Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

Details Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

2011-01-31

arxiv.org/abs/1101.6022v1

Biology

Quantitative Biology

Quantitative Methods

21 pages, 1 figure, submitted to J. Phys. A

Scientific paper

We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in- and outdegrees and prescribed degree-degree correlation functions. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies and complexities of these ensembles, and for information-theoretic distances. The results are applied to data on gene regulation networks.

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