The recent fast progress in statistical physics of
evolving networks
is reviwed. 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 “smallworld” 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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