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In this work, we study the percolation transition and large deviationproperties of generalized canonical network ensembles. This new type of randomnetworks might have a very rich complex structure, including high heterogeneousdegree sequences, non-trivial community structure or specific spatialdependence of the link probability for networks embedded in a metric space. Wefind the cluster distribution of the networks in these ensembles by mapping theproblem to a fully connected Potts model with heterogeneous couplings. We showthat the nature of the Potts model phase transition, linked to the birth of agiant component, has a crossover from second to first order when the number ofcritical colors $q_c = 2$ in all the networks under study. These results shedlight on the properties of dynamical processes defined on these networkensembles.

Percolation transition and distribution of connected components in generalized random network ensembles