Message-passing approach to higher-order percolation

Hypergraph describes real-world networks widely because it captures pairwise and multiple nodes’ interactions. Various kinds of damages, such as network attacks, hardware malfunctions, and communication disruptions, may impair the function of those real-world systems. We propose a generalized higher-order percolation model to investigate the robustness of the hypergraph, in which the nodes and hyperedges were randomly removed with probabilities. An accurate approach to studying the higher-order percolation model should overcome non-local tree-like structures and higher-order interactions, which makes the classical mean-field approach invalid. To this end, we develop a message-passing approach in which we first transform the hypergraph into a factor graph then develop a message-passing approach on the factor graph. Through extensive experimental studies on both artificial and real-world hypergraphs, our theory can accurately predict numerical results. The experimental data demonstrate that our theory achieves average accuracy rates in calculating giant connected component (GCC) size of 99.87% for artificial loopless hypergraphs, 99.24% for artificial hypergraphs with loops, and 99.65% for real-world hypergraphs. Our findings provide another way to understand the robustness of hypergraphs, and also provide certain ideas for studying complex systems in various fields.