Higher-order percolation processes on multiplex hypergraphs

TL;DR

This paper develops a comprehensive framework for analyzing higher-order percolation in multiplex hypergraphs, revealing how structural correlations influence critical phenomena and transitions relevant to contagion and epidemic spreading.

Contribution

It introduces a general model for higher-order percolation on multiplex hypergraphs, linking it to existing percolation processes and highlighting the impact of structural correlations.

Findings

Structural correlations significantly affect percolation thresholds.

Higher-order percolation exhibits diverse critical behaviors, including discontinuous transitions.

The framework applies to epidemic spreading and contagion in complex systems.

Abstract

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex systems and allow 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 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.