超图中的高阶最短路径
Higher-order shortest paths in hypergraphs
AI总结：
本文提出用路径规模刻画超图高阶连通性，并在多种经验网络中量化非二元关系对最短路径的作用，揭示其核心地位及二元边对外围节点的必要性。
摘要：
复杂网络的决定性特征之一，是我们观察到的由局部相互作用中涌现出的连通性。近来，超图已成为一种通用工具，用于对具有非二元高阶相互作用的网络进行建模。然而，现实世界超图的连通性在很大程度上仍未得到充分研究。在本工作中，我们引入路径规模作为刻画高阶连通性的度量，并在一系列包含与不包含时间信息的多样化经验网络中，量化非二元关系对于高效最短路径的相关性。通过将我们的结果与简单随机零模型进行比较，分析呈现出一幅细致的图景：非二元关系通常处于核心地位，对系统连通性至关重要，而二元边对于连接更外围的节点仍然必不可少，这一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。
英文摘要：
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.
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