Shannon entropy and degree correlations in complex networks

A wide range of empirical networks - whether biological, technological, information-related or linguistic - genetically exhibit important degree-degree anticorrelations (i.e., they are disassortative), the only exceptions usually being social ones, which tend to be positively correlated (assortative). With a view to understanding where this universality originates, we obtain the Shannon entropy of a network and find that the partition of maximum entropy does not in general correspond to uncorrelated networks but, in the case of heterogeneous (scale-free) degree distributions, to a certain disassortativity. This approach not only gives a parsimonious explanation to a long-standing question, but also provides a neutral model against which to compare experimental data, and thus determine whether there are specific correlating mechanisms at work among the forces behind the evolution of a given real-world network.