The entropic origin of disassortativity in complex networks

TL;DR

This paper explains the widespread disassortativity in empirical networks, especially scale-free ones, by showing that maximum entropy principles naturally lead to anticorrelations, providing a neutral model for network correlations.

Contribution

It introduces an entropy-based framework to understand degree-degree correlations, revealing that disassortativity arises naturally in heterogeneous networks as a maximum entropy state.

Findings

Maximum entropy often corresponds to disassortative networks in scale-free cases.

Real-world networks frequently match the neutral maximum entropy predictions.

Deviations from the neutral model indicate specific underlying correlation mechanisms.

Abstract

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated, i.e. disassortative? With a view to answering this long-standing question, we define a general class of degree-degree correlated networks and obtain the associated Shannon entropy as a function of parameters. It turns out that the maximum entropy does not typically correspond to uncorrelated networks, but to either assortative (correlated) or disassortative (anticorrelated) ones. More specifically, for highly heterogeneous (scale-free) networks, the maximum entropy principle usually leads to disassortativity, providing a parsimonious explanation to the question above. Furthermore, by comparing the correlations measured in some real-world networks with those yielding maximum entropy for the same degree sequence, we find a remarkable agreement in various cases. 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. In cases in which empirical observations deviate from the neutral predictions -- as happens in social networks -- one can then infer that there are specific correlating mechanisms at work.