Statistical mechanics of complex networks

Rev. Mod. Phys. 74, 47 – Published 30 January 2002
Réka Albert and Albert-László Barabási

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, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.

DOI: http://dx.doi.org/10.1103/RevModPhys.74.47

  • Published 30 January 2002

© 2002 The American Physical Society

Authors & Affiliations

Réka Albert* and Albert-László Barabási

  • Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556

  • *Present address: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455.

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