Hyperlink communities in higher-order networks

Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have emerged as a fundamental tool for modelling systems where interactions are not limited to pairs but may involve an arbitrary number of nodes. In this study, we adopt a dual approach to community detection and extend the concept of link communities to hypergraphs. This extension allows us to extract informative clusters of highly related hyperedges. We analyze the dendrograms obtained by applying hierarchical clustering to distance matrices among hyperedges across a variety of real-world data, showing that hyperlink communities naturally highlight the hierarchical and multiscale structure of higher-order networks. Moreover, hyperlink communities enable us to extract overlapping memberships from nodes, overcoming limitations of traditional hard clustering methods. Finally, we introduce higher-order network cartography as a practical tool for categorizing nodes into different structural roles based on their interaction patterns and community participation. This approach aids in identifying different types of individuals in a variety of real-world social systems. Our work contributes to a better understanding of the structural organization of real-world higher-order systems.