Multi-species grandcanonical models for networks with reciprocity

TL;DR

This paper introduces a novel grandcanonical model for directed networks that accurately reproduces reciprocity patterns observed in real-world data, using a particle-based analogy with Fermi statistics.

Contribution

It presents the first theoretical framework capable of generating networks with realistic reciprocity, extending existing models with a particle-based approach.

Findings

Model accurately reproduces reciprocity in empirical networks

Extensions of classical random graph models included

Theoretical predictions match observed data well

Abstract

Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grandcanonical class of models reproducing the observed patterns of reciprocity by regarding single and double links as Fermi particles of different `chemical species' governed by the corresponding chemical potentials. Within this framework we find interesting special cases such as the extensions of random graphs, the configuration model and hidden-variable models. Our theoretical predictions are also in excellent agreement with the empirical results for networks with well studied reciprocity.