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      Evolution of networks

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          Abstract

          We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -- a feature known as the ``small-world'' effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc.

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          Author and article information

          Journal
          2001-06-07
          2001-09-07
          Article
          10.1080/00018730110112519
          cond-mat/0106144
          Custom metadata
          Adv. Phys. 51, 1079 (2002)
          67 pages, updated, revised, and extended version of review, submitted to Adv. Phys
          cond-mat.stat-mech q-bio

          Condensed matter, Quantitative & Systems biology

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