Title: Higher-order shortest paths in hypergraphs Show Chinese title

Title: 高阶最短路径在超图中

Abstract: One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order interactions. Nevertheless, the connectivity properties of real-world hypergraphs remain largely understudied. In this work we introduce path size as a measure to characterise higher-order connectivity and quantify the relevance of non-dyadic ties for efficient shortest paths in a diverse set of empirical networks with and without temporal information. By comparing our results with simple randomised null models, our analysis presents a nuanced picture, suggesting that non-dyadic ties are often central and are vital for system connectivity, while dyadic edges remain essential to connect more peripheral nodes, an effect which is particularly pronounced for time-varying systems. Our work contributes to a better understanding of the structural organisation of systems with higher-order interactions. Show Chinese abstract

Abstract: 复杂网络的一个显著特征是我们从局部相互作用中观察到的连通性特性。 最近，超图作为一种多功能工具被提出，用于建模具有非二元、高阶相互作用的网络。 然而，现实世界中超图的连通性特性仍然研究不足。 在本工作中，我们引入路径大小作为衡量标准，以表征高阶连通性，并量化非二元关系在包含和不包含时间信息的多种实证网络中对高效最短路径的相关性。 通过将我们的结果与简单的随机化零模型进行比较，我们的分析呈现出一种细致的画面，表明非二元关系通常处于核心位置，并对系统连通性至关重要，而二元边则仍然对于连接更外围的节点至关重要，这种效应在时变系统中尤为明显。 我们的工作有助于更好地理解具有高阶相互作用的系统的结构组织。