Reciprocity of Networks with Degree Correlations and Arbitrary Degree Sequences

TL;DR

This paper develops a theoretical framework to understand reciprocity in complex networks with arbitrary degree sequences and correlations, highlighting the importance of degree correlations in real-world network reciprocity.

Contribution

It introduces a statistical ensemble approach to analytically predict reciprocity considering degree correlations and validates findings with numerical experiments.

Findings

Degree correlations significantly influence network reciprocity

A hierarchy of correlation effects on reciprocity is identified

Analytical predictions align well with numerical simulations

Abstract

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with an arbitrary degree sequence and a broad class of degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to $r$ is revealed. Numerical experiments using novel network randomization methods show very good agreement to our analytical estimations.