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

Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.

Journal of Physics A 47, 435101 (2014)

E. Roberts, A. Coolen

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

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.

More in Intelligence of graphs

  • JPhys Complexity

    Transitions in loopy graphs

    The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

  • Journal of Economic Interaction and Coordination

    Bursting dynamic networks

    A mathematical model captures the temporal and steady state behaviour of networks whose two sets of nodes either generate or destroy links.

  • Journal of Physics A

    Exactly solvable random graphs

    An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.

  • Journal of Physics A

    Tailored random graph ensembles

    New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.

  • Physical Review E

    Unbiased randomization

    Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.

  • Journal of Physics A

    Spin systems on Bethe lattices

    Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.

  • ESAIM: Proceedings and surveys

    Random graphs with short loops

    The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.