Reciprocity of weighted networks

TL;DR

This paper introduces a novel analytical framework for understanding reciprocity in weighted directed networks, revealing new measures that classify and track reciprocity patterns, which are crucial for network dynamics.

Contribution

It develops a general approach with analytically solved models to quantify and analyze reciprocity in weighted networks, addressing gaps in prior binary-focused studies.

Findings

New measures classify weighted networks based on reciprocity patterns.

Reciprocity can be inferred from global to local structures in some networks.

Previous similarity-based measures are uninformative for weighted reciprocity.

Abstract

All types of networks arise as intricate combinations of dyadic building blocks formed by pairs of vertices. In directed networks, the dyadic patterns are entirely determined by reciprocity, i.e. the tendency to form, or to avoid, mutual links. Reciprocity has dramatic effects on every networks dynamical processes and the emergence of structures like motifs and communities. The binary reciprocity has been extensively studied: that of weighted networks is still poorly understood. We introduce a general approach to it, by defining quantities capturing the observed patterns (from dyad-specific to vertex-specific and network-wide) and introducing analytically solved models (Exponential Random Graphs-type). Counter-intuitively, the previous reciprocity measures based on the similarity of the mutual links-weights are uninformative. By contrast, our measures can classify different weighted networks, track the temporal evolution of a networks reciprocity, identify patterns. We show that in some networks the local reciprocity structure can be inferred from the global one.