# Multilayer Modularity Belief Propagation To Assess Detectability Of Community Structure

## TL;DR

This paper extends belief propagation for modularity-based community detection to multilayer networks, incorporating a resolution parameter, and demonstrates its effectiveness and practical advantages through synthetic and real-world network analyses.

## Contribution

It introduces a multilayer modularity belief propagation method with a resolution parameter, enabling better community detection and interpretability in complex networks.

## Key findings

- Method performs comparably to state-of-the-art tools on benchmarks.
- Adjusting the resolution parameter influences convergence and community structure.
- Node-level marginals offer insights into node attachment strengths.

## Abstract

Modularity based community detection encompasses a number of widely used, efficient heuristics for identification of structure in networks. Recently, a belief propagation approach to modularity optimization provided a useful guide for identifying non-trivial structure in single-layer networks in a way that other optimization heuristics have not. In this paper, we extend modularity belief propagation to multilayer networks. As part of this development, we also directly incorporate a resolution parameter. We show that adjusting the resolution parameter affects the convergence properties of the algorithm and yields different community structures than the baseline. We compare our approach with a widely used community detection tool, GenLouvain, across a range of synthetic, multilayer benchmark networks, demonstrating that our method performs comparably to the state of the art. Finally, we demonstrate the practical advantages of the additional information provided by our tool by way of two real-world network examples. We show how the convergence properties of the algorithm can be used in selecting the appropriate resolution and coupling parameters and how the node-level marginals provide an interpretation for the strength of attachment to the identified communities. We have released our tool as a Python package for convenient use.