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Evolution of networks : from biological nets to the Internet and WWW /

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This text provides a concise introduction to the principles of the organization and evolution of both natural and artificial networks.

Bibliographic Details
Main Authors: Dorogovt︠s︡ev, S. N. (Sergeĭ N.) (Author), Mendes, J. F. F. (José F. F.) (Author)
Format: eBook
Language:English
Language Notes:English.
Published: Oxford ; New York : Oxford University Press, ©2003.
Subjects:
Computer networks.
System analysis.
Information networks.
Computer Communication Networks
Systems Analysis
Réseaux d'ordinateurs.
Analyse de systèmes.
Réseaux d'information.
systems analysis.
Computer networks
Information networks
System analysis
Grafentheorie.
Wiskundige modellen.
Computernetwerken.
Netwerken.
Especificação de sistemas e programas.
Redes de informação.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Machine derived contents note: 0 Modern architecture of random graphs 1
  • 1 What are networks? 6
  • 1.1 Basic notions 6
  • 1.2 Adjacency matrix 10
  • 1.3 Degree distribution 10
  • 1.4 Clustering 14
  • 1.5 Small worlds 16
  • 1.6 Giant components 19
  • 1.7 List of basic constructions 22
  • 1.8 List of main characteristics 23
  • 2 Popularity is attractive 25
  • 2.1 Attachment of edges without preference 25
  • 2.2 Preferential linking 28
  • 3 Real networks 31
  • 3.1 Networks of citations of scientific papers 31
  • 3.2 Communication networks: the WWW and the Internet 34
  • 3.2.1 Structure of the WWW 35
  • 3.2.2 Search in the WWW 45
  • 3.2.3 Structure of the Internet 46
  • 3.3 Networks of collaborations 52
  • 3.4 Biological networks 54
  • 3.4.1 Neural networks 54
  • 3.4.2 Networks of metabolic reactions 56
  • 3.4.3 Genome and protein networks 59
  • 3.4.4 Ecological and food webs 60
  • 3.4.5 Word Web of human language 63
  • 3.5 Telephone call graph 66
  • 3.6 Mail networks 66
  • 3.7 Power grids and industrial networks 69
  • 3.8 Electronic circuits 70
  • 3.9 Nets of software components 71
  • 3.10 Energy landscape networks 73
  • 3.11 Overview 76
  • 4 Equilibrium networks 84
  • 4.1 Statistical ensembles of random networks 84
  • 4.2 Classical random graphs 86
  • 4.3 How to build an equilibrium net 88
  • 4.4 Econophysics: condensation of wealth 96
  • 4.5 Condensation of edges in equilibrium networks 101
  • 4.6 Correlations in equilibrium networks 102
  • 4.7 Small-world networks 104
  • 4.7.1 The Watts-Strogatz model and its variations 105
  • 4.7.2 The smallest-world network 110
  • 5 Non-equilibrium networks 112
  • 5.1 Growing exponential networks 112
  • 5.2 The Barabasi-Albert model 115
  • 5.3 Linear preference 118
  • 5.4 How the preferential linking emerges 121
  • 5.5 Scaling 124
  • 5.6 Generic scale of 'scale-free' networks 126
  • 5.7 More realistic models 127
  • 5.8 Estimations for the WWW 130
  • 5.9 Non-linear preference 131
  • 5.10 Types of preference providing scale-free networks 133
  • 5.11 Condensation of edges in inhomogeneous nets 135
  • 5.12 Correlations in growing networks 140
  • 5.13 How to obtain a strong clustering 142
  • 5.14 Deterministic graphs 143
  • 5.15 Accelerated growth of networks 148
  • 5.16 Evolution of language 151
  • 5.17 Partial copying and duplication 156
  • 5.18 Non-equilibrium non-growing networks 159
  • 6 Global topology of networks 161
  • 6.1 Topology of undirected equilibrium networks 161
  • 6.2 Topology of directed equilibrium networks 174
  • 6.3 Failures and attacks 179
  • 6.4 Resilience against random breakdowns 181
  • 6.5 How viruses spread within networks 187
  • 6.6 The Ising model on a net 190
  • 6.7 Mesoscopics in networks 196
  • 6.8 How to destroy a network 200
  • 6.9 How to stop an epidemic 202
  • 6.10 BKT percolation transition in growing networks 203
  • 6.11 When loops and correlations are important 210
  • 7 Growth of networks and self-organized criticality 212
  • 7.1 Preferential linking and the Simon model 212
  • 7.2 Econophysics: wealth distribution in evolving societies 214
  • 7.3 Multiplicative stochastic processes 217
  • 8 Philosophy of a small world 219
  • A Relations for an adjacency matrix 221
  • B How to measure a distribution 222
  • C Statistics of cliques 224
  • D Power-law preference 226
  • E Inhomogeneous growing net 228
  • F Z-transform 230
  • G Critical phenomena in networks 232
  • H A guide to the network literature 237
  • References 241
  • Index 263.