Slides - SNAP - Stanford University

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Where should we place social networks? Clustered? Random? 10/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
Could a network with high clustering be at the same time a small world? How can we at the same time have high clustering and small diameter? High clustering High diameter Clustering implies edge “locality” Randomness enables “shortcuts” Low clustering Low diameter 10/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9
Page 1 and 2: CS224W: Social and Information Netw
Page 3 and 4: (1) What is the structure of a soci
Page 5 and 6: 10/6/2011 Jure Leskovec, Stanford C
Page 7: Consequence of expansion: Short pa
Page 11 and 12: High clustering High diameter N h =
Page 13 and 14: Alternative formulation of the mode
Page 15 and 16: Could a network with high clusterin
Page 17 and 18: s only knows locations of its frien
Page 19 and 20: Model: 2-dim grid where each node h
Page 21 and 22: Claim: Expected search time is ≥
Page 23 and 24: Claim: Getting from s to t takes
Page 25 and 26: Model [Kleinberg, Nature ‘01] No
Page 27 and 28: We need to calculate: P(v → w) =
Page 29 and 30: We have: I ... interval of d/2 aro
Page 31 and 32: Small α: too many long links Big
Page 33 and 34: h(u,v) = tree-distance (height of t
Page 35: Extension: Multiple hierarchies -
Page 38 and 39: Generalized hierar. model: Arbitra
Page 40 and 41: P(u→v) = rank u(v) -α What is b
Page 42 and 43: Decentralized search in a LiveJourn
Page 44 and 45: Getting close (10km) is very easy.
Page 46: Why is rank exponent close to -1?
Page 49 and 50: 10/6/2011 Jure Leskovec, Stanford C
Page 51 and 52: Napster existed from June ‘99 and
Page 53 and 54: Protocol Chord consistently maps ke
Page 55 and 56: Assume we have N nodes and K keys (
Page 57 and 58: A node maintains a table of m=log(N
Page 59 and 60:
N42+1 = N48 N42+2 = N48 N42+4 = N48
Page 61:
We start the search at node n Let
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