARL 

OFFICE NAT. DETUDES ET 

DE REC. AEROSPATIALES 

ROSENHEIMER GLASTECH. 

BRPR987001 

502896 

G4RD-CT-2000-00178 

ENK6-CT-2002-30023 

G4RD-CT-2001-00403 

G4RD-CT-2002-00795 

RUDOLF BRAUNS AND CO. KG 

CENTRE DE RECH. METALLURG. 

7215-PP/031 

502889 

SHERPA ENGINEERING SARL 

7210-PR/233 VOEST-ALPINE STAHL 

G4RD-CT-2000-00395 

CATALYSE SARL 

INST. DE RECHERCHES 

DE LA SIDERURGIE FR 

THYSSENKRUPP STAHL A.G. 

EVG3-CT-2002-80012 

T3.2/99 

DISENO DE SISTEMAS EN SILICIO 

CENTRE FOR EUROP. ECONOMIC 

SMT4982223 

ILEVO AB 

FONDAZIONE ENI - ENRICO MATTEI 

7210-PR/095 

UNIV. DER BUNDESWEHR MUENCHEN 

CSTB 

IST-2001-35358 

JERNKONTORET 

HPSE-CT-2002-00108 

BUILDING RESEARCH 

CHIPIDEA - MICROELECTRONICA, S.A. 

LANDIS & GYR - EUROPE AG 

ENEL.IT 

UNIV. PANTHEON-ASSAS - PARIS II 

OESTERREICHISCHER BERGRETTUNGSDIENST 

SSAB TUNNPL¯T 

IFEN GES. FUER SATELLITENNAVIGATION 

JOE3980089 

7215-PP/034 

RESEARCH INST. OF THE FINNISH ECONOMY 

IST-2000-30158 

WYKES ENGINEERING COMPANY 

LH AGRO EAST S.R.O. 

QLK6-CT-2002-02292 

INST. CARTOGRAFIC DE CATALUNYA 

CINAR LTD. 

TECHNOFARMING S.R.L. 

T3.5/99 

HELP SERVICE REMOTE SENSING 

LESPROJEKT SLUZBY S.R.O. 

THE AARHUS SCHOOL OF BUSINESS 

MEFOS, FOUNDATION FOR 

METALLURGICAL RESEARCH 

HPSE-CT-2002-00143 

BAYER. ROTES KREUZ 

ENERGY RESEARCH CENTRE NL 

JOR3980200 

FRAUENHOFER INST. FUER 

MATERIALFLUSS UND LOGISTIK 

ENK5-CT-2000-00335 

IST-2000-28177 

AGRO-SAT CONSULTING 

DATASYS S.R.O. 

BRITISH STEEL 

7210-PR/142 

UNIV. OF MACEDONIA 

UNIV. OF ABERDEEN 

BBL 

ORAD HI TEC SYS. POLAND 

CRE GROUP LTD. 

DFA DE FERNSEHNACHRICHTEN AGENTUR 

MJM GROUP, A.S. 

FRIMEKO INT. AB 

INOX PNEUMATIC AS 

CENTRE DE ROBOTIQUE 

TPS TERMISKA PROCESSER AB 

KOMMANDITGES. HAMBURG 1 

PROLEXIA 

FERNSEHEN BETEILIGUNGS & CO 

A.S.M. S.A. ZAMISEL D.O.O 

DPME ROBOTICS AB 

INGENIORHOJSKOLEN HELSINGOR TEKNIKUM IST-1999-56418 

511758 

GATE5 AG 

LKSOFTWARE 

UAB LKSOFT BALTIC 

BRST985352 

INDUSTRIAS ROYO 

WISDOM TELE VISION 

SPORTART 

IST-2000-30082 

ALBERTSEN & HOLM AS 

ASM - DIMATEC INGENIERIA 

FFT ESPANA TECH. DE AUTOMOCION, 

SVETS & TILLBEHOR AB 

ENERGITEKNIK HEATEX AB 

SUPERELECTRIC DI 

CARLO PAGLIALUNGA & C. SAS 

IST-1999-57451 

OK GAMES DI ALESSANDRO CARTA 

YAHOO! DE OSAUHING EETRIUKSUS 

EDAG ENGINEERING + DESIGN 

BROD THOMASSON 

GUNNESTORPS SMIDE & MEKANISKA AB 

UNIV. DE ZARAGOZA 


ARMINES 

BUURSKOV 

DE ZENTRUM FUER LUFT 

UND RAUMFAHRT E.V. 

DASSAULT AVIATION 

TQT SRL 

ESI SOFTWARE SA 

CHALMERS TEKNISKA HOEGSKOLA 

VOLKSWAGEN AG 

DAIMLER CHRYSLER AG 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

Uzbekistan 

Armenia 

India 

✫ 

Kazakhstan 

Georgia 

Belarus 

Canada 

Japan 

Azerbaijan 

Analysis of Countries.net 

Liechtenstein 

France 

Moldavia China 

United Kingdom 

Russian F. 

Italia 

Finland 

The Netherlands 

Germany Greece 

Portugal 

Spain 

Turkey 

Malta 

Thailand 

Switzerland 

Israel 

Turkmenistan 

Cyprus 

Sweden Denmark Austria 

Estonia 

USA 

Slovakia 

Belgium 

Norway 

Serbia-Montenegro 

Ukraine 

Macedonia 

Croatia 

Poland 

Slovenia 

Hungary 

Luxembourg 

Ireland 

Latvia 

Bulgaria Czech R. 

Lithuania 

Afghanistan 

Iceland 

Romania 

Morocco 

Tunisia 

Jordan 

Ecuador 

Lebanon 

Algeria 

Albania 


To obtain picture in which the 

stronger lines cover weaker lines we 

have to sort them 

Net/Transform/Sort 

lines/Line values/Ascending 

For dense (sub)networks we get 

better visualization by using matrix 

display. In this case we also recoded 

values (2,10,50). To determine 

clusters we used Ward’s clustering 

procedure with dissimilarity measure 

d5 (corrected Euclidean distance). 

The permutation determined by hierarchy can often be improved by 

changing the positions of clusters – for the New Year 2006 Andrej added 

this option in Pajek. We get a typical center-periphery structure. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 


Ecuador 

Thailand 

Armenia 

Turkmenist 

Uzbekistan 

Moldavia 

Japan 

Kazakhstan 

Azerbaijan 

India 

Macedonia 

Albania 

Liechtenst 

Serbia-Mon 

Iceland 

Canada 

Estonia 

China 

Belarus 

Georgia 

Tunisia 

Lebanon 

Jordan 

Algeria 

Malta 

Morocco 

Afghanista 

Luxembourg 

Croatia 

Latvia 

Lithuania 

Cyprus 

Turkey 

Bulgaria 

Ukraine 

Slovenia 

Romania 

Slovakia 

USA 

Portugal 

Denmark 

Poland 

Finland 

Switzerlan 

Austria 

Czech R. 

Ireland 

Norway 

Hungary 

Israel 

Russian F. 

Sweden 

Greece 

Belgium 

Spain 

The Nether 

France 

United Kin 

Germany 

Italia 

✫ 

Analysis of Countries.net 


Ecuador 

Thailand 

Armenia 

Turkmenist 

Uzbekistan 

Moldavia 

Japan 

Kazakhstan 

Azerbaijan 

India 

Macedonia 

Albania 

Liechtenst 

Serbia-Mon 

Iceland 

Canada 

Estonia 

China 

Belarus 

Georgia 

Afghanista 

Morocco 

Malta 

Tunisia 

Lebanon 

Jordan 

Algeria 

Croatia 

Latvia 

Lithuania 

Luxembourg 

Cyprus 

Turkey 

Bulgaria 

Ukraine 

Slovenia 

Romania 

Slovakia 

USA 

Russian F. 

Israel 

Hungary 

Ireland 

Czech R. 

Norway 

Poland 

Finland 

Portugal 

Denmark 

Switzerlan 

Austria 

Sweden 

Greece 

Belgium 

Spain 

The Nether 

Italia 

France 

United Kin 

Germany 

Ecuador 

Thailand 

Armenia 

Turkmenist 

Uzbekistan 

Moldavia 

Japan 

Kazakhstan 

Azerbaijan 

India 

Macedonia 

Albania 

Liechtenst 

Serbia-Mon 

Iceland 

Canada 

Estonia 

China 

Belarus 

Georgia 

Afghanista 

Morocco 

Malta 

Tunisia 

Lebanon 

Jordan 

Algeria 

Croatia 

Latvia 

Lithuania 

Luxembourg 

Cyprus 

Turkey 

Bulgaria 

Ukraine 

Slovenia 

Romania 

Slovakia 

USA 

Russian F. 

Israel 

Hungary 

Ireland 

Czech R. 

Norway 

Poland 

Finland 

Portugal 

Denmark 

Switzerlan 

Austria 

Sweden 

Greece 

Belgium 

Spain 

The Nether 

Italia 

France 

United Kin 

Germany 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

U.A.S.ZITTAU/GOERLITZ 

U.THE AEGEAN MIT-MANAGEMENT INTELLIGENTER TECH.N 

U.PARIS-DAUPHINE 

OTTO VON GUERICKE MAGDEBURG U. 

COVENTRY U. 

FACULTY OF ELECTRICAL ENG. 

FED.UNITARY DAEDALUS ENTERPRISE 

INFORMATICS LTD FL-SOFT V/JENS 

ALL-RUSSIAN SCIENTIFIC 

U.PARIS 

CENTER 

VI PIERRE ET JOERGEN MARIE CURIE OESTERGAARD 

BELIMO AUTOMATIONU.LA 

LAGUNA 

SOFIISKI U.SVETI KLIMENT OHRIDSKI 

THE U.COURT OF THE U.OF ABERDEEN 

SENTIENT MACHINE RESEARCH B.V. SIEMENS BUILDING TECH.S AG 

U.OULU I.OF INFORMATION TECH.S 

AS.CONOCIMIENTO 

DATAMED HEALTHCARE INF.SYS. STICHTING NEURALE NETWERKEN 

NOTTINGHAM TRENT U. U.E DE COIMBRA T.U.CLAUSTHAL 

MOMATEC 

U.CRETE 

U.ULSTER 

CITY U.LONDON 

GOETHE U.FRANKFURT AM MAIN 

U.WIEN 

ALLOGG AB 

RAUTARUUKKI OY 

SOFTECO SISMAT 

U.WALES, ABERYSTWYTH 

DE MONTFORT U. 

I.DALLE MOLLE DI STUDI SULLIA U.JYVASKYLA 

BULGARIAN ACAD. 

U.ZAGREB 

U.CYPRUS OF SCIENCES 

U.OF CHEMICAL TECH. 

AND METALLURGY 

ASS.RECH.SCIENTIFIQUE BOURNEMOUTH U. 

ENTE PER LE 

ELITE EUROP.LAB 

KINGS COLLEGE LONDON 

NUOVE TECNOLOGIE 

FOR INTELLIGENT 

STICHTING 

TECH. 

U.NYENRODE 

I.FUER NATURSTOFF-FORSCHUNG E.V. 

I.NAT.POLITEC.DE TOULOUSE 

U.GIRONA 

U.AMSTERDAM 

U.GENT 

AUSTRIAN I.AI 

START ENGINEERING JSCO 

T.U.DELFT 

ENERGY RESEARCH C.NL I.NAT.DE RECHERCHE SUR 

LES TRANSPORTS ET LEUR SECURITE 

U.GRANADA 

TEKNILLINEN KORKEAKOULU 

HELSINKI T.U. 

✫ 

Analysis of Institutions.net 

NAT.U.IRELAND,MAYNOOTH 

U.TWENTE 

TSS-TRANSPORT SIMULATION SYS.S.L. 

U.KLINIKUM AACHEN 

KATHOLIEKE U.LEUVEN 

U.BRISTOL 

FRIEDRICH-SCHILLER-U.JENA 

ERASMUS U.ROTTERDAM 

CONSEJO SUP.DE 

AABO AKADEMI U 

INVEST.CIENTIFICAS 

U.MARIBOR 

U.P.MADRID 

U.PAUL SABATIER DE TOULOUSE III 

U.VALLADOLID 

U.P.CATALUNYA 

JOZEF STEFAN I. 

U.PAISLEY 

U.STRATHCLYDE 

QINETIQ DEP.OF ENVIRONMENT, 

GKSS TRANSPORT - FORSCHUNGSZENTRUM AND THE REGIONS GEESTHACHT 

EUROP.SPACE AGENCY 

MANNESMANN VDO AG 

TECHSOFT ENGINEERING S.R.O. 

U.LEEDS 

TECNOLOGIAS CAE AVANZADAS S.L. 

U.S.GENOVA 

PT.TORINO 

PT.BARI 

DAIMLER CHRYSLER AG 

U.DORTMUND 

LOUGHBOROUGH T.U. 

BRITISH TELEC. 

NAT.T.U.ATHENS 

I.SUPERIOR TECNICO 

U.SHEFFIELD 

POLISH ACAD.OF SCIENCES 

RISOE NAT.LAB 

U.NOTTINGHAM 

U.MANCHESTER 

BAE SYSTEMS 

CZECH T.U.PRAGUE 

T.U.V KOSICIACH 

FUNDACION LABEIN 

C.SVILUPPO MATERIALI 

HERMSDORFER I.FUER TECH. 

OXFORD BROOKES U. 

U.S.PADOVA SAFE TECH. 

NOKIA MOBILE PHONES LTD 

AVIO S.P.A. 

FOKKER SPACE BV 

ANAKON 

NCODE INT. 

FINITE ELEMENT ANALYSIS LTD. 

TUN ABDUL RAZAK RESEARCH C.LTD. 

DANMARKS T.U. 

U.GREENWICH 

U.C.LOUVAIN 

CRANFIELD U. 

FUNDACION INASMET 

IFP SICOMP AB 

PRINCIPIA INGENIEROS CONSULTORES 

STAVANGER U.COLLEGE 

SULZER MARKETS AND TECH.AG, 

SULZER INNOTEC 

CHALMERS TEKNISKA HOEGSKOLA 

DAMT LTD 

SKF R&D COMPANY B.V. 

U.S.NAPOLI 

CAESAR SYSTEMS LTD 

A.U.THESSALONIKI INTES - INGENIEURGES. 

NAFEMS LTD. 

C.INT.LENGINYERIA 

NL ORG.FOR APPLIED 

FUER TECH.SOFTWARE ENGIN SOFT TRADING SRL 

U.DURHAM 

MARITIME HYDRAULICS AS 

INBIS TECH.LTD 

SCIENTIFIC RESEARCH-TNO 

C.R.FIAT S.C.P.A. CAD - FEM 

U.S.TRIESTE 

FEMSYS LTD 

SOFISTK AG 

C.NAT.DE LA 

RECHERCHE SCIENTIFIQUE 

MSC SOFTWARE 

QUEENS U.BELFAST 

ABS CONSULTING 

ALTAIR ENGINEERING 

SAMTECH SA 

NLSE VERENIGDE SCHEEPSBOUW BUREAUS B.V. 

LEUVEN MEASUREMENTS AND SYS.INT.NV 

MERITOR HEAVY VEHICLE 

CREA CONSULTANTS 

BRAKING 

LTD 

SYS.- UK LTD 

TRL 

ACCESS E.V. 

PD&E AUTOMOTIVE B.V. 

NEW TECH.ENGINEERING LTD 

ROCKFIELD SOFTWARE LTD. 

U.NEWCASTLE UPON TYNE 

BEHR &CO. 

AIRBUS FRANCE SAS 

NAT.NUCLEAR CORP.LTD. 

U.GLASGOW 

FEMCOS INGENIEURBUERO MBH 

ST MECANICA APLICADA S.L. 

GERMAN AEROSPACE CENTRE 

FRAUENHOFER I.FUER 

INGENIEURBUERO FUER 

BIOMEDICAL ENGINEERING TRAGWERKSPLANUNG 

ROYAL I.OF TECH. 

DUNLOP STANDARD 

KATHOLIEKE HOGESCHOOL SINT-LIEVEN 

U.HANNOVER 

AEROSPACE GROUP 

GIFFORD AND PARTNERS LTD. 

VOLVO AERO CORP.AB 

MECAS S.R.O. 

LULEAA T.U. 

ATOS ORIGIN ENG. 

STRUCTURAL INTEGRITY 

ASSESSMENTS LTD 

CORK I.OF TECHNOLOGY 

NORUT TEKNOLOGI HAHN-SCHICKARD-GES. 

A.S. 

WS ATKINS CONSULTANTS LTD. EASI ENGINEERING 

U.E DO MINHO 

U.SPLIT 

NUMERICAL ANALYSIS 

WILDE AND TECHNISCH PARTNERS LTD ADVIESBUREAU N.V. AND DESIGN&CO KG 

INTEGRATED DESIGN & 

FEGS 

RANDOM LOADING 

AWE 

ANALYSIS DESIGN 

PLC 

CONSULTANTS LTD 

MERKLE UND PARTNER D C WHITE&PARTNERS LTD 

DR THELLEN 

EATEC LTD 

To identify the most important institu- 

tions we first computed pS-cores vec- 

tor and use it to determine the cor- 

responding vertex islands. We got 

essentially one large island. Again 

the corresponding subnetwork is very 

dense. We prepared also a matrix dis- 

play. 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 


ALLOGG AB 

AS. CONOCI 

ASS. RECH. 

AUSTRIAN I 

BELIMO AUT 

COVENTRY U 

DAEDALUS I 

DATAMED H 

FACULTY OF 

FED. UNITA 

FL-SOFT V/ 

INST. OF I 

GOETHE UNI 

MIT-MANAGE 

MOMATEC 

NAT. UNIV. 

NOTTINGHAM 

POLITECNIC 

SENTIENT M 

SIEMENS BU 

SOFIISKI U 

START ENGI 

STICHTING 

STICHTING 

THE UNIV. 

UNIV. DE L 

UNIV.SKLIN 

UNIV. DE G 

UNIV. PARI 

UNIV. OF A 

UNIV. OF C 

UNIV. OF C 

UNIV. OF W 

UNIV. OF Z 

INST. DALL 

RAUTARUUKK 

UNIV.E DE 

UNIV. OF U 

SOFTECO SI 

UNIV. GENT 

TSS - TRAN 

UNIV. DE G 

UNIV. DE V 

UNIVERZA V 

UNIV. PAUL 

TECH. UNIV 

UNIV. WIEN 

UNIV. VAN 

ENERGY RES 

TEKNILLINE 

DE MONTFOR 

CITY UNIVE 

UNIV. OF J 

AABO AKADE 

RISOE NAT. 

KINGS COLL 

UNIV. DORT 

FRIEDRICH- 

UNIV. OF C 

INST. NAT. 

BULGARIAN 

ENTE PER L 

LOUGHBOROU 

HELSINKI U 

CRANFIELD 

UNIV. CATH 

OTTO VON G 

UNIV. DEGL 

UNIV. OF O 

UNIV. OF T 

ELITE EURO 

ERASMUS UN 

INST. FUER 

UNIV. PARI 

BRITISH TE 

BOURNEMOUT 

UNIV. OF B 

UNIV. OF S 

DANMARKS T 

DAIMLER CH 

INST. NAT. 

INST. SUPE 

POLITECNIC 

POLISH ACA 

UNIV. POLI 

NAT. TEC. 

CONSEJO SU 

KATHOLIEKE 

UNIV. TWEN 

TECH. UNIV 

UNIV. POLI 

CENTRE NAT 

TEC. UNIV. 

UNIV. OF P 

FUNDACION 

JOZEF STEF 

CZECH TECH 

UNIV. OF N 

UNIV. OF S 

BAE SYSTEM 

UNIV. OF M 

ABS CONSUL 

ALTAIR ENG 

ANAKON 

ATOS ORIGI 

AWE PLC 

BEHR & CO 

CAESAR SYS 

CORK INST. 

CREA CONSU 

D C WHITE 

DAMT LTD 

DEP. OF E 

DR THELLEN 

DUNLOP STA 

EASI ENGIN 

EATEC LTD 

FEMSYS LTD 

FOKKER SPA 

FORSCHUNGS 

GIFFORD AN 

HAHN-SCHIC 

HERMSDORFE 

INBIS TECH 

INGENIEURB 

INTEGRATED 

KATHOLIEKE 

MANNESMANN 

MARITIME H 

MECAS S.R. 

MERITOR HE 

MERKLE UND 

NAFEMS LTD 

NCODE INT. 

NLSE VEREN 

NEW TECH. 

NOKIA MOBI 

NORUT TEKN 

NUMERICAL 

OXFORD BRO 

PD & E AUT 

RANDOM LOA 

SAFE TECH. 

SKF R & D 

SOFISTK AG 

ST MECANIC 

STAVANGER 

STRUCTURAL 

SULZER MAR 

TECHNISCH 

TECHSOFT E 

TECNOLOGIA 

TUN ABDUL 

UNIV.E DO 

UNIV. OF S 

WILDE AND 

FRAUENHOFE 

GKSS - FOR 

NAT. NUCLE 

UNIV. OF D 

ENGIN SOFT 

FEGS 

IFP SICOMP 

INTES - IN 

UNIV. DEGL 

PRINCIPIA 

FINITE ELE 

ROCKFIELD 

WS ATKINS 

ROYAL INST 

UNIV. HANN 

UNIV. DEGL 

UNIV. OF G 

UNIV. OF N 

CAD - FEM 

C. SVILUPP 

TRL 

LEUVEN MEA 

A. UNIV. T 

GERMAN AER 

CENTRE INT 

UNIV. DEGL 

QINETIQ 

UNIV. OF L 

FUNDACION 

ACCESS E.V 

EUROP. SPA 

UNIV. OF G 

SAMTECH SA 

VOLVO AERO 

AVIO S.P.A 

MSC SOFTWA 

LULEAA UNI 

QUEENS UNI 

AIRBUS FRA 

C. R. FIAT 

NL ORG. FO 

CHALMERS T 

Analysis of Institutions.net 


ALLOGG AB 

AS. CONOCI 

ASS. RECH. 

AUSTRIAN I 

BELIMO AUT 

COVENTRY U 

DAEDALUS I 

DATAMED H 

FACULTY OF 

FED. UNITA 

FL-SOFT V/ 

INST. OF I 

GOETHE UNI 

MIT-MANAGE 

MOMATEC 

NAT. UNIV. 

NOTTINGHAM 

POLITECNIC 

SENTIENT M 

SIEMENS BU 

SOFIISKI U 

START ENGI 

STICHTING 

STICHTING 

THE UNIV. 

UNIV. DE L 

UNIV.SKLIN 

UNIV. DE G 

UNIV. PARI 

UNIV. OF A 

UNIV. OF C 

UNIV. OF C 

UNIV. OF W 

UNIV. OF Z 

INST. DALL 

RAUTARUUKK 

UNIV.E DE 

UNIV. OF U 

SOFTECO SI 

UNIV. GENT 

TSS - TRAN 

UNIV. DE G 

UNIV. DE V 

UNIVERZA V 

UNIV. PAUL 

TECH. UNIV 

UNIV. WIEN 

UNIV. VAN 

ENERGY RES 

TEKNILLINE 

DE MONTFOR 

CITY UNIVE 

UNIV. OF J 

AABO AKADE 

RISOE NAT. 

KINGS COLL 

UNIV. DORT 

FRIEDRICH- 

UNIV. OF C 

INST. NAT. 

BULGARIAN 

ENTE PER L 

LOUGHBOROU 

HELSINKI U 

CRANFIELD 

UNIV. CATH 

OTTO VON G 

UNIV. DEGL 

UNIV. OF O 

UNIV. OF T 

ELITE EURO 

ERASMUS UN 

INST. FUER 

UNIV. PARI 

BRITISH TE 

BOURNEMOUT 

UNIV. OF B 

UNIV. OF S 

DANMARKS T 

DAIMLER CH 

INST. NAT. 

INST. SUPE 

POLITECNIC 

POLISH ACA 

UNIV. POLI 

NAT. TEC. 

CONSEJO SU 

KATHOLIEKE 

UNIV. TWEN 

TECH. UNIV 

UNIV. POLI 

CENTRE NAT 

TEC. UNIV. 

UNIV. OF P 

FUNDACION 

JOZEF STEF 

CZECH TECH 

UNIV. OF N 

UNIV. OF S 

BAE SYSTEM 

UNIV. OF M 

C. R. FIAT 

NL ORG. FO 

CHALMERS T 

SAMTECH SA 

VOLVO AERO 

AVIO S.P.A 

MSC SOFTWA 

LULEAA UNI 

QUEENS UNI 

AIRBUS FRA 

CAD - FEM 

C. SVILUPP 

TRL 

LEUVEN MEA 

A. UNIV. T 

GERMAN AER 

CENTRE INT 

UNIV. DEGL 

QINETIQ 

UNIV. OF L 

FUNDACION 

ACCESS E.V 

EUROP. SPA 

UNIV. OF G 

UNIV. DEGL 

UNIV. OF G 

UNIV. OF N 

FINITE ELE 

ROCKFIELD 

WS ATKINS 

ROYAL INST 

UNIV. HANN 

FRAUENHOFE 

GKSS - FOR 

NAT. NUCLE 

UNIV. OF D 

ENGIN SOFT 

FEGS 

IFP SICOMP 

INTES - IN 

UNIV. DEGL 

PRINCIPIA 

ABS CONSUL 

ALTAIR ENG 

ANAKON 

ATOS ORIGI 

AWE PLC 

BEHR & CO 

CAESAR SYS 

CORK INST. 

CREA CONSU 

D C WHITE 

DAMT LTD 

DEP. OF E 

DR THELLEN 

DUNLOP STA 

EASI ENGIN 

EATEC LTD 

FEMSYS LTD 

FOKKER SPA 

FORSCHUNGS 

GIFFORD AN 

HAHN-SCHIC 

HERMSDORFE 

INBIS TECH 

INGENIEURB 

INTEGRATED 

KATHOLIEKE 

MANNESMANN 

MARITIME H 

MECAS S.R. 

MERITOR HE 

MERKLE UND 

NAFEMS LTD 

NCODE INT. 

NLSE VEREN 

NEW TECH. 

NOKIA MOBI 

NORUT TEKN 

NUMERICAL 

OXFORD BRO 

PD & E AUT 

RANDOM LOA 

SAFE TECH. 

SKF R & D 

SOFISTK AG 

ST MECANIC 

STAVANGER 

STRUCTURAL 

SULZER MAR 

TECHNISCH 

TECHSOFT E 

TECNOLOGIA 

TUN ABDUL 

UNIV.E DO 

UNIV. OF S 

WILDE AND 

ALLOGG AB 

AS. CONOCI 

ASS. RECH. 

AUSTRIAN I 

BELIMO AUT 

COVENTRY U 

DAEDALUS I 

DATAMED H 

FACULTY OF 

FED. UNITA 

FL-SOFT V/ 

INST. OF I 

GOETHE UNI 

MIT-MANAGE 

MOMATEC 

NAT. UNIV. 

NOTTINGHAM 

POLITECNIC 

SENTIENT M 

SIEMENS BU 

SOFIISKI U 

START ENGI 

STICHTING 

STICHTING 

THE UNIV. 

UNIV. DE L 

UNIV.SKLIN 

UNIV. DE G 

UNIV. PARI 

UNIV. OF A 

UNIV. OF C 

UNIV. OF C 

UNIV. OF W 

UNIV. OF Z 

INST. DALL 

RAUTARUUKK 

UNIV.E DE 

UNIV. OF U 

SOFTECO SI 

UNIV. GENT 

TSS - TRAN 

UNIV. DE G 

UNIV. DE V 

UNIVERZA V 

UNIV. PAUL 

TECH. UNIV 

UNIV. WIEN 

UNIV. VAN 

ENERGY RES 

TEKNILLINE 

DE MONTFOR 

CITY UNIVE 

UNIV. OF J 

AABO AKADE 

RISOE NAT. 

KINGS COLL 

UNIV. DORT 

FRIEDRICH- 

UNIV. OF C 

INST. NAT. 

BULGARIAN 

ENTE PER L 

LOUGHBOROU 

HELSINKI U 

CRANFIELD 

UNIV. CATH 

OTTO VON G 

UNIV. DEGL 

UNIV. OF O 

UNIV. OF T 

ELITE EURO 

ERASMUS UN 

INST. FUER 

UNIV. PARI 

BRITISH TE 

BOURNEMOUT 

UNIV. OF B 

UNIV. OF S 

DANMARKS T 

DAIMLER CH 

INST. NAT. 

INST. SUPE 

POLITECNIC 

POLISH ACA 

UNIV. POLI 

NAT. TEC. 

CONSEJO SU 

KATHOLIEKE 

UNIV. TWEN 

TECH. UNIV 

UNIV. POLI 

CENTRE NAT 

TEC. UNIV. 

UNIV. OF P 

FUNDACION 

JOZEF STEF 

CZECH TECH 

UNIV. OF N 

UNIV. OF S 

BAE SYSTEM 

UNIV. OF M 

C. R. FIAT 

NL ORG. FO 

CHALMERS T 

SAMTECH SA 

VOLVO AERO 

AVIO S.P.A 

MSC SOFTWA 

LULEAA UNI 

QUEENS UNI 

AIRBUS FRA 

CAD - FEM 

C. SVILUPP 

TRL 

LEUVEN MEA 

A. UNIV. T 

GERMAN AER 

CENTRE INT 

UNIV. DEGL 

QINETIQ 

UNIV. OF L 

FUNDACION 

ACCESS E.V 

EUROP. SPA 

UNIV. OF G 

UNIV. DEGL 

UNIV. OF G 

UNIV. OF N 

FINITE ELE 

ROCKFIELD 

WS ATKINS 

ROYAL INST 

UNIV. HANN 

FRAUENHOFE 

GKSS - FOR 

NAT. NUCLE 

UNIV. OF D 

ENGIN SOFT 

FEGS 

IFP SICOMP 

INTES - IN 

UNIV. DEGL 

PRINCIPIA 

ABS CONSUL 

ALTAIR ENG 

ANAKON 

ATOS ORIGI 

AWE PLC 

BEHR & CO 

CAESAR SYS 

CORK INST. 

CREA CONSU 

D C WHITE 

DAMT LTD 

DEP. OF E 

DR THELLEN 

DUNLOP STA 

EASI ENGIN 

EATEC LTD 

FEMSYS LTD 

FOKKER SPA 

FORSCHUNGS 

GIFFORD AN 

HAHN-SCHIC 

HERMSDORFE 

INBIS TECH 

INGENIEURB 

INTEGRATED 

KATHOLIEKE 

MANNESMANN 

MARITIME H 

MECAS S.R. 

MERITOR HE 

MERKLE UND 

NAFEMS LTD 

NCODE INT. 

NLSE VEREN 

NEW TECH. 

NOKIA MOBI 

NORUT TEKN 

NUMERICAL 

OXFORD BRO 

PD & E AUT 

RANDOM LOA 

SAFE TECH. 

SKF R & D 

SOFISTK AG 

ST MECANIC 

STAVANGER 

STRUCTURAL 

SULZER MAR 

TECHNISCH 

TECHSOFT E 

TECNOLOGIA 

TUN ABDUL 

UNIV.E DO 

UNIV. OF S 

WILDE AND 


❙ ▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

▲ 

✩ 

✪


✬ 

✫ 

What else? 

In 2005 we introduced in Pajek also support for multi-relational networks 

that combined with temporal networks enable analysis of new kinds of 

networks – such as KEDS networks (Kansas Event Data System or Tabari). 

You can use URLs in description of vertices (Nov 2005). 

Still in the implementation phase is the hierarchical clustering in large 

networks based on Ferligoj and Batagelj (1982 and 1983). 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Selected Books on SNA 

• J. P Scott: Social Network Analysis: A Handbook. SAGE Publications, 2000. Amazon. 

• A. Degenne, M. Forsé: Introducing Social Networks. SAGE Publications, 1999. 

Amazon. 

• S. Wasserman, K. Faust: Social Network Analysis: Methods and Applications. CUP, 

1994. Amazon. 

• W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis with Pajek, 

CUP, 2005. Amazon. ESNA page. 

• P. Doreian, V. Batagelj, A. Ferligoj: Generalized Blockmodeling, CUP, 2004. Amazon. 

• E. Lazega: The Collegial Phenomenon: The Social Mechanisms of Cooperation among 

Peers in a Corporate Law Partnership. OUP, 2001. Amazon. 

• P.J. Carrington, J. Scott, S. Wasserman (Eds.): Models and Methods in Social Network 

Analysis. CUP, 2005. Amazon. 

• U. Brandes, T. Erlebach (Eds.): Network Analysis: Methodological Foundations. LNCS, 

Springer, Berlin 2005. Amazon. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Courses on NA 

• James Moody, The Ohio State University 

• Steve Borgatti, UCINET 

• Barry Wellman, University of Toronto 

• Douglas White, University of California Irvine 

• Lada Adamic, University of Michigan 

• Mark Newman, University of Michigan 

• Jon Kleinberg, Cornell University 

• Robert A. Hanneman, University of California, Riverside; workshop 

• Noah Friedkin, University of California, Santa Barbara 

• John Levi Martin, University of Wisconsin, Madison 

• Vladimir Batagelj, University of Ljubljana 

• Andrej Mrvar, University of Ljubljana 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪


✬ 

✫ 

Software for SNA 

UCINET, NetDraw Pajek Netminer 

Visone SNA/R StOCNET 

Negopy InFlow GUESS 

NetworkX prefuse JUNG 

BGL/Python 

See also the INSNA list and recent overview by M. Huisman and M.A.J. 

van Duijn. 


❙ ▲ 

▲ 

▲ 

● ❙ ▲ 

▲ 

☛ ✖ 

✩ 

✪

'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?