Introduction to the Modeling and Analysis of Complex Systems

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15.6. GENERATING RANDOM GRAPHS 321sions where you want to have a randomly generated network. Here are some examplesof NetworkX’s built-in functions that can generate random graph samples:Code 15.21: random-graphs.pyfrom pylab import *import networkx as nxsubplot(2, 2, 1)nx.draw(nx.gnm_random_graph(10, 20))title(’random graph with\n10 nodes, 20 edges’)subplot(2, 2, 2)nx.draw(nx.gnp_random_graph(20, 0.1))title(’random graph with\n 20 nodes, 10% edge probability’)subplot(2, 2, 3)nx.draw(nx.random_regular_graph(3, 10))title(’random regular graph with\n10 nodes of degree 3’)subplot(2, 2, 4)nx.draw(nx.random_degree_sequence_graph([3,3,3,3,4,4,4,4,5,5]))title(’random graph with\n degree sequence\n[3,3,3,3,4,4,4,4,5,5]’)show()The output is shown in Fig. 15.10. The first example, gnm_random_graph(n, m), simplygenerates a random graph made of n nodes and m edges. The second example,gnp_random_graph(n, p), generates a random graph made of n nodes, where eachnode pair is connected to each other with probability p. These two types of randomgraphs are called Erdős-Rényi random graphs after two Hungarian mathematicians PaulErdős and Alfréd Rényi who studied random graphs in the 1950s [63]. The third example,random_regular_graph(k, n), generates a random regular graph made of n nodes thatall have the same degree k. The fourth example, random_degree_sequence_graph(list),generates a random graph whose nodes have degrees specified in list. In this particularexample, four nodes have degree 3, four nodes have degree 4, and two nodes have degree5. Note that this function may not be able to generate a graph within a given numberof trials (which is set to 10 by default). You can increase the number of trials by specifyingthe tries option in the function, e.g., tries = 100.
322 CHAPTER 15. BASICS OF NETWORKSrandom graph with10 nodes, 20 edgesrandom graph with20 nodes, 10% edge probabilityrandom regular graph with10 nodes of degree 3random graph withdegree sequence[3,3,3,3,4,4,4,4,5,5]Figure 15.10: Visual output of Code 15.21.
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Introduction to the Modeling and An
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iiiAbout the TextbookIntroduction t
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New York. He is also a Fellow of th
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PrefaceThis is an introductory text
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a comprehensive view of the related
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Chen, Hal Lewis, Vlad Miskovic, Chu
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xviCONTENTS5 Discrete-Time Models I
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xviiiCONTENTS15.3 Constructing Netw
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Chapter 1Introduction1.1 Complex Sy
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1.1. COMPLEX SYSTEMS IN A NUTSHELL
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1.2. TOPICAL CLUSTERS 7The possibil
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1.2. TOPICAL CLUSTERS 9these topica
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12 CHAPTER 2. FUNDAMENTALS OF MODEL
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Part IISystems with a Small Number
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30 CHAPTER 3. BASICS OF DYNAMICAL S
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36 CHAPTER 4. DISCRETE-TIME MODELS
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Chapter 6Continuous-Time Models I:
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6.2. CLASSIFICATIONS OF MODEL EQUAT
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6.3. CONNECTING CONTINUOUS-TIME MOD
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6.4. SIMULATING CONTINUOUS-TIME MOD
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6.4. SIMULATING CONTINUOUS-TIME MOD
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6.5. BUILDING YOUR OWN MODEL EQUATI
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112 CHAPTER 7. CONTINUOUS-TIME MODE
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Chapter 8Bifurcations8.1 What Are B
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8.2. BIFURCATIONS IN 1-D CONTINUOUS
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8.3. HOPF BIFURCATIONS IN 2-D CONTI
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8.3. HOPF BIFURCATIONS IN 2-D CONTI
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8.4. BIFURCATIONS IN DISCRETE-TIME
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Chapter 9Chaos9.1 Chaos in Discrete
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9.1. CHAOS IN DISCRETE-TIME MODELS
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Next phase space9.3. LYAPUNOV EXPON
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9.3. LYAPUNOV EXPONENT 159easily co
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9.3. LYAPUNOV EXPONENT 16110Lyapuno
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9.4. CHAOS IN CONTINUOUS-TIME MODEL
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Chapter 10Interactive Simulation of
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10.2. INTERACTIVE SIMULATION WITH P
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10.4. SIMULATION WITHOUT PYCX 181Co
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10.4. SIMULATION WITHOUT PYCX 183re
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Chapter 11Cellular Automata I: Mode
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11.1. DEFINITION OF CELLULAR AUTOMA
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11.1. DEFINITION OF CELLULAR AUTOMA
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11.2. EXAMPLES OF SIMPLE BINARY CEL
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11.3. SIMULATING CELLULAR AUTOMATA
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11.5. EXAMPLES OF BIOLOGICAL CELLUL
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Chapter 12Cellular Automata II: Ana
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12.2. PHASE SPACE VISUALIZATION 211
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12.2. PHASE SPACE VISUALIZATION 213
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12.3. MEAN-FIELD APPROXIMATION 215E
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12.3. MEAN-FIELD APPROXIMATION 217T
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12.4. RENORMALIZATION GROUP ANALYSI
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228 CHAPTER 13. CONTINUOUS FIELD MO
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OutIn232 CHAPTER 13. CONTINUOUS FIE
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Chapter 17Dynamical Networks II: An
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17.1. NETWORK SIZE, DENSITY, AND PE
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17.1. NETWORK SIZE, DENSITY, AND PE
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17.2. SHORTEST PATH LENGTH 37717.2
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17.2. SHORTEST PATH LENGTH 379Eccen
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17.3. CENTRALITIES AND CORENESS 381
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17.4. CLUSTERING 387while the numer
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17.5. DEGREE DISTRIBUTION 3891.00.8
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17.5. DEGREE DISTRIBUTION 391er = n
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17.5. DEGREE DISTRIBUTION 393Pk = [
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17.5. DEGREE DISTRIBUTION 395logkda
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17.6. ASSORTATIVITY 397Assortativit
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17.6. ASSORTATIVITY 399>>> nx.degre
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17.7. COMMUNITY STRUCTURE AND MODUL
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406CHAPTER 18. DYNAMICAL NETWORKS I
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428 CHAPTER 19. AGENT-BASED MODELSE
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430 CHAPTER 19. AGENT-BASED MODELS
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432 CHAPTER 19. AGENT-BASED MODELST
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434 CHAPTER 19. AGENT-BASED MODELSI
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436 CHAPTER 19. AGENT-BASED MODELSt
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438 CHAPTER 19. AGENT-BASED MODELSF
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440 CHAPTER 19. AGENT-BASED MODELSY
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442 CHAPTER 19. AGENT-BASED MODELS3
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444 CHAPTER 19. AGENT-BASED MODELSn
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450 CHAPTER 19. AGENT-BASED MODELSF
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452 CHAPTER 19. AGENT-BASED MODELSe
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454 CHAPTER 19. AGENT-BASED MODELSf
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458 CHAPTER 19. AGENT-BASED MODELSi
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460 CHAPTER 19. AGENT-BASED MODELSw
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462 CHAPTER 19. AGENT-BASED MODELSi
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464 CHAPTER 19. AGENT-BASED MODELSB
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466 BIBLIOGRAPHY[12] “The Human C
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468 BIBLIOGRAPHY[39] H. Sayama, “
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470 BIBLIOGRAPHY[65] P. Holme and J
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Indexaction potential, 202actor, 29
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INDEX 475equilibrium point, 61, 111
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INDEX 477partial differential equat
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Introduction to the Modeling and Analysis of Complex Systems

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