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Phys Rev Lett. 2010 Mar 12;104(10):108702. Epub 2010 Mar 11.

Entropic origin of disassortativity in complex networks.

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1
Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Facultad de Ciencias, University of Granada, 18071 Granada, Spain.

Abstract

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define the ensemble of correlated networks and obtain the associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in the case of highly heterogeneous, scale-free networks a certain disassortativity is predicted--offering a parsimonious explanation for the question above. Our approach provides a neutral model from which, in the absence of further knowledge regarding network evolution, one can obtain the expected value of correlations. When empirical observations deviate from the neutral predictions--as happens for social networks--one can then infer that there are specific correlating mechanisms at work.

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