Evolution of Networks

S.N. Dorogovtsev and J.F.F. Mendes,
Evolution of Networks: From Biological Nets to the Internet and WWW
(Oxford University Press, Oxford, 2003).

WWWWWWWWWWw CONTENTS

0xxi Modern architecture of random graphs

1xxi What are networks?
xxxx1.1xxi Basic notions
xxxx1.2xxi Adjacency matrix
xxxx1.3xxi Degree distribution
xxxx1.4xxi Clustering
xxxx1.5xxi Small worlds
xxxx1.6xxi Giant components
xxxx1.7xxi List of basic constructions
xxxx1.8xxi List of main characteristics

2xxi Popularity is attractive
xxxx2.1xxi Attachment of edges without preference
xxxx2.2xxi Preferential linking

3xxi Real networks
xxxx3.1xxi Networks of citations of scientific papers
xxxx3.2xxi Communication networks: the WWW and the Internet
xxxxxxxxxi3.2.1xxi Structure of the WWW
xxxxxxxxxi3.2.2xxi Search in the WWW
xxxxxxxxxi3.2.3xxi Structure of the Internet
xxxx3.3xxi Networks of collaborations
xxxx3.4xxi Biological networks
xxxxxxxxxi3.4.1xxi Neural networks
xxxxxxxxxi3.4.2xxi Networks of metabolic reactions
xxxxxxxxxi3.4.3xxi Genome and protein networks
xxxxxxxxxi3.4.4xxi Ecological and food webs
xxxxxxxxxi3.4.5xxi Word Web of human language
xxxx3.5xxi Telephone call graph
xxxx3.6xxi Mail networks
xxxx3.7xxi Power grids and industrial networks
xxxx3.8xxi Electronic circuits
xxxx3.9xxi Nets of software components
xxx3.10xxi Energy landscape networks
xxx3.11xxi Overview

4xxi Equilibrium networks
xxxx4.1xxi Statistical ensembles of random networks
xxxx4.2xxi Classical random graphs
xxxx4.3xxi How to build an equilibrium net
xxxx4.4xxi Econophysics: condensation of wealth
xxxx4.5xxi Condensation of edges in equilibrium networks
xxxx4.6xxi Correlations in equilibrium networks
xxxx4.7xxi Small-world networks
xxxxxxxxxi4.7.1xxi The Watts--Strogatz model and its variations
xxxxxxxxxi4.7.2xxi The smallest-world network

5xxi Non-equilibrium networks
xxxx5.1xxi Growing exponential networks
xxxx5.2xxi The Barab'asi--Albert model
xxxx5.3xxi Linear preference
xxxx5.4xxi How the preferential linking emerges
xxxx5.5xxi Scaling
xxxx5.6xxi Generic scale of `scale-free' networks
xxxx5.7xxi More realistic models
xxxx5.8xxi Estimations for the WWW
xxxx5.9xxi Non-linear preference
xxx5.10xxi Types of preference providing scale-free networks
xxx5.11xxi Condensation of edges in inhomogeneous nets
xxx5.12xxi Correlations in growing networks
xxx5.13xxi How to obtain a strong clustering
xxx5.14xxi Deterministic graphs
xxx5.15xxi Accelerated growth of networks
xxx5.16xxi Evolution of language
xxx5.17xxi Partial copying and duplication
xxx5.18xxi Non-equilibrium non-growing networks

6xxi Global topology of networks
xxxx6.1xxi Topology of undirected equilibrium networks
xxxx6.2xxi Topology of directed equilibrium networks
xxxx6.3xxi Failures and attacks
xxxx6.4xxi Resilience against random breakdowns
xxxx6.5xxi How viruses spread within networks
xxxx6.6xxi The Ising model on a net
xxxx6.7xxi Mesoscopics in networks
xxxx6.8xxi How to destroy a network
xxxx6.9xxi How to stop an epidemic
xxx6.10xxi BKT percolation transition in growing networks
xxx6.11xxi When loops and correlations are important

7xxi Growth of networks and self-organized criticality
xxxx7.1xxi Preferential linking and the Simon model
xxxx7.2xxi Econophysics: wealth distribution in evolving societies
xxxx7.3xxi Multiplicative stochastic processes

8xxi Philosophy of a small world

Axxi Relations for an adjacency matrix

Bxxi How to measure a distribution

Cxxi Statistics of cliques

Dxxi Power-law preference

Exxi Inhomogeneous growing net

Fxxi Z-transform

Gxxi Critical phenomena in networks

Hxxi A guide to the network literature

References

Index