Evolution of Networks. Dorogovtsev and J. It represents an attempt to review the astonishing progress made in this subject during recent years, both from a theoretical and empirical point of view. Networks are mathematical representations of interacting systems in which vertices represent the typical units and edges the interaction between these units. Unlike regular lattices, with strong local ordering, complex networks usually involve some type of randomness in their connections leading to considerable heterogeneity in properties of individual units and loss of the metric structure.
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Abstract We review a recent fast progress in statistical physics of evolving networks. Interest focuses mainly on the structure properties of random hierarchically organized networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind were created recently.
This opens a wide field for research of their topology, evolution, and complex processes proceeding in them. Such networks possess a rich set of scaling properties. A number of them is scale-free and show striking resilience against random breakdowns.
Their features make them appropriate for numerous applications. We discuss how growing networks self-organize into scale-free structure and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in networks.
We present a number of models demonstrating the main features of evolving networks and discuss existing approaches to their simulation and analytical study. Applications of the general results to the 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, Keyphrases.
Evolution of 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.
Evolution of networks