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

E. S. Roberts; A. C C Coolen

doi:10.1088/1751-8113/47/43/435101

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

E. S. Roberts^*, A. C C Coolen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 generalized degree distributions.

Original language	English
Article number	435101
Journal	Journal of Physics A
Volume	47
Issue number	43
DOIs	https://doi.org/10.1088/1751-8113/47/43/435101
Publication status	Published - 31 Oct 2014

Keywords

bipartite graphs
entropy
generalized degrees
networks
random graphs

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10.1088/1751-8113/47/43/435101

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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 generalized degree distributions.",

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AB - 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 generalized degree distributions.

KW - bipartite graphs

KW - entropy

KW - generalized degrees

KW - networks

KW - random graphs

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

Abstract

Keywords

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