Higher-order interdependent percolation on hypergraphs

Abstract

A fundamental concern on the robustness of hypergraphs lies in comprehending how the failure of individual nodes affects the hyperedges they are associated with. To address the issue, we propose a simple but novel percolation model that takes into account the dependency of hyperedges on their internal nodes, where the failure of a single node can lead to the dissolution of its associated hyperedge with a probability β. Based on a newly proposed analytical method of percolation theory on hypergraphs, our research reveals that the impact of mean cardinality on the system robustness varies with β. For a large value of β, a larger mean cardinality increases the fragility of hypergraphs, while for a small β, a larger mean cardinality enhances the robustness of hypergraphs. Additionally, our research uncovers divergent effects of hyperdegree distribution on system robustness between monolayer and double-layer hypergraphs. Specifically, monolayer hypergraphs with scale-free hyperdegree distribution exhibit higher robustness, while Poisson hyperdegree distributions lead to stronger robustness in double-layer hypergraphs. These findings provide valuable insights into the robustness of hypergraphs and its dependency on hyperdegree distributions and mean cardinality, contributing to a more comprehensive understanding of the complexities of robustness in complex systems. Furthermore, the development of the percolation model enriches our understanding of node-hyperedge interactions within complex systems.