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Complex scale-free networks. (English) Zbl 1027.90501
Summary: Systems as diverse as the world wide web or the cell are described by networks with complex topology. Traditionally it has been assumed that these networks are random. However, recent studies indicate that such complex systems emerge as a result of self-organizing processes governed by simple but generic laws, resulting in topologies strikingly different from those predicted by random networks. Such studies also lead to a paradigm shift regarding our approach to complex networks, allowing us to view them as dynamical systems rather than static graphs. In this paper, we briefly review the network models and discuss recent empirical results on network topology and the implications of these findings, including Internet and biological application.
MSC:
82B41Random walks, random surfaces, lattice animals, etc. (statistical mechanics)
82B44Disordered systems (equilibrium statistical mechanics)