Growth Models for Networks
Definition of the Subject
For several decades, mathematicians, biologists, and physicists have studied growing networks and their models. In physics and physical chemistry, models of this kind were first proposed in the theory of polymers (Flory 1941; Stockmayer 1943/1944). In graph theory and its applications, e.g., to biology and to computer science, very simple growing networks – random recursive trees – were an issue of wide interest for many years, see, for example, early articles (Na and Rapoport 1970; Moon 1974). Growth models for networks have become, maybe, the hottest topic in statistical mechanics, graph theory, and multidisciplinary research after the work (Barabási and Albert 1999), where these models were used to explain universal complex structures of the Internet, the World Wide Web, and other real networks.
Numerous natural and artificial networks have essentially more complex architectures than classical random graphs in graph theory. The classical random...
The author thanks A. V. Goltsev, J. F. F. Mendes, and A. N. Samukhin for numerous discussions. This work was partially supported by projects POCI: FAT/46241, MAT/46176, FIS/61665, and BIA-BCM/62662, and DYSONET.
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