On certain perturbations of the Erdos-Renyi random graph

Details On certain perturbations of the Erdos-Renyi random graph On certain perturbations of the Erdos-Renyi random graph

2003-10-08

arxiv.org/abs/cond-mat/0310170v1

Physics

Condensed Matter

Statistical Mechanics

Authors : Stephane Coulomb, Michel Bauer

Scientific paper

10.1023/B:JOSS.0000028060.07802.

We study perturbations of the Erdos-Renyi model for which the statistical weight of a graph depends on the abundance of certain geometrical patterns. Using the formal correspondance with an exactly solvable effective model, we show the existence of a percolation transition in the thermodynamical limit and derive perturbatively the expression of the threshold. The free energy and the moments of the degree distribution are also computed perturbatively in that limit and the percolation criterion is compared with the Molloy-Reed criterion.

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