A Simplex Hypergraph Clustering Method for Detecting Higher-order Modules in Microbial Network

Microbial interactions are of great importance for maintaining ecological balance and regulating human health. Most of the previous studies focus on the paired relationships and pay less attention to the higher-order interaction relationships in the microbial communities. The hypergraph was applied to establish higher-order interaction networks among microbes in microbial communities and the result of hypergraph clustering depends on hyperedge weights. So, we adopt simplex and take advantage of its volume for reconstructing each hyperedge weight to improve hypergraph clustering. We proposed a novel hypergraph clustering algorithm based on simplex (HCBS) here to detect the higher-order interaction modules in the network in a manner of clustering. The HCBS algorithm achieves the hyperedge weight from a unique higher-order relationship by calculating the joint contribution of all nodes in each hyperedge. The maximum modularity was utilized to optimize the clustering number of the hypergraph in the paper. The experimental results illustrate that the HCBS algorithm emphasis the differences of hyperedge weights and it is very effective in detecting microbial higher-order modules.