Mean-field theory for scale-free random networks

Details Mean-field theory for scale-free random networks Mean-field theory for scale-free random networks

1999-07-05

arxiv.org/abs/cond-mat/9907068v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 6 figures

Scientific paper

10.1016/S0378-4371(99)00291-5

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.

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