Statistical mechanics of complex networks
Abstract
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, smallworld and scalefree networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
 Publication:

Reviews of Modern Physics
 Pub Date:
 January 2002
 DOI:
 10.1103/RevModPhys.74.47
 arXiv:
 arXiv:condmat/0106096
 Bibcode:
 2002RvMP...74...47A
 Keywords:

 05.20.y;
 89.20.Hh;
 05.40.a;
 01.30.Vv;
 02.10.v;
 02.40.Pc;
 02.50.r;
 82.20.Wt;
 Classical statistical mechanics;
 World Wide Web Internet;
 Fluctuation phenomena random processes noise and Brownian motion;
 Book reviews;
 Logic set theory and algebra;
 General topology;
 Probability theory stochastic processes and statistics;
 Computational modeling;
 simulation;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Networking and Internet Architecture;
 Mathematical Physics;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 54 pages, submitted to Reviews of Modern Physics