Maximal entropy random networks with given degree distribution

Details Maximal entropy random networks with given degree distribution Maximal entropy random networks with given degree distribution

2002-06-10

arxiv.org/abs/cond-mat/0206150v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

22 pages, LateX, no figure

Scientific paper

Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the distribution of connected components. We determine the size of the percolation cluster above the percolation threshold. The conditional degree distribution on the percolation cluster is also given. We briefly present the analogous discussion for oriented graphs, giving for example the percolation criterion.

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