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Network Science
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Table of Contents

Preface/Foreword ix 1 Origins 1 1.1 What Is Network Science?, 5 1.2 A Brief History of Network Science, 8 1.3 General Principles, 19 2 Graphs 23 2.1 Set-Theoretic Definition of a Graph, 25 2.2 Matrix Algebra Definition of a Graph, 33 2.3 The Bridges of Konigsberg Graph, 38 2.4 Spectral Properties of Graphs, 42 2.5 Types of Graphs, 46 2.6 Topological Structure, 54 2.7 Graphs in Software, 63 2.8 Exercises, 68 3 Regular Networks 71 3.1 Diameter, Centrality, and Average Path Length, 74 3.2 Binary Tree Network, 79 3.3 Toroidal Network, 85 3.4 Hypercube Networks, 89 3.5 Exercises, 95 4 Random Networks 97 4.1 Generation of Random Networks, 100 4.2 Degree Distribution of Random Networks, 106 4.3 Entropy of Random Networks, 110 4.4 Properties of Random Networks, 118 4.5 Weak Ties in Random Networks, 125 4.6 Randomization of Regular Networks, 127 4.7 Analysis, 128 4.8 Exercises, 129 5 Small-World Networks 131 5.1 Generating a Small-World Network, 135 5.2 Properties of Small-World Networks, 142 5.3 Phase Transition, 156 5.4 Navigating Small Worlds, 160 5.5 Weak Ties in Small-World Networks, 169 5.6 Analysis, 171 5.7 Exercises, 173 6 Scale-Free Networks 177 6.1 Generating a Scale-Free Network, 180 6.2 Properties of Scale-Free Networks, 190 6.3 Navigation in Scale-Free Networks, 203 6.4 Analysis, 207 6.5 Exercises, 214 7 Emergence 217 7.1 What is Network Emergence?, 219 7.2 Emergence in the Sciences, 223 7.3 Genetic Evolution, 225 7.4 Designer Networks, 233 7.5 Permutation Network Emergence, 243 7.6 An Application of Emergence, 252 7.7 Exercises, 258 8 Epidemics 261 8.1 Epidemic Models, 264 8.2 Persistent Epidemics in Networks, 275 8.3 Network Epidemic Simulation Software, 287 8.4 Countermeasures, 289 8.5 Exercises, 297 9 Synchrony 299 9.1 To Sync or Not to Sync, 300 9.2 A Cricket Social Network, 307 9.3 Kirchhoff Networks, 324 9.4 Pointville Electric Power Grid, 331 9.5 Exercises, 335 10 Influence Networks 337 10.1 Anatomy of Buzz, 340 10.2 Power in Social Networks, 347 10.3 Conflict in I-Nets, 357 10.4 Command Hierarchies, 360 10.5 Emergent Power in I-Nets, 362 10.6 Exercises, 371 11 Vulnerability 375 11.1 Network Risk, 378 11.2 Critical Node Analysis, 382 11.3 Game Theory Considerations, 407 11.4 The General Attacker?Defender Network Risk Problem, 408 11.5 Critical Link Analysis, 410 11.6 Stability Resilience in Kirchhoff Networks, 428 11.7 Exercises, 430 12 NetGain 433 12.1 Classical Diffusion Equations, 436 12.2 Multiproduct Networks, 443 12.3 Java Method for Netgain Emergence, 447 12.4 Nascent Market Networks, 448 12.5 Creative Destruction Networks, 453 12.6 Merger and Acquisition Networks, 463 12.7 Exercises, 466 13 Biology 469 13.1 Static Models, 471 13.2 Dynamic Analysis, 475 13.3 Protein Expression Networks, 481 13.4 Mass Kinetics Modeling, 484 13.5 Exercises, 490 Bibliography 493 About the Author 503 Index 505

About the Author

T. G. Lewis is Professor of Computer Science at the Naval Postgraduate School, Monterey, CA. He has written over thirty books during the course of his extensive career. Dr. Lewis is the former vice president of development for Eastman Kodak.

Reviews

"This book provides a comprehensive study of network science, specifically of different network classes and their respective properties. The chapters are easy to understand, each containing an extensive introduction that prepares the reader for what is to follow." (Computing Reviews, 1 November 2010) "This fascinating book is a tour de force review of the application of network theory to a number of real-life and wildly different areas." ( Computing Reviews , July 2009)

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