Statistical mechanics of directed networks

TL;DR

This paper develops a statistical mechanics framework for directed networks, modeling them as ensembles of interacting fermions to analyze their structure and dynamics with a focus on reciprocity.

Contribution

It introduces a novel formalism controlling reciprocity and other features, providing new models and analytical tools for empirical analysis of directed networks.

Findings

Framework models directed networks as fermion ensembles.

Controls reciprocity to analyze bidirectional interactions.

Provides new tools for empirical network studies.

Abstract

Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources flow within a network, fundamentally shaping the behavior of dynamical processes and distinguishing directed networks from their undirected counterparts. Robust null models are crucial for identifying meaningful patterns in these representations, yet designing models that preserve key features remains a significant challenge. One such critical feature is reciprocity, which reflects the balance of bidirectional interactions in directed networks and provides insights into the underlying structural and dynamical principles that shape their connectivity. This paper introduces a statistical mechanics framework for directed networks, modeling them as ensembles of interacting fermions. By controlling reciprocity and other network properties, our formalism offers a principled approach to analyzing directed network structures and dynamics, introducing a new perspectives, and models and analytical tools for empirical studies.