Accelerated growth of networks

In many real growing networks the mean number of connections per vertex increases with time. The Internet, the Word Wide Web, collaboration networks, and many others display this behavior. Such a growth can be called {\em accelerated}. We show that this acceleration influences distribution of connections and may determine the structure of a network. We discuss general consequences of the acceleration and demonstrate its features applying simple illustrating examples. In particular, we show that the accelerated growth fairly well explains the structure of the Word Web (the network of interacting words of human language). Also, we use the models of the accelerated growth of networks to describe a wealth condensation transition in evolving societies.
29 pages, 11 figures, a brief review of the accelerated growth including applications to econophysics, Contribution to `Handbook of Graphs and Networks: From the Genome to the Internet', eds. S. Bornholdt and H.G. Schuster (Wiley-VCH, Berlin, 2002), to be published