title: Entropies of complex networks with hierarchically constrained topologies.
abstract: The entropy of a hierarchical network topology in an ensemble of sparse random networks, with "hidden variables" associated with 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 keys with which to solve the general problem of "fitting" a given network with an appropriate ensemble of random networks.
authors.affiliation: Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy.
authors.forename: Ginestra
authors.initials: G
authors.lastname: Bianconi
authors.forename: Anthony C C
authors.initials: AC
authors.lastname: Coolen
authors.forename: Conrad J
authors.initials: CJ
authors.lastname: Perez Vicente