  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.
