Large Scale Structure And Dynamics Of Complex Networks

From Information Technology To Finance And Natural Science

By: Alessandro Vespignani (Editor), Guido Caldarelli (Editor)

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Hardcover | 28 June 2007

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264 Pages

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22.86 x 15.24 x 1.91

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This book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive at a unifying picture of complex networks. The contributed chapters form a reference for the various problems in data analysis visualization and modeling of complex networks.

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Non-Fiction Computing & I.T.Computer Networking & Communications Databases Data Capture & Analysis Computer Science Artificial Intelligence Neural Networks & Fuzzy Systems Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

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Preface	p. v
Introduction	p. 1
Preliminaries and Basic Definitions in Network Theory	p. 5
Introduction	p. 5
Basic definitions	p. 5
Different kinds of graphs	p. 7
Weighted, directed and oriented graphs	p. 7
Subgraphs	p. 8
Partited graphs	p. 9
Paths and cycles	p. 9
Trees	p. 10
Statistics on graphs	p. 11
Small world properties	p. 11
Clustering coefficient	p. 12
Degree distribution	p. 12
Complexity	p. 14
What is next	p. 15
Models of Complex Networks	p. 17
Introduction	p. 17
Random networks	p. 18
Erdos-Renyi networks	p. 18
Fitness networks	p. 21
Preferential attachment networks	p. 23
The Barabasi-Albert model	p. 25
Duplication-divergence models	p. 27
Growing weighted networks	p. 30
The small-world model	p. 32
Outlook	p. 33
Correlations in Complex Networks	p. 35
Introduction	p. 35
Detailed balance condition	p. 36
Empirical measurement of correlations	p. 39
Two vertices correlations: ANND	p. 41
Three vertices correlations: Clustering	p. 45
Networks in the real world	p. 47
Pretty-good-privacy web of trust	p. 51
Modeling correlations	p. 54
Disassortative correlations	p. 55
The configuration model	p. 55
Growing models	p. 56
Assortativity generators	p. 57
Modeling clustered networks	p. 59
Random graphs with attributes	p. 60
Hidden color models	p. 61
Fitness or hidden variables models	p. 62
Fitness and preferential attachment models	p. 64
Outlook	p. 65
The Architecture of Complex Weighted Networks: Measurements and Models	p. 67
Introduction	p. 67
Tools for the characterization of weighted networks	p. 68
Weights	p. 68
Degree and weight distributions	p. 68
Weighted degree: Strength	p. 68
Weighted clustering	p. 69
Weighted assortativity: Affinity	p. 70
Local heterogeneity	p. 71
Weighted networks: Empirical results	p. 72
Transportation networks	p. 73
Airport network	p. 73
Urban and inter-urban movement networks	p. 77
Transportation networks: Summary	p. 78
Social network: Example of the scientific collaboration network	p. 79
Biological network: The case of the metabolic network	p. 83
Modeling weighted networks	p. 83
Coupling weight and topology	p. 83
A simple model: Weight perturbation and "busy get busier" effects	p. 84
Local heterogeneities, nonlinearities and space-topology coupling	p. 88
Other models coupling traffic and topology	p. 90
Outlook	p. 91
Community Structure Identification	p. 93
Introduction	p. 93
Definitions of communities	p. 94
Evaluating community identification	p. 96
Link removal methods	p. 97
Shortest path centrality	p. 97
Current-flow and random walk centrality	p. 98
Information centrality	p. 99
Link clustering	p. 100
Agglomerative methods	p. 100
Hierarchical clustering	p. 100
L-shell method	p. 101
Methods based on maximising modularity	p. 102
Greedy algorithm	p. 102
Simulated annealing methods	p. 102
Extremal optimisation	p. 103
Spectral analysis methods	p. 104
Spectral bisection	p. 104
Multi dimensional spectral analysis	p. 105
Constrained optimisation	p. 106
Approximate resistance networks	p. 106
Other methods	p. 107
Clustering and curvature	p. 107
Random walk based methods	p. 108
Q-potts model	p. 110
Comparative evaluation	p. 111
Conclusion	p. 113
Visualizing Large Complex Networks	p. 115
Introduction	p. 115
Global methods for visualizing large graphs	p. 116
Spring embedder based methods	p. 117
Properties	p. 118
Spectral layout	p. 121
Properties	p. 122
Analytical layouts	p. 124
Centrality and status layouts	p. 125
Clustered layouts	p. 126
Case studies	p. 129
Modeling the Webgraph: How Far We Are	p. 133
Introduction	p. 133
Preliminaries	p. 134
WebBase	p. 137
In-degree and out-degree	p. 138
PageRank	p. 140
Bipartite cliques	p. 141
Strongly connected components	p. 142
Stochastic models of the webgraph	p. 142
Models of the webgraph	p. 143
A multi-layer model	p. 144
Large scale simulation	p. 146
Algorithmic techniques for generating and measuring webgraphs	p. 149
Data representation and multifiles	p. 151
Generating webgraphs	p. 152
Traversal with two bits for each node	p. 154
Semi-external breadth first search	p. 154
Semi-external depth first search	p. 155
Computation of the SCCs	p. 155
Computation of the bow-tie regions	p. 156
Disjoint bipartite cliques	p. 157
PageRank	p. 160
Summary and outlook	p. 161
The Large Scale Structure of the Internet	p. 162
Introduction	p. 163
Internet maps	p. 164
Heavy tailed distributions	p. 168
Sampling biases and the scale-free nature of the Internet	p. 171
Hierarchies and correlations	p. 173
Outlook	p. 183
Spanning Trees in Ecology	p. 185
Introduction	p. 185
Graph-theoretical formalism	p. 186
Basic notions	p. 187
Connected subgraphs and minimum spanning trees	p. 188
Graphs and spanning trees in ecology	p. 189
Spanning trees in food webs	p. 189
Spanning trees in taxonomy	p. 192
Empirical results	p. 195
Food webs	p. 195
Taxonomic trees	p. 198
Summary and outlook	p. 202
Social and Financial Networks	p. 205
Introduction	p. 205
Social networks: Examples and general features	p. 206
Degree distribution	p. 208
Open questions on degree distribution	p. 210
Assortativity	p. 210
Open questions on assortativity	p. 212
Clustering	p. 213
Open questions on clustering	p. 214
Community structure	p. 214
Open questions on community structure	p. 216
Economical networks: The case-study of the board of directors	p. 218
Board and directors network as bipartite graphs	p. 220
Topological properties of boards and directors Networks	p. 222
Average quantities	p. 222
Degree distributions and assortativity	p. 224
Lobbies	p. 226
Modeling boards of directors networks	p. 228
Interlock structure and decision making dynamics	p. 228
Single board decision making model	p. 229
Multiple boards decision making model	p. 232
Conclusion	p. 233
References	p. 235
Index	p. 249
Table of Contents provided by Ingram. All Rights Reserved.

Large Scale Structure And Dynamics Of Complex Networks

From Information Technology To Finance And Natural Science

At a Glance

Hardcover

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