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arXiv · 1101.6022

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

E. S. Roberts·A. C. C. Coolen·T. Schlitt
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Abstract

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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E. S. Roberts, A. C. C. Coolen, T. Schlitt. 2011-01-31. Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs. https://doi.org/10.1088/1751-8113/44/27/275002

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