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E-book: Fundamentals of Complex Networks: Models, Structures and Dynamics

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  • Format: EPUB+DRM
  • Pub. Date: 29-Dec-2014
  • Publisher: John Wiley & Sons Inc
  • Language: eng
  • ISBN-13: 9781118718148
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Fundamentals of Complex Networks: Models, Structures and DynamicsLarger Image
  • Format: EPUB+DRM
  • Pub. Date: 29-Dec-2014
  • Publisher: John Wiley & Sons Inc
  • Language: eng
  • ISBN-13: 9781118718148
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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. In particular, advanced societies have become dependent on large infrastructural networks to an extent beyond our capability to plan (modeling) and to operate (control). The recent spate of collapses in power grids and ongoing virus attacks on the Internet illustrate the need for knowledge about modeling, analysis of behaviors, optimized planning and performance control in such networks. For advancement of techniques, it has become clear that more fundamental knowledge will be needed in an engineering context about how dynamical networks emerge, behave, adapt, self-organize, evolve, and how they can be controlled. The aim of this book is to present the status of these topics and some basic techniques of various complex dynamical networks. Those with undergraduate education in calculus and linear algebra can read and study this introductory book without any technical difficulty.

About the Authors xi
Preface xiii
Acknowledgements xv
Part I FUNDAMENTAL THEORY
1 Introduction
3(12)
1.1 Background and Motivation
3(2)
1.2 A Brief History of Complex Network Research
5(6)
1.2.1 The Konigsburg Seven-Bridge Problem
5(2)
1.2.2 Random Graph Theory
7
1.2.3 Small-World Experiments
1(9)
1.2.4 Strengths of Weak Ties
10(1)
1.2.5 Heterogeneity and the WWW
10(1)
1.3 New Era of Complex-Network Studies
11(4)
Exercises
13(1)
References
13(2)
2 Preliminaries
15(88)
2.1 Elementary Graph Theory
15(37)
2.1.1 Background
15(1)
2.1.2 Basic Concepts
15(9)
2.1.3 Adjacency, Incidence and Laplacian Matrices
24(2)
2.1.4 Degree Correlation and Assortativity
26(5)
2.1.5 Some Basic Results on Graphs
31(4)
2.7.6 Eulerian and Hamiltonian Graphs
35(2)
2.1.7 Plane and Planar Graphs
37(2)
2.1.8 Trees and Bipartite Graphs
39(2)
2.1.9 Directed Graphs
41(4)
2.1.10 Weighted Graphs
45(1)
2.1.11 Some Applications
46(6)
2.2 Elementary Probability and Statistics
52(10)
2.2.1 Probability Preliminaries
52(6)
2.2.2 Statistics Preliminaries
58(1)
2.2.3 Law of Large Numbers and Central Limit Theorem
59(2)
2.2.4 Markov Chains
61(1)
2.3 Elementary Dynamical Systems Theory
62(41)
2.3.1 Background and Motivation
62(8)
2.3.2 Some Analytical Tools
70(2)
2.3.3 Chaos in Nonlinear Systems
72
2.3.4 Kolmogorov-Sinai Entropy
11(67)
2.3.5 Some Examples of Chaotic Systems
78(7)
2.3.6 Stabilities of Nonlinear Systems
85(5)
Exercises
90(10)
References
100(3)
3 Network Topologies: Basic Models and Properties
103(36)
3.1 Introduction
103(1)
3.2 Regular Networks
103(2)
3.3 ER Random-Graph Model
105(3)
3.4 Small-World Network Models
108(4)
3.4.1 WS Small-World Network Model
108(1)
3.4.2 NW Small-World Network Model
108(1)
3.4.3 Statistical Properties of Small-World Network Models
109(3)
3.5 Navigable Small-World Network Model
112(2)
3.6 Scale-Free Network Models
114(25)
3.6.1 BA Scale-Free Network Model
114(4)
3.6.2 Robustness versus Fragility
118(4)
3.6.3 Modified BA Models
122(4)
3.6.4 A Simple Model with Power-Law Degree Distribution
126(1)
3.6.5 Local-World and Multi-Local-World Network Models
126(7)
Exercises
133(2)
References
135(4)
Part II APPLICATIONS - SELECTED TOPICS
4 Internet: Topology and Modeling
139(56)
4.1 Introduction
139(2)
4.2 Topological Properties of the Internet
141(14)
4.2.1 Power--Law Node-Degree Distribution
141(2)
4.2.2 Hierarchical Structure
143(2)
4.2.3 Rich-Club Structure
145(2)
4.2.4 Disassortative Property
147(1)
4.2.5 Coreness and Betweenness
148(3)
4.2.6 Growth of the Internet
151(1)
4.2.7 Router-Level Internet Topology
152(1)
4.2.8 Geographic Layout of the Internet
153(2)
4.3 Random-Graph Network Topology Generator
155(1)
4.4 Structural Network Topology Generators
156(3)
4.4.1 Tiers Topology Generator
157(1)
4.4.2 Transit-Stub Topology Generator
158(1)
4.5 Connectivity-Based Network Topology Generators
159(8)
4.5.1 Inet
160(1)
4.5.2 BRITE Model
161(2)
4.5.3 GLP Model
163(2)
4.5.4 PFP Model
165(1)
4.5.5 TANG Model
166(1)
4.6 Multi-Local-World Model
167(11)
4.6.1 Theoretical Considerations
167(2)
4.6.2 Numerical Results with Comparison
169(7)
4.6.3 Performance Comparison
176(2)
4.7 HOT Model
178(3)
4.8 Dynamical Behaviors of the Internet Topological Characteristics
181(1)
4.9 Traffic Fluctuation on Weighted Networks
181(14)
4.9.1 Weighted Networks
183(1)
4.9.2 GRD Model
183(1)
4.9.3 Data Traffic Fluctuations
184(6)
References
190(5)
5 Epidemic Spreading Dynamics
195(30)
5.1 Introduction
195(1)
5.2 Epidemic Threshold Theory
196(10)
5.2.1 Epidemic (SI, SIS, SIR) Models
196(1)
5.2.2 Epidemic Thresholds on Homogenous Networks
197(1)
5.2.3 Statistical Data Analysis
198(1)
5.2.4 Epidemic Thresholds on Heterogeneous Networks
199(1)
5.2.5 Epidemic Thresholds on BA Networks
200(2)
5.2.6 Epidemic Thresholds on Finite-Sized Scale-Free Networks
202(1)
5.2.7 Epidemic Thresholds on Correlated Networks
202(1)
5.2.8 SIR Model of Epidemic Spreading
203(2)
5.2.9 Epidemic Spreading on Quenched Networks
205(1)
5.3 Epidemic Spreading on Spatial Networks
206(7)
5.3.1 Spatial Networks
206(1)
5.3.2 Spatial Network Models for Infectious Diseases
207(2)
5.3.3 Impact of Spatial Clustering on Disease Transmissions
209(2)
5.3.4 Large-Scale Spatial Epidemic Spreading
211(1)
5.3.5 Impact of Human Location-Specific Contact Patterns
212(1)
5.4 Immunization on Complex Networks
213(2)
5.4.1 Random Immunization
213(1)
5.4.2 Targeted Immunization
213(2)
5.4.3 Acquaintance Immunization
215(1)
5.5 Computer Virus Spreading over the Internet
215(10)
5.5.1 Random Constant-Spread Model
216(1)
5.5.2 A Compartment-Based Model
217(2)
5.5.3 Spreading Models of Email Viruses
219(2)
5.5.4 Effects of Computer Virus on Network Topologies
221(1)
References
222(3)
6 Community Structures
225(32)
6.1 Introduction
225(5)
6.1.1 Various Scenarios in Real-World Social Networks
225(1)
6.1.2 Generalization of Assortativity
226(4)
6.2 Community Structure and Modularity
230(4)
6.2.1 Community Structure
230(1)
6.2.2 Modularity
230(3)
6.2.3 Modularity of Weighted and Directed Networks
233(1)
6.3 Modularity-Based Community Detecting Algorithms
234(6)
6.3.1 CNM Scheme
234(2)
6.5.2 BGLL Scheme
236(1)
6.3.3 Multi-Slice Community Detection
237(3)
6.3.4 Detecting Spatial Community Structures
240(1)
6.4 Other Community Partitioning Schemes
240(13)
6.4.1 Limitations of the Modularity Measure
240(2)
6.4.2 Clique Percolation Scheme
242(2)
6.4.3 Edge-Based Community Detection Scheme
244(5)
6.4.4 Evaluation Criteria for Community Detection Algorithms
249(4)
6.5 Some Recent Progress
253(4)
References
253(4)
7 Network Gaines
257(32)
7.1 Introduction
257(4)
7.2 Two-Player/Two-Strategy Evolutionary Games on Networks
261(12)
7.2.1 Introduction to Games on Networks
261(1)
7.2.2 Two-Player/Two-Strategy Games on Regular Lattices
261(3)
7.2.3 Two-Player/Two-Strategy Games on BA Scale-Free Networks
264(3)
7.2.4 Two-Player/Two-Strategy Games on Correlated Scale-Free Networks
267(4)
7.2.5 Two-Player/Two-Strategy Games on Clustered Scale-Free Networks
271(2)
7.3 Multi-Player/Two-Strategy Evolutionary Games on Networks
273(11)
7.3.1 Introduction to Public Goods Game
273(1)
7.3.2 Multi-Player/Two-Strategy Evolutionary Games on BA Networks
273(3)
7.3.3 Multi-Player/Two-Strategy Evolutionary Games on Correlated Scale-free Networks
276(4)
7.3.4 Multi-Player/Two-Strategy Evolutionary Games on Clustered Scale-free Networks
280(4)
7.4 Adaptive Evolutionary Games on Networks
284(5)
References
286(3)
8 Network Synchronization
289(30)
8.1 Introduction
289(1)
8.2 Complete Synchronization of Continuous-Time Networks
290(9)
8.2.1 Complete Synchronization of General Continuous-Time Networks
293(4)
8.2.2 Complete Synchronization of Linearly Coupled Continuous-Time Networks
297(2)
8.3 Complete Synchronization of Some Typical Dynamical Networks
299(7)
8.3.1 Complete Synchronization of Regular Networks
300(1)
8.3.2 Synchronization of Small-World Networks
301(1)
8.3.3 Synchronization of Scale-Free Networks
302(4)
8.3.4 Complete Synchronization of Local-World Networks
306(1)
8.4 Phase Synchronization
306(13)
8.4.1 Phase Synchronization of the Kuramoto Model
308(2)
8.4.2 Phase Synchronization of Small-World Networks
310(1)
8.4.3 Phase Synchronization of Scale-Free Networks
310(4)
8.4.4 Phase Synchronization of Nonuniformly Coupled Networks
314(2)
References
316(3)
9 Network Control
319(24)
9.1 Introduction
319(1)
9.2 Spatiotemporal Chaos Control on Regular CML
319(3)
9.3 Pinning Control of Complex Networks
322(4)
9.3.1 Augmented Network Approach
322(1)
9.3.2 Pinning Control of Scale-Free Networks
323(3)
9.4 Pinning Control of General Complex Networks
326(7)
9.4.1 Stability Analysis of General Networks under Pinning Control
326(2)
9.4.2 Pinning and Virtual Control of General Networks
328(2)
9.4.3 Pinning and Virtual Control of Scale-Free Networks
330(3)
9.5 Time-Delay Pinning Control of Complex Networks
333(2)
9.6 Consensus and Flocking Control
335(8)
References
340(3)
10 Brief Introduction to Other Topics
343(20)
10.1 Human Opinion Dynamics
343(3)
10.2 Human Mobility and Behavioral Dynamics
346(2)
10.3 Web PageRank, SiteRank and BrowserRank
348(1)
10.3.1 Methods Based on Edge Analysis
348(1)
10.3.2 Methods Using Users' Behavior Data
348(1)
10.4 Recommendation Systems
349(1)
10.5 Network Edge Prediction
350(1)
10.6 Living Organisms and Bionetworks
351(2)
10.7 Cascading Reactions on Networks
353(10)
References
356(7)
Index 363
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
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