Guanrong Chen, Xiaofan Wang, Xiang Li

Fundamentals of Complex Networks (eBook, ePUB)

Models, Structures and Dynamics

• Format: ePub

Produktbeschreibung

Complex networks such as the Internet, WWW, transportation networks, power grids, biological neural networks, and scientific cooperation networks of all kinds provide challenges for future technological development. * The first systematic presentation of dynamical evolving networks, with many up-to-date applications and homework projects to enhance study * The authors are all very active and well-known in the rapidly evolving field of complex networks * Complex networks are becoming an increasingly important area of research * Presented in a logical, constructive style, from basic through to complex, examining algorithms, through to construct networks and research challenges of the future

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 384
• Erscheinungstermin: 29. Dezember 2014
• Englisch
• ISBN-13: 9781118718148
• Artikelnr.: 42140820

Autorenporträt

GUANRONG CHEN City University of Hong Kong, Hong Kong SAR, China XIAOFAN WANG Shanghai Jiao Tong University, Shanghai, China XIANG LI Fudan University, Shanghai, China

Inhaltsangabe

About the Authors xi Preface xiii Acknowledgements xv Part I FUNDAMENTAL
THEORY 1 Introduction 3 1.1 Background and Motivation 3 1.2 A Brief History
of Complex Network Research 5 1.2.1 The Königsburg Seven-Bridge Problem 5
1.2.2 Random Graph Theory 7 1.2.3 Small-World Experiments 7 1.2.4 Strengths
of Weak Ties 10 1.2.5 Heterogeneity and the WWW 10 1.3 New Era of
Complex-Network Studies 11 Exercises 13 References 13 2 Preliminaries 15
2.1 Elementary Graph Theory 15 2.1.1 Background 15 2.1.2 Basic Concepts 15
2.1.3 Adjacency, Incidence and Laplacian Matrices 24 2.1.4 Degree
Correlation and Assortativity 26 2.1.5 Some Basic Results on Graphs 31
2.1.6 Eulerian and Hamiltonian Graphs 35 2.1.7 Plane and Planar Graphs 37
2.1.8 Trees and Bipartite Graphs 39 2.1.9 Directed Graphs 41 2.1.10
Weighted Graphs 45 2.1.11 Some Applications 46 2.2 Elementary Probability
and Statistics 52 2.2.1 Probability Preliminaries 52 2.2.2 Statistics
Preliminaries 58 2.2.3 Law of Large Numbers and Central Limit Theorem 59
2.2.4 Markov Chains 61 2.3 Elementary Dynamical Systems Theory 62 2.3.1
Background and Motivation 62 2.3.2 Some Analytical Tools 70 2.3.3 Chaos in
Nonlinear Systems 72 2.3.4 Kolmogorov-Sinai Entropy 77 2.3.5 Some Examples
of Chaotic Systems 78 2.3.6 Stabilities of Nonlinear Systems 85 Exercises
90 References 100 3 Network Topologies: Basic Models and Properties 103 3.1
Introduction 103 3.2 Regular Networks 103 3.3 ER Random-Graph Model 105 3.4
Small-World Network Models 108 3.4.1 WS Small-World Network Model 108 3.4.2
NW Small-World Network Model 108 3.4.3 Statistical Properties of
Small-World Network Models 109 3.5 Navigable Small-World Network Model 112
3.6 Scale-Free Network Models 114 3.6.1 BA Scale-Free Network Model 114
3.6.2 Robustness versus Fragility 118 3.6.3 Modified BA Models 122 3.6.4 A
Simple Model with Power-Law Degree Distribution 126 3.6.5 Local-World and
Multi-Local-World Network Models 126 Exercises 133 References 135 Part II
APPLICATIONS - SELECTED TOPICS 4 Internet: Topology and Modeling 139 4.1
Introduction 139 4.2 Topological Properties of the Internet 141 4.2.1
Power-Law Node-Degree Distribution 141 4.2.2 Hierarchical Structure 143
4.2.3 Rich-Club Structure 145 4.2.4 Disassortative Property 147 4.2.5
Coreness and Betweenness 148 4.2.6 Growth of the Internet 151 4.2.7
Router-Level Internet Topology 152 4.2.8 Geographic Layout of the Internet
153 4.3 Random-Graph Network Topology Generator 155 4.4 Structural Network
Topology Generators 156 4.4.1 Tiers Topology Generator 157 4.4.2
Transit-Stub Topology Generator 158 4.5 Connectivity-Based Network Topology
Generators 159 4.5.1 Inet 160 4.5.2 BRITE Model 161 4.5.3 GLP Model 163
4.5.4 PFP Model 165 4.5.5 TANG Model 166 4.6 Multi-Local-World Model 167
4.6.1 Theoretical Considerations 167 4.6.2 Numerical Results with
Comparison 169 4.6.3 Performance Comparison 176 4.7 HOT Model 178 4.8
Dynamical Behaviors of the Internet Topological Characteristics 181 4.9
Traffic Fluctuation on Weighted Networks 181 4.9.1 Weighted Networks 183
4.9.2 GRD Model 183 4.9.3 Data Traffic Fluctuations 184 References 190 5
Epidemic Spreading Dynamics 195 5.1 Introduction 195 5.2 Epidemic Threshold
Theory 196 5.2.1 Epidemic (SI, SIS, SIR) Models 196 5.2.2 Epidemic
Thresholds on Homogenous Networks 197 5.2.3 Statistical Data Analysis 198
5.2.4 Epidemic Thresholds on Heterogeneous Networks 199 5.2.5 Epidemic
Thresholds on BA Networks 200 5.2.6 Epidemic Thresholds on Finite-Sized
Scale-Free Networks 202 5.2.7 Epidemic Thresholds on Correlated Networks
202 5.2.8 SIR Model of Epidemic Spreading 203 5.2.9 Epidemic Spreading on
Quenched Networks 205 5.3 Epidemic Spreading on Spatial Networks 206 5.3.1
Spatial Networks 206 5.3.2 Spatial Network Models for Infectious Diseases
207 5.3.3 Impact of Spatial Clustering on Disease Transmissions 209 5.3.4
Large-Scale Spatial Epidemic Spreading 211 5.3.5 Impact of Human
Location-Specific Contact Patterns 212 5.4 Immunization on Complex Networks
213 5.4.1 Random Immunization 213 5.4.2 Targeted Immunization 213 5.4.3
Acquaintance Immunization 215 5.5 Computer Virus Spreading over the
Internet 215 5.5.1 Random Constant-Spread Model 216 5.5.2 A
Compartment-Based Model 217 5.5.3 Spreading Models of Email Viruses 219
5.5.4 Effects of Computer Virus on Network Topologies 221 References 222 6
Community Structures 225 6.1 Introduction 225 6.1.1 Various Scenarios in
Real-World Social Networks 225 6.1.2 Generalization of Assortativity 226
6.2 Community Structure and Modularity 230 6.2.1 Community Structure 230
6.2.2 Modularity 230 6.2.3 Modularity of Weighted and Directed Networks 233
6.3 Modularity-Based Community Detecting Algorithms 234 6.3.1 CNM Scheme
234 6.3.2 BGLL Scheme 236 6.3.3 Multi-Slice Community Detection 237 6.3.4
Detecting Spatial Community Structures 240 6.4 Other Community Partitioning
Schemes 240 6.4.1 Limitations of the Modularity Measure 240 6.4.2 Clique
Percolation Scheme 242 6.4.3 Edge-Based Community Detection Scheme 244
6.4.4 Evaluation Criteria for Community Detection Algorithms 249 6.5 Some
Recent Progress 253 References 253 7 Network Games 257 7.1 Introduction 257
7.2 Two-Player/Two-Strategy Evolutionary Games on Networks 261 7.2.1
Introduction to Games on Networks 261 7.2.2 Two-Player/Two-Strategy Games
on Regular Lattices 261 7.2.3 Two-Player/Two-Strategy Games on BA
Scale-Free Networks 264 7.2.4 Two-Player/Two-Strategy Games on Correlated
Scale-Free Networks 267 7.2.5 Two-Player/Two-Strategy Games on Clustered
Scale-Free Networks 271 7.3 Multi-Player/Two-Strategy Evolutionary Games on
Networks 273 7.3.1 Introduction to Public Goods Game 273 7.3.2
Multi-Player/Two-Strategy Evolutionary Games on BA Networks 273 7.3.3
Multi-Player/Two-Strategy Evolutionary Games on Correlated Scale-free
Networks 276 7.3.4 Multi-Player/Two-Strategy Evolutionary Games on
Clustered Scale-free Networks 280 7.4 Adaptive Evolutionary Games on
Networks 284 References 286 8 Network Synchronization 289 8.1 Introduction
289 8.2 Complete Synchronization of Continuous-Time Networks 290 8.2.1
Complete Synchronization of General Continuous-Time Networks 293 8.2.2
Complete Synchronization of Linearly Coupled Continuous-Time Networks 297
8.3 Complete Synchronization of Some Typical Dynamical Networks 299 8.3.1
Complete Synchronization of Regular Networks 300 8.3.2 Synchronization of
Small-World Networks 301 8.3.3 Synchronization of Scale-Free Networks 302
8.3.4 Complete Synchronization of Local-World Networks 306 8.4 Phase
Synchronization 306 8.4.1 Phase Synchronization of the Kuramoto Model 308
8.4.2 Phase Synchronization of Small-World Networks 310 8.4.3 Phase
Synchronization of Scale-Free Networks 310 8.4.4 Phase Synchronization of
Nonuniformly Coupled Networks 314 References 316 9 Network Control 319 9.1
Introduction 319 9.2 Spatiotemporal Chaos Control on Regular CML 319 9.3
Pinning Control of Complex Networks 322 9.3.1 Augmented Network Approach
322 9.3.2 Pinning Control of Scale-Free Networks 323 9.4 Pinning Control of
General Complex Networks 326 9.4.1 Stability Analysis of General Networks
under Pinning Control 326 9.4.2 Pinning and Virtual Control of General
Networks 328 9.4.3 Pinning and Virtual Control of Scale-Free Networks 330
9.5 Time-Delay Pinning Control of Complex Networks 333 9.6 Consensus and
Flocking Control 335 References 340 10 Brief Introduction to Other Topics
343 10.1 Human Opinion Dynamics 343 10.2 Human Mobility and Behavioral
Dynamics 346 10.3 Web PageRank, SiteRank and BrowserRank 348 10.3.1 Methods
Based on Edge Analysis 348 10.3.2 Methods Using Users' Behavior Data 348
10.4 Recommendation Systems 349 10.5 Network Edge Prediction 350 10.6
Living Organisms and Bionetworks 351 10.7 Cascading Reactions on Networks
353 References 356 Index 363