AI 中文总结
研究针对高阶相互作用下复杂网络拓扑度量推广问题，利用新超图距离公式推广了三个基于距离的拓扑度量，通过示例和数据集分析，揭示超图可分三类及特定相互作用阶次主导情况，为简化分析提供实用指导。
AI 中文摘要
高阶相互作用给复杂网络引入了额外的结构维度，这需要对经典拓扑度量进行一致的推广。在超图中，节点间距离的定义不唯一：除了从团投影得出的传统度量外，最近还提出了一种明确纳入超边大小、它们的交集大小及其权重的替代公式。在此，我们使用这种新的超图距离对基于距离的三个拓扑度量，即接近中心性、中介中心性和节点偏心度进行推广。通过易于处理的示例，我们证明了用这两种距离得到的结果之间的差异是系统性的，且源于高阶网络的有结构意义的特征。此外，通过分析一系列现实世界数据集，我们表明超图可分为三个不同类别，对应于特定相互作用阶次在其一般度量结构上可能的主导地位。这为将分析限制在某些特定相互作用阶次的可能性提供了实用指导，在保持系统完整信息的同时降低其复杂性。
英文摘要
Higher-order interactions introduce an additional structural dimension to complex networks, requiring consistent generalizations of classical topological measures. In hypergraphs, the definition of distance between nodes is not unique: beyond the conventional measure derived from clique projection, an alternative formulation that explicitly incorporates the sizes of hyperedges, those of their intersection and their weights has been recently proposed. Here, we generalize three distance-based topological measures, namely closeness centrality, betweenness centrality and node eccentricity, using this new hypergraph distance. Trough tractable illustrative examples, we demonstrate that the differences between results obtained with the two distances are systematic and arise from structurally meaningful features of the higher-order networks. Also, analyzing a series of real-world datasets, we show that hypergraphs can be divided into three distinct classes, corresponding to the possible dominance of specific orders of interaction over their general metric structure. This provides practical guidance on the possibility of limiting the analysis to only some specific interaction orders, reducing its complexity while maintaining the full information of the system.
Comments10 pages, 8 figures
Journal refChaos, Soliton. Fract. 211, 118836 (2026)
DOI：10.1016/j.chaos.2026.118836
