Gibbs entropy of networks ensembles by cavity methods

TL;DR

This paper derives an exact relationship between the Gibbs entropy of network ensembles and large deviations in canonical ensembles using cavity methods, providing insights into network order and randomness.

Contribution

It introduces a novel exact method to connect Gibbs entropy with large deviations in network ensembles via cavity techniques for hard constraints.

Findings

Derived exact expressions for Gibbs entropy in network ensembles.

Linked microcanonical and canonical ensemble properties through cavity methods.

Enhanced understanding of network structure and randomness.

Abstract

The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of a given real network. Here we show how to relate this entropy to large deviations of conjugated canonical ensembles. We derive exact expression for this correspondence using the cavity methods for some hard constraints.