Abstract
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erdös-Rényi 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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