Entropies of complex networks with hierarchically constrained topologies
Ginestra Bianconi, Anthony Coolen and Conrad Perez-Vicente
Physical Review E
The 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.