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Higher-order percolation processes on multiplex hypergraphs
Physical Review E ( IF 2.4 ) Pub Date : 2021-09-15 , DOI: 10.1103/physreve.104.034306
Hanlin Sun 1 , Ginestra Bianconi 1, 2
Affiliation  

Higher-order interactions are increasingly recognized as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraphs as well as simplicial complexes capture the higher-order interactions of complex systems and allow us to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensemble where each layer is characterized by hyperedges of given cardinality. We observe that in presence of the structural cutoff the ensemble of multiplex hypergraphs can be mapped to an ensemble of multiplex bipartite networks. We reveal the relation between higher-order percolation processes in random multiplex hypergraphs, interdependent percolation of multiplex networks, and K-core percolation. The structural correlations of the random multiplex hypergraphs are shown to have a significant effect on their percolation properties. The wide range of critical behaviors observed for higher-order percolation processes on multiplex hypergraphs elucidates the mechanisms responsible for the emergence of discontinuous transition and uncovers interesting critical properties which can be applied to the study of epidemic spreading and contagion processes on higher-order networks.

中文翻译:

多重超图上的高阶渗透过程

高阶交互越来越被认为是从大脑到社会联系网络的复杂系统的一个基本方面。超图和单纯复形捕捉复杂系统的高阶相互作用,并允许我们研究它们的高阶结构与其功能之间的关系。在这里,我们建立了一个用于评估超图稳健性的通用框架,并描述了简单和高阶渗透过程的关键特性。这个通用框架建立在随机多路超图集合的公式之上,其中每一层都以给定基数的超边为特征。我们观察到,在存在结构截止的情况下,多重超图的集合可以映射到多重二分网络的集合。-核心渗透。随机多重超图的结构相关性对其渗透特性有显着影响。在多重超图上观察到的高阶渗透过程的广泛关键行为阐明了导致不连续过渡出现的机制,并揭示了有趣的关键特性,可应用于研究高阶网络上的流行病传播和传染过程。
更新日期:2021-09-16
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