Entropies of complex networks with hierarchically constrained topologies ## AbstractThe entropy of a hierarchical network topology in an ensemble of sparse random networks, with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble. We obtain a general formula for this entropy, which has a clear interpretation in some simple limiting cases. The results provide new keys with which to solve the general problem of ``fitting'' a given network with an appropriate ensemble of random networks.
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