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.

翻译：许多网络可以通过存在社区来表征，这些社区是由紧密连接的单元组成的群体。识别这些社区对于理解系统的整体功能至关重要。近年来，超图已成为建模系统中相互作用不限于成对节点、而可能涉及任意数量节点的基本工具。在本研究中，我们采用双重方法进行社区检测，并将链接社区的概念扩展到超图。这一扩展使得我们能够提取高度相关的超边信息聚类。通过分析对各种真实世界数据中超边间距离矩阵进行层次聚类得到的树状图，我们表明超链接社区自然地凸显了高阶网络的层次性和多尺度结构。此外，超链接社区使我们能够从节点中提取重叠成员关系，克服了传统硬聚类方法的局限性。最后，我们引入高阶网络图谱作为实用工具，根据交互模式和社区参与度将节点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个体。我们的工作有助于更好地理解真实世界高阶系统的结构组织。