From Biological Nets to the Internet and WWW

SN Dorogovtsev | JFF Mendes

**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**