Table of Contents:
“…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.…”
Call Number: TK5105.5 .D67 2003
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