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Network Science: Theory and Applications

ISBN: 978-0-470-33188-0
524 pages
March 2009
Network Science: Theory and Applications (0470331887) cover image
A comprehensive look at the emerging science of networks

Network science helps you design faster, more resilient communication networks; revise infrastructure systems such as electrical power grids, telecommunications networks, and airline routes; model market dynamics; understand synchronization in biological systems; and analyze social interactions among people.

This is the first book to take a comprehensive look at this emerging science. It examines the various kinds of networks (regular, random, small-world, influence, scale-free, and social) and applies network processes and behaviors to emergence, epidemics, synchrony, and risk. The book's uniqueness lies in its integration of concepts across computer science, biology, physics, social network analysis, economics, and marketing.

The book is divided into easy-to-understand topical chapters and the presentation is augmented with clear illustrations, problems and answers, examples, applications, tutorials, and a discussion of related Java software. Chapters cover:

  • Origins
  • Graphs

  • Regular Networks

  • Random Networks

  • Small-World Networks

  • Scale-Free Networks

  • Emergence

  • Epidemics

  • Synchrony

  • Influence Networks

  • Vulnerability

  • Net Gain

  • Biology

This book offers a new understanding and interpretation of the field of network science. It is an indispensable resource for researchers, professionals, and technicians in engineering, computing, and biology. It also serves as a valuable textbook for advanced undergraduate and graduate courses in related fields of study.

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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 Ko¨nigsberg 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

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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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"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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