Inferring community structure in attributed hypergraphs using stochastic block models

Hypergraphs are a representation of complex systems involving interactions among more than two entities and allow to investigation of higher-order structure and dynamics in real-world complex systems. Community structure is a common property observed in empirical networks in various domains. Stochastic block models have been employed to investigate community structure in networks. Node attribute data, often accompanying network data, has been found to potentially enhance the learning of community structure in dyadic networks. In this study, we develop a statistical framework that incorporates node attribute data into the learning of community structure in a hypergraph, employing a stochastic block model. We demonstrate that our model, which we refer to as HyperNEO, enhances the learning of community structure in synthetic and empirical hypergraphs when node attributes are sufficiently associated with the communities. Furthermore, we found that applying a dimensionality reduction method, UMAP, to the learned representations obtained using stochastic block models, including our model, maps nodes into a two-dimensional vector space while largely preserving community structure in empirical hypergraphs. We expect that our framework will broaden the investigation and understanding of higher-order community structure in real-world complex systems.Comment: 28 pages, 11 figures, 8 table

On Maximal Cliques with Connectivity Constraints in Directed Graphs

Finding communities in the form of cohesive subgraphs is a fundamental problem in network analysis. In domains that model networks as undirected graphs, communities are generally associated with dense subgraphs, and many community models have been proposed. Maximal cliques are arguably the most widely studied among such models, with early works dating back to the \u2760s, and a continuous stream of research up to the present. In domains that model networks as directed graphs, several approaches for community detection have been proposed, but there seems to be no clear model of cohesive subgraph, i.e., of what a community should look like. We extend the fundamental model of clique to directed graphs, adding the natural constraint of strong connectivity within the clique. We characterize the problem by giving a tight bound for the number of such cliques in a graph, and highlighting useful structural properties. We then exploit these properties to produce the first algorithm with polynomial delay for enumerating maximal strongly connected cliques