Statistical Mechanics of Multi-Edge Networks

TL;DR

This paper develops a statistical mechanics framework for multi-edge networks, which are graphs with multiple distinguishable connections, providing insights into their properties and implications for agent-based systems.

Contribution

It introduces a novel statistical mechanics approach to analyze multi-edge networks, bridging the gap between weighted and multi-edge graph representations.

Findings

Multi-edge networks can be characterized using a comprehensive statistical framework.

Binary projections of multi-edge networks can be understood through multi-edge processes.

The approach has significant implications for modeling agent-based systems.

Abstract

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos variables and those where they account for discrete, distinguishable events, which we call multi-edge networks. In this work we face this problem introducing multi-edge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multi-edges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multi-edge processes. The implications of these results are important as many real agent based problems mapped onto graphs require of this treatment for a proper characterization of its collective behavior.