How to calculate the main characteristics of random uncorrelated networks

Details How to calculate the main characteristics of random uncorrelated networks How to calculate the main characteristics of random uncorrelated networks

2005-02-28

arxiv.org/abs/cond-mat/0502663v1

AIP Conf. Proc. 776, 52 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

AIP conference proceedings format, 17 pages, 6 figures

Scientific paper

10.1063/1.1985377

We present an analytic formalism describing structural properties of random uncorrelated networks with arbitrary degree distributions. The formalism allows to calculate the main network characteristics like: the position of the phase transition at which a giant component first forms, the mean component size below the phase transition, the size of the giant component and the average path length above the phase transition. We apply the approach to classical random graphs of Erdos and Renyi, single-scale networks with exponential degree distributions and scale-free networks with arbitrary scaling exponents and structural cut-offs. In all the cases we obtain a very good agreement between results of numerical simulations and our analytical predictions.

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