Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world hypergraphs, focusing on the encapsulation of their hyperedges, which is the extent that smaller hyperedges are subsets of larger hyperedges. Building on the concept of line graphs, our measures quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation–whose encapsulation would be maximum. We then turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate the spreading in the system.

中文翻译：

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超图中的封装结构和动力学


超图已成为一种强大的建模框架，用于表示具有多路交互的系统，即交​​互可能涉及任意数量的代理的系统。在这里，我们探索现实世界超图的属性，重点关注其超边的封装，即较小的超边是较大超边的子集。基于折线图的概念，我们的措施量化了不同大小的超边之间存在的关系，并且作为副产品，数据与简单复杂表示的兼容性 - 其封装将是最大的。然后，我们转向观察到的结构模式对扩散动力学的影响，重点关注阈值模型的变体，称为封装动力学，并证明非随机模式可以加速系统中的扩散。