Evolution of networks

Abstract

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