Network Science

1. ORIGINS
1.1 What is Network Science?
1.2 A Brief History of Network Science
1.3 General Principles
2. GRAPHS
2.1 Set Theoretical Definition of a Graph
2.2 Matrix Algebra Definition of a Graph
2.4 Spectral Properties of Graphs
2.5 Types of Graphs
2.6 Topological Structure
2.7 Graphs in Software
2.8. Exercises
3. REGULAR NETWORKS
3.1 Diameter, Centrality, and Average Path Length
3.2 Binary Tree Network
3.3 Toroidal Network
3.4 Hypercube Networks
3.5 Exercises
4. RANDOM NETWORKS
4.1 Generation of Random Networks
4.2 Degree Distribution of Random Networks
4.3 Entropy of Random Networks
4.4 Diameter, Centrality, and Closeness in Random Networks
4.5. Weak Ties in Random Networks
4.6 Randomization of Regular Networks
4.7 Analysis
4.8 Exercises
5. SMALL WORLD NETWORKS
5.1 Generating a Small World Network
5.2 Properties of Small World Networks
5.3 Phase Transition
5.4 Navigating Small Worlds
5.5 Weak Ties in Small World Networks
5.6 Analysis
5.7 Exercises
6. SCALE FREE NETWORKS
6.1 Generating a Scale-Free Network
6.2 Properties of Scale-Free Networks
6.3 Navigation in Scale-Free Networks
6.4 Analysis
6.5 Exercises
7. EMERGENCE
7.1 What is Network Emergence?
7.2 Emergence in the Sciences
7.3 Genetic Evolution
7.4 Designer Networks
7.5 Permutation Network Emergence
7.6 An Application of Emergence
7.7 Exercises
8. EPIDEMICS
8.1. Epidemic Models
8.2 Persistent Epidemics in Networks
8.3 Network Epidemic Simulation Software
8.4 Countermeasures
8.5 Exercises
9. SYNCHRONY
9.1 To Sync or Not To Sync
9.2 A Cricket Social Network
9.3 Kirchhoff Networks
9.4 Anatomy of Buzz
9.5 Exercises
10. INFLUENCE NETWORKS
10.1 Anatomy of Buzz
10.2 Power in Social Networks
10.3 Conflict in I-nets
10.4 Command Hierarchies
10.5 Emergent Power in I-nets
10.6 Exercises
11. VULNERABILITY
11.1 Network Risk
11.2 Critical Node Analysis
11.3 Game Theory Considerations
11.4 The General Attacker-Defender Network Risk Problem
11.5

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)