Modularity belief propagation on multilayer networks to detect significant community structure

Modularity based community detection encompasses a number of widely used, efficient heuristics for identification of structure in single-and multilayer networks. Recently, a belief propagation approach to modularity optimization provided a useful guide for identifying non-trivial structure 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 the resolution parameter affects the convergence properties of the algorithm and yields different community structures than the baseline. We demonstrate our extension on synthetic multilayer networks, showing how our tool achieves near optimal performance and prevents overfitting. We highlight these advantages in comparison to another widely used tool, GenLouvain for multilayer modularity. Finally, we apply multilayer modularity belief propagation to two real-world multilayer networks and discuss practical concerns in implementing our method, which we have released as a Python package for general use