Maximal entropy random networks with given degree distribution

2002/06/10 by M. Bauer, D. Bernard, Bauer, M. +1
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0206150

22 pages, LateX, no figure

arxiv created 2002/06/10 · arxiv updated 2009/11/30

Abstract

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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