5 research outputs found
Evolution of networks
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.Comment: 67 pages, updated, revised, and extended version of review, submitted
to Adv. Phy