Principles of statistical mechanics of random networks

Details Principles of statistical mechanics of random networks Principles of statistical mechanics of random networks

2002-04-04

arxiv.org/abs/cond-mat/0204111v2

Nucl.Phys. B666 (2003) 396-416

Physics

Condensed Matter

Statistical Mechanics

14 pages, an extended version

Scientific paper

10.1016/S0550-3213(03)00504-2

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.

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