Many networks can be characterised by the presence of communities, which are groups of units that are closely linked and can be relevant in 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. Using a dual approach to community detection, in this study we extend the concept of link communities to hypergraphs, allowing us to extract informative clusters of highly related hyperedges. We analyze the dendrograms obtained by applying hierarchical clustering to distance matrices among hyperedges on a variety of real-world data, showing that hyperlink communities naturally highlight the hierarchical and multiscale structure of higher-order networks. Moreover, by using hyperlink communities, we are able 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 helps identify 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.

翻译：许多网络可以通过存在社区来表征，社区是由紧密连接的单元组成，并且有助于理解系统的整体功能。近年来，超图已成为模拟交互不限于一对节点而可能涉及任意数量节点的系统的基础工具。本研究采用社区检测的双重方法，将链接社区的概念扩展到超图，从而提取高度相关的超边的信息簇。我们分析了通过对各种真实世界数据集中的超边间的距离矩阵应用层次聚类得到的树状图，表明超链接社区自然地突显了高阶网络的层次和多尺度结构。此外，通过使用超链接社区，我们能够提取节点的重叠成员关系，克服了传统硬聚类方法的局限性。最后，我们引入高阶网络映射作为实用工具，根据节点的交互模式和社区参与程度将其分类为不同的结构角色。该方法有助于识别各种真实世界社会系统中的不同类型的个体。我们的工作有助于更深入地理解真实世界高阶系统的结构组织。