Network Science (ePub)

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

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.

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