Entropies of complex networks with hierarchically constrained topologies

TL;DR

This paper derives a general formula for the entropy of hierarchical network topologies within ensembles of sparse random networks, aiding in understanding and fitting complex network structures.

Contribution

It introduces a new analytical expression for the entropy of hierarchically constrained networks, enhancing the ability to model and analyze complex network topologies.

Findings

Derived a general entropy formula for hierarchical networks

Provided interpretations in limiting cases

Facilitated network ensemble fitting

Abstract

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 simple 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.