TABLE OF CONTENTS
| Preface | |||
| 0 Modern architecture of random graphs | |||
| 1 What are networks? | |||
| 1.1 Basic notions | |||
| 1.2 Adjacency matrix | |||
| 1.3 Degree distribution | |||
| 1.4 Clustering | |||
| 1.5 Small worlds | |||
| 1.6 Giant components | |||
| 1.7 List of basic constructions | |||
| 1.8 List of main characteristics | |||
| 2 Popularity is attractive | |||
| 2.1 Attachment of edges without preference | |||
| 2.2 Preferential linking | |||
| 3 Real networks | |||
| 3.1 Networks of citations of scientific papers | |||
| 3.2 Communication networks: the WWW and the Internet | |||
| 3.2.1 Structure of the WWW | |||
| 3.2.2 Search in the WWW | |||
| 3.2.3 Structure of the Internet | |||
| 3.3 Networks of collaborations | |||
| 3.4 Biological networks | |||
| 3.4.1 Neural networks | |||
| 3.4.2 Networks of metabolic reactions | |||
| 3.4.3 Genome and protein networks | |||
| 3.4.4 Ecological and food webs | |||
| 3.4.5 Word Web of human language | |||
| 3.5 Telephone call graph | |||
| 3.6 Mail networks | |||
| 3.7 Power grids and industrial networks | |||
| 3.8 Electronic circuits | |||
| 3.9 Nets of software components | |||
| 3.10 Energy landscape networks | |||
| 3.11 Overview | |||
| 4 Equilibrium networks | |||
| 4.1 Statistical ensembles of random networks | |||
| 4.2 Classical random graphs | |||
| 4.3 How to build an equilibrium net | |||
| 4.4 Econophysics: condensation of wealth | |||
| 4.5 Condensation of edges in equilibrium networks | |||
| 4.6 Correlations in equilibrium networks | |||
| 4.7 Small-world networks | |||
| 4.7.1 The Watts--Strogatz model and its variations | |||
| 4.7.2 The smallest-world network | |||
| 5 Non-equilibrium networks | |||
| 5.1 Growing exponential networks | |||
| 5.2 The Barab'asi--Albert model | |||
| 5.3 Linear preference | |||
| 5.4 How the preferential linking emerges | |||
| 5.5 Scaling | |||
| 5.6 Generic scale of `scale-free' networks | |||
| 5.7 More realistic models | |||
| 5.8 Estimations for the WWW | |||
| 5.9 Non-linear preference | |||
| 5.10 Types of preference providing scale-free networks | |||
| 5.11 Condensation of edges in inhomogeneous nets | |||
| 5.12 Correlations in growing networks | |||
| 5.13 How to obtain a strong clustering | |||
| 5.14 Deterministic graphs | |||
| 5.15 Accelerated growth of networks | |||
| 5.16 Evolution of language | |||
| 5.17 Partial copying and duplication | |||
| 5.18 Non-equilibrium non-growing networks | |||
| 6 Global topology of networks | |||
| 6.1 Topology of undirected equilibrium networks | |||
| 6.2 Topology of directed equilibrium networks | |||
| 6.3 Failures and attacks | |||
| 6.4 Resilience against random breakdowns | |||
| 6.5 How viruses spread within networks | |||
| 6.6 The Ising model on a net | |||
| 6.7 Mesoscopics in networks | |||
| 6.8 How to destroy a network | |||
| 6.9 How to stop an epidemic | |||
| 6.10 BKTpercolation transition in growing networks | |||
| 6.11 When loops and correlations are important | |||
| 7 Growth of networks and self-organized criticality | |||
| 7.1 Preferential linking and the Simon model | |||
| 7.2 Econophysics: wealth distribution in evolving societies | |||
| 7.3 Multiplicative stochastic processes | |||
| 8 Philosophy of a small world | |||
| Appendix | |||
| A Relations for an adjacency matrix | |||
| B How to measure a distribution | |||
| C Statistics of cliques | |||
| D Power-law preference | |||
| E Inhomogeneous growing net | |||
| F Z-transform | |||
| G Critical phenomena in networks | |||
| H A guide to the network literature | |||
| References | |||
| Index | |||