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Exchangeability is a desired statistical property of network ensemblesrequiring their invariance upon relabelling of the nodes. However combiningsparsity of network ensembles with exchangeability is challenging. Here wepropose a statistical physics framework and a Metropolis-Hastings algorithmdefining exchangeable sparse network ensembles. The model generates networkswith heterogeneous degree distributions by enforcing only global constraintswhile existing (non exchangeable) exponential random graphs enforce anextensive number of local constraints. This very general theoretical frameworkto describe exchangeable networks is here first formulated for uncorrelatedsimple networks and then it is extended to treat simple networks with degreecorrelations, directed networks, bipartite networks and generalized networkstructures including multiplex networks and simplicial complexes. In particularhere we formulate and treat both uncorrelated and correlated exchangeableensembles of simplicial complexes using statistical mechanics approaches.

Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes