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：许多网络可通过社群的存在来表征，社群是紧密相连的单元组，对理解系统的整体功能具有重要作用。近年来，超图已成为建模交互不限于两两节点而可涉及任意数量节点系统的基础工具。在本研究中，我们采用社区检测的对偶方法，将链接社群概念扩展到超图，从而提取高度相关的超边信息聚类。通过对多种真实世界数据的超边间距离矩阵进行层次聚类所获得的树状图进行分析，我们展示了超链接社群自然凸显了高阶网络的层次与多尺度结构。此外，通过利用超链接社群，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，我们引入高阶网络制图学作为实用工具，根据节点的交互模式与社群参与度将其划分为不同结构角色。该方法有助于识别各类真实世界社会系统中的不同个体类型。我们的工作促进了对真实世界高阶系统结构组织的深入理解。