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

Ensembles of tailored random graphs allow us to reason quantitatively about the complexity of system.

Journal of Physics A 47, 435101 (2014)

E. Roberts, A. Coolen

Ensembles of tailored random graphs allow us to reason quantitatively about the complexity of system.

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 neigh- bourhood distributions, and graph ensembles constrained by specified gen- eralized degree distributions.