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On Certain Perturbations of the Erdös–Renyi Random Graph

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Abstract

We study perturbations of the Erdös–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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Authors and Affiliations

  1. Service de Physique Théorique de Saclay, Laboratoire de la Direction des Sciences de la Matière du Commisariat à l'Energie Atomique, URA2306 du CNRS, CE Saclay, 91191, Gif sur Yvette, France

    Stéphane Coulomb & Michel Bauer

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  1. Stéphane Coulomb
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  2. Michel Bauer
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Coulomb, S., Bauer, M. On Certain Perturbations of the Erdös–Renyi Random Graph. Journal of Statistical Physics 115, 1251–1282 (2004). https://doi.org/10.1023/B:JOSS.0000028060.07802.9d

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  • DOI: https://doi.org/10.1023/B:JOSS.0000028060.07802.9d

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