Message passing approach to analyze the robustness of hypergraph

Abstract

Hypergraph networks are closer to real life because they can reflect higher-order interactions, so researchers have begun using them to build models for real-world networks. The mean-field approach is the current tool for studying the percolation problem on hypergraph networks. However, we found that when there is a loop in the hypergraph network, the calculated results using this approach deviate from the real results. Therefore, in this paper, we rephrase the percolation on the hypergraph network as a message passing process, thus obtaining a message passing approach. Our proposed approach has been tested in several hypergraph networks with loops, and the experimental results are more accurate than those under the mean-field approach. This is helpful to analyze and understand the robustness of hypergraph networks with loops. In addition, we also specifically analyzed how four different types of loops affect the accuracy of the experiment. Our proposed message passing approach also provides another way to study percolation on hypergraph networks.

Percolation Theories for Quantum Networks

“…It has been shown that higher-order interactions may significantly change the physical properties of dynamical processes from those on ordinary networks with only pairwise connections [53,132,138,139]. However, there are only a few works exploring the robustness or the percolation of hypergraphs [140][141][142][143][144][145]. Specifically, Coutinho et al introduced two generalizations of core percolation to hypergraphs, and offered analytical solutions to certain types of random hypergraphs accordingly [140].…”