Robustness of networks of hypergraphs
Phys. Rev. E 113, 064312 – Published 25 June, 2026
DOI: https://doi.org/10.1103/kh2t-59zq
Abstract
Hypergraphs provide a natural representation of complex systems with higher-order interactions and are commonly interdependent with each other. In this work, based on a bipartite network representation of hypergraphs, we propose a framework of networks of hypergraphs (NOH) to describe the structures among subsystems represented by hypergraphs. An NOH is composed of supernodes and superedges connecting them. A supernode represents the set of node-type vertices or the set of hyperedge-type vertices in the bipartite representation of a hypergraph. Thus, in the NOH, each hypergraph is represented by two supernodes, and the superedge connecting them characterizes the structure of the corresponding hypergraph. We analyze the robustness of NOHs under both quenched and annealed structural configurations. Our findings reveal the combined effects of intrahypergraph and interhypergraph structures on the overall system robustness. Our study provides a unifying framework for understanding the robustness of complex systems with higher-order interactions in which subsystems are intricately coupled.
