The Structure of Complex Networks Theory and

This book deals with the analysis of the structure of complex networks by combining results from graph theory, physics, and pattern recognition. The book is divided into parts. 12 chapters are dedicated to the development of theoretical tools for the structural analysis of networks, and 7 chapters illustrate, in a critical way, applications of these tools real world scenarios. The first chapters provide detailed coverage of adjacency as well as metric and topological properties of networks, followed by chapters devote to the analysis of individual fragments based global invariants in complex networks. Analysis of the concepts of communicability, centrality, bipartivity, expansibility, and communities in networks follow. The second part of this book is devoted to the analysis of genetic, protein residue, protein-protein interaction, intercellular, ecological, and socio-economic networks, including important breakthroughs as well as examples of the misuse of structural concepts. Book jacket.

Ernesto Estrada is Full Professor and Chair in Complexity Science, Department of Mathematics and Department of Physics, University of Strathclyde, Glasgow.

Theory	p. 1
Introduction	p. 3
What are networks?	p. 3
When did the story begin?	p. 4
A formal definition	p. 6
Why do we study their structure?	p. 9
How can we speak their 'language'?	p. 14
Adjacency relations in networks	p. 25
Node adjacency relationship	p. 25
Degree distributions	p. 27
Degree-degree correlations	p. 31
Link adjacency and beyond	p. 36
Discrete Laplacian operator	p. 37
Spectral properties of networks	p. 39
Metric and topological structure of networks	p. 47
Shortest path distance	p. 47
Resistance distance	p. 50
Generalized network distances	p. 55
Topological structure of networks	p. 57
Fragments (subgraphs) in complex networks	p. 73
Network 'graphlets'	p. 74
Network motifs	p. 76
Closed walks and subgraphs	p. 78
Counting small undirected subgraphs analytically	p. 79
Fragment ratios	p. 82
Accounting for all parts (subgraphs)	p. 89
The Estrada index	p. 90
Parameterised Estrada index	p. 95
Network entropy and free energy	p. 97
Network returnability	p. 103
A brief on matrix functions	p. 106
Communicabilify functions in networks	p. 109
Network communicability	p. 109
Communicability in directed and weighted networks	p. 113
Generalised communicability functions	p. 114
Communicability based on network vibrations	p. 115
Centralify measures	p. 121
Degree centrality	p. 121
Centrality beyond nearest-neighbours	p. 125
Closeness centrality	p. 140
Betweenness centrality	p. 142
Information centrality	p. 146
Global network invariants	p. 149
Adjacency-based invariants	p. 149
Distance-based invariants	p. 159
Clumpiness of central nodes	p. 161
Self-similarity of complex networks	p. 166
Expansion and network classes	p. 171
Network expansion	p. 171
Universal topological classes of network	p. 173
Topological classification of real-world networks	p. 181
Community structure of networks	p. 187
Network partition methods	p. 190
Methods based on link centrality	p. 198
Methods based on modularity	p. 203
Clustering based on similarity	p. 206
Communities based on communicability	p. 209
Network bipartivity	p. 215
Bipartivity measures	p. 216
How do we find bipartitions in networks?	p. 220
Bipartitions in undirected networks	p. 224
Bipartitions in directed networks	p. 227
Random models of networks	p. 233
'Classical' random networks	p. 233
Small-world random networks	p. 238
'Scale-free' networks	p. 243
Random geometric networks	p. 250
Other random models	p. 252
Applications	p. 257
Genetic networks	p. 259
A primer on gene networks	p. 259
Topological properties of gene coexpression networks	p. 263
Topological properties of gene regulatory networks	p. 267
Other gene networks	p. 274
Protein residue networks	p. 277
A primer on protein structure	p. 277
Protein residue networks	p. 280
Small-worldness of residue networks	p. 282
Degree distributions of residue networks	p. 285
Centrality in residue networks	p. 287
Global topological properties	p. 295
Protein-protein interaction networks	p. 301
A primer on protein-protein interactions	p. 301
Global structure of PPI networks	p. 304
Subgraph-based techniques in PPI networks	p. 311
Bipartite structures in PPI networks	p. 316
Local structure of PPI networks	p. 319
The structure of reaction networks	p. 325
Organic chemical reaction networks	p. 326
Reaction networks in the atmospheres of astronomical bodies	p. 330
Metabolic networks	p. 333
Anatomical networks	p. 345
Intercellular networks	p. 345
Vascular networks	p. 353
Brain networks	p. 355
Ecological networks	p. 373
Global topological properties	p. 374
Searching for keystone species	p. 383
Landscape networks	p. 389
Other network-based ecological studies	p. 395
Social and economic networks	p. 399
Brief on socioeconomic network data	p. 400
Global topology of social networks	p. 401
Social network communities	p. 408
Centrality in social networks	p. 412
Economic networks	p. 415
Appendix	p. 423
Brain networks	p. 423
Ecological networks	p. 423
Informational networks	p. 424
PPI networks	p. 424
Protein residue networks	p. 425
Social and economic networks	p. 425
Technological networks	p. 426
Transcription networks	p. 426
Software	p. 425
References	p. 429
Index	p. 457
Table of Contents provided by Ingram. All Rights Reserved.

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The Structure of Complex Networks Theory and Applications

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