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

TY - JOUR

T1 - Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

AU - Roberts, E. S.

AU - Schlitt, T.

AU - Coolen, A. C. C.

PY - 2011/7/8

Y1 - 2011/7/8

N2 - 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 out-degrees 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.

AB - 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 out-degrees 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.

M3 - Article

SN - 1751-8121

VL - 44

JO - Journal Of Physics A-Mathematical And Theoretical

JF - Journal Of Physics A-Mathematical And Theoretical

IS - 27

M1 - 275002

ER -