Community Detection and Hyperlink Prediction in Multilayer Hypergraphs

Real-world systems often involve multiple interaction types and complex higher order relationships that go beyond simple pairwise connections, making multilayer hypergraphs a powerful framework for modeling such intricate structures. Community detection, a fundamental problem in network science, is particularly significant in the context of multilayer hypergraphs. However, existing research in this area remains limited. Current approaches often rely on heuristic techniques, such as clustering and random walks, which lack robust theoretical foundations and flexibility, or on layer fusion methods that compress all layers into a single-layer network, thereby discarding valuable cross-layer information and yielding hard partitioning results. In this article, we propose a statistically grounded generative model—the stochastic block model for multilayer hypergraphs—that employs the expectation–maximization algorithm to infer community structures and community interaction strength matrix for each layer. Our framework enables soft partitioning, allowing nodes to belong to multiple communities with probabilistic assignments, while simultaneously leveraging cross-layer information to enhance hyperlink prediction within specific layers. Experiments on synthetic and real-world networks demonstrate the model’s superior performance in community detection and hyperlink prediction, showcasing its ability to capture the complexity of multilayer higher order interactions effectively.