Evolution of networks : from biological nets to the Internet and WWW / S.N. Dorogovtsev, University of Aveiro and Ioffe Institute, St Petersburg, J.F.F. Mendes, University of Aveiro.

Reprint of the resource originally published: 2003.

Includes bibliographical references (pages 237-262) and index.

Print version record.

Cover ; Evolution of Networks: From Biological Nets to the Internet and WWW; Copyright; PREFACE TO THE PAPERBACK EDITION; REFERENCES IN THE PAPERBACK EDITION PREFACE; PREFACE; CONTENTS; 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; Betweenness; 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; Equilibrium network; Growing network; 2.2 Preferential linking.

3: REAL NETWORKS3.1 Networks of citations of scientific papers; In- and out-degree distributions; Evolution of the average number of references; Preferential linking; 3.2 Communication networks: the WWW and the Internet; 3.2.1 Structure of the WWW; How new pages appear in the WWW; In- and out-degree distributions; Various categories of Web pages; Components of the WWW; Shortest paths in the Web; Betweenness; Cliques in the WWW; 3.2.2 Search in the WWW; 3.2.3 Structure of the Internet; Interdomain level; Router level; Geographic factor; 3.3 Networks of collaborations; 3.4 Biological networks.

3.4.1 Neural networks3.4.2 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; Microcanonical ensemble; Canonical ensemble; Grand canonical ensemble; Correspondence between ensembles.

4.4 Econophysics: condensation of wealthA 'shark' in equilibrium; 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 Barabási-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; Linking in the body of a net; Preference and indifference.

5.8 Estimations for the WWWIn-degree distribution; Out-degree distribution; 5.9 Non-linear preference; 5.10 Types of preference providing scale-free networks; 5.11 Condensation of edges in inhomogeneous nets; Econophysics; Anomalous relaxation; 5.12 Correlations in growing networks; Degree-degree correlations; In- and out-degree correlations; 5.13 How to obtain a strong clustering; 5.14 Deterministic graphs; How to generate evolving random nets; 5.15 Accelerated growth of networks; General relations; Scaling; 5.16 Evolution of language; Core of language; 5.17 Partial copying and duplication.

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