Louvain-like methods for community detection in multilayer hypergraphs

Community detection is a relevant problem in graph theory and, in particular, in the study of complex networks. Hypergraphs are a natural modeling paradigm for networked systems with multiway interactions. On the other hand, many complex systems are represented as multilayer networks, where each layer represents one of many possible types of interactions. We combine these two notions and focus our attention on developing a method for community detection in multilayer hypergraphs. One of the most common approaches is to replace hypergraphs with their corresponding clique expansion graphs or their weighted projections to simple graphs, causing loss of information and low accuracy. We propose a method that preserves their structure and simultaneously takes into account multiple layers. We then perform numerical experiments on synthetic multilayer hypergraphs.