Sun Hanlin, Bianconi Ginestra
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
The Alan Turing Institute, The British Library, 96 Euston Road, London NW1 2DB, United Kingdom.
Phys Rev E. 2021 Sep;104(3-1):034306. doi: 10.1103/PhysRevE.104.034306.
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.
高阶相互作用日益被视为从大脑到社会联系网络等复杂系统的一个基本方面。超图以及单纯复形捕捉了复杂系统的高阶相互作用，并使我们能够研究它们的高阶结构与其功能之间的关系。在此，我们建立了一个评估超图鲁棒性的通用框架，并刻画了简单和高阶渗流过程的关键特性。这个通用框架基于随机多重超图系综的公式化，其中每一层都由给定基数的超边来表征。我们观察到，在存在结构截止的情况下，多重超图系综可以映射到多重二分网络系综。我们揭示了随机多重超图中的高阶渗流过程、多重网络的相互依存渗流以及K核渗流之间的关系。随机多重超图的结构相关性被证明对其渗流特性有显著影响。在多重超图上观察到的高阶渗流过程的广泛临界行为阐明了导致不连续转变出现的机制，并揭示了可应用于高阶网络上流行病传播和传染过程研究的有趣临界特性。
