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arXiv · 2007.12971

Approximating the cumulant generating function of triangles in the Erd\"os-R\'enyi random graph

Cristian Giardinà·Claudio Giberti·Elena Magnanini
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Abstract

We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erd\"os-R\'enyi random graph. By analyzing finite graphs of increasing volume, as well as the graphon variational problem in the infinite volume limit, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.

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Cristian Giardinà, Claudio Giberti, Elena Magnanini. 2020-07-25. Approximating the cumulant generating function of triangles in the Erd\"os-R\'enyi random graph. https://arxiv.org/abs/2007.12971

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