Entropy of microcanonical finite-graph ensembles

Abstract

The entropy of random graph ensembles has gained widespread attention in the field of graph theory and network science. We consider microcanonical ensembles of simple graphs with prescribed degree sequences. We demonstrate that the mean-field approximations of the generating function using the Chebyshev-Hermite polynomials provide estimates for the entropy of finite-graph ensembles. Our estimate reproduces the Bender-Canfield formula in the limit of large graphs.

7 pages, 3 figures

References in corpus (8)

• The entropy of network ensembles
• The entropy of randomized network ensembles
• Efficient and exact sampling of simple graphs with given arbitrary degree sequence
• Entropies of complex networks with hierarchically constrained topologies
• Unbiased sampling of network ensembles
• Disentangling homophily, community structure and triadic closure in networks
• Grand canonical ensembles of sparse networks and Bayesian inference
• Entropy of labeled versus unlabeled networks

Cited by in corpus (4)

• A Gaussian integral that counts regular graphs
• Ensemble inequivalence and phase transitions in unlabeled networks
• First return times on sparse random graphs
• Statistical field theory of random graphs with prescribed degrees