Patterns of link reciprocity in directed networks

TL;DR

This paper introduces a new measure for link reciprocity in directed networks, revealing consistent correlation patterns across different network types and highlighting limitations of existing models.

Contribution

It proposes a novel reciprocity measure, analyzes real networks' correlation patterns, and introduces a generalized framework with conditional connection probabilities.

Findings

Real networks are either correlated or anticorrelated.

Networks of similar types show similar reciprocity values.

Current models fail to reproduce observed reciprocity patterns.

Abstract

We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.