Finding multifaceted communities in multiplex networks

Identifying communities in multilayer networks is crucial for understanding the structural dynamics of complex systems. Traditional community detection algorithms often overlook the presence of overlapping edges within communities, despite the potential significance of such relationships. In this work, we introduce a novel modularity measure designed to uncover communities where nodes share specific multiple facets of connectivity. Our approach leverages a null network, an empirical layer of the multiplex network, not a random network, that can be one of the network layers or a complement graph of that, depending on the objective. By analyzing real-world social networks, we validate the effectiveness of our method in identifying meaningful communities with overlapping edges. The proposed approach offers valuable insights into the structural dynamics of multiplex systems, shedding light on nodes that share similar multifaceted connections.