Entropies of tailored random graph ensembles: bipartite graphs, generalised degrees, and node neighbourhoods

TL;DR

This paper derives explicit formulas for the Shannon entropies of various tailored random graph ensembles, including bipartite graphs and those with specified degree and neighborhood distributions, advancing understanding of their structural complexity.

Contribution

It provides the first explicit entropy formulas for these complex graph ensembles, broadening analytical tools in network theory.

Findings

Derived formulas for bipartite graph entropy with degree constraints

Calculated entropy for graphs with specified neighborhood distributions

Extended entropy calculations to generalized degree constrained graphs

Abstract

We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles with imposed (and possibly distinct) degree distributions for the two node sets, graph ensembles constrained by specified node neighbourhood distributions, and graph ensembles constrained by specified generalised degree distributions.