EVOLUTION OF NETWORKS
From Biological Nets to the Internet and WWW
SN Dorogovtsev | JFF Mendes

TABLE OF CONTENTS

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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

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