Network Science

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.

"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)

• Preface/Foreword ix 1 Origins 11.1 What Is Network Science?, 51.2 A Brief History of Network Science, 81.3 General Principles, 192 Graphs 232.1 Set-Theoretic Definition of a Graph, 252.2 Matrix Algebra Definition of a Graph, 332.3 The Bridges of Ko¨nigsberg Graph, 382.4 Spectral Properties of Graphs, 422.5 Types of Graphs, 462.6 Topological Structure, 542.7 Graphs in Software, 632.8 Exercises, 683 Regular Networks 713.1 Diameter, Centrality, and Average Path Length, 743.2 Binary Tree Network, 793.3 Toroidal Network, 853.4 Hypercube Networks, 893.5 Exercises, 954 Random Networks 974.1 Generation of Random Networks, 1004.2 Degree Distribution of Random Networks, 1064.3 Entropy of Random Networks, 1104.4 Properties of Random Networks, 1184.5 Weak Ties in Random Networks, 1254.6 Randomization of Regular Networks, 1274.7 Analysis, 1284.8 Exercises, 1295 Small-World Networks 1315.1 Generating a Small-World Network, 1355.2 Properties of Small-World Networks, 1425.3 Phase Transition, 1565.4 Navigating Small Worlds, 1605.5 Weak Ties in Small-World Networks, 1695.6 Analysis, 1715.7 Exercises, 1736 Scale-Free Networks 1776.1 Generating a Scale-Free Network, 1806.2 Properties of Scale-Free Networks, 1906.3 Navigation in Scale-Free Networks, 2036.4 Analysis, 2076.5 Exercises, 2147 Emergence 2177.1 What is Network Emergence?, 2197.2 Emergence in the Sciences, 2237.3 Genetic Evolution, 2257.4 Designer Networks, 2337.5 Permutation Network Emergence, 2437.6 An Application of Emergence, 2527.7 Exercises, 2588 Epidemics 2618.1 Epidemic Models, 2648.2 Persistent Epidemics in Networks, 2758.3 Network Epidemic Simulation Software, 2878.4 Countermeasures, 2898.5 Exercises, 2979 Synchrony 2999.1 To Sync or Not to Sync, 3009.2 A Cricket Social Network, 3079.3 Kirchhoff Networks, 3249.4 Pointville Electric Power Grid, 3319.5 Exercises, 33510 Influence Networks 33710.1 Anatomy of Buzz, 34010.2 Power in Social Networks, 34710.3 Conflict in I-Nets, 35710.4 Command Hierarchies, 36010.5 Emergent Power in I-Nets, 36210.6 Exercises, 37111 Vulnerability 37511.1 Network Risk, 37811.2 Critical Node Analysis, 38211.3 Game Theory Considerations, 40711.4 The General Attacker–Defender Network Risk Problem, 40811.5 Critical Link Analysis, 41011.6 Stability Resilience in Kirchhoff Networks, 42811.7 Exercises, 43012 NetGain 43312.1 Classical Diffusion Equations, 43612.2 Multiproduct Networks, 44312.3 Java Method for Netgain Emergence, 44712.4 Nascent Market Networks, 44812.5 Creative Destruction Networks, 45312.6 Merger and Acquisition Networks, 46312.7 Exercises, 46613 Biology 46913.1 Static Models, 47113.2 Dynamic Analysis, 47513.3 Protein Expression Networks, 48113.4 Mass Kinetics Modeling, 48413.5 Exercises, 490Bibliography 493About the Author 503Index 505