通过超核视角看时间超图的结构演化
The structural evolution of temporal hypergraphs through the lens of hyper-cores
AI总结：
本文提出了一系列基于超核分解的方法，用于在多尺度上分析时间超图的结构特性与动态演化，并验证了其在真实数据集和合成模型中的有效性。
摘要：
许多复杂系统的丰富性源于其组件之间的交互。这些交互的高阶特性（即同时涉及多个单元）及其时间动态性，是塑造系统自身行为的关键属性。时间超图将这些特征整合在同一框架内，为这些系统提供了恰当的描述。然而，用于其时间和拓扑表征的工具仍然稀缺。在此，我们开发了一系列专门设计的方法，用于在多个尺度上分析时间超图的结构特性。利用超图的超核分解，我们追踪超核随时间的演化，在不同拓扑尺度上表征超图结构及其时间动态，并量化系统的多尺度结构稳定性。我们还定义了两种静态超核度中心性度量，以提供对节点聚合结构行为的总体描述。我们将这些表征方法应用于多个数据集，建立了结构特性与系统内特定活动之间的联系。最后，我们展示了如何将所提方法用作合成时间超图的模型验证工具，区分不同模型生成的高阶结构和动态与经验数据的不同，从而识别重现经验超图结构和演化所需的必要模型机制。我们的工作开辟了多个研究方向，从理解时间高阶网络上的动态过程到设计新的时变超图模型。
英文摘要：
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the behaviour of the system itself. An adequate description of these systems is offered by temporal hypergraphs, that integrate these features within the same framework. However, tools for their temporal and topological characterization are still scarce. Here we develop a series of methods specifically designed to analyse the structural properties of temporal hypergraphs at multiple scales. Leveraging the hyper-core decomposition of hypergraphs, we follow the evolution of the hyper-cores through time, characterizing the hypergraph structure and its temporal dynamics at different topological scales, and quantifying the multi-scale structural stability of the system. We also define two static hypercoreness centrality measures that provide an overall description of the nodes aggregated structural behaviour. We apply the characterization methods to several data sets, establishing connections between structural properties and specific activities within the systems. Finally, we show how the proposed method can be used as a model-validation tool for synthetic temporal hypergraphs, distinguishing the higher-order structures and dynamics generated by different models from the empirical ones, and thus identifying the essential model mechanisms to reproduce the empirical hypergraph structure and evolution. Our work opens several research directions, from the understanding of dynamic processes on temporal higher-order networks to the design of new models of time-varying hypergraphs.
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