Detecting communities in higher-order networks by using their derivative graphs

Similar to what happens in the pairwise network domain, the communities of nodes of a hypergraph (also called higher-order network) are formed by groups of nodes that share many hyperedges, so that the number of hyperedges they share with the rest of the nodes is significantly smaller, and therefore these communities can be considered as independent compartments (or super-clusters) of the hypergraph. In this work we present a method, based on the so-called derivative graph of a hypergraph, which allows the detection of communities of a higher-order network without high computational cost and several simulations are presented that show the significant computational advantages of the proposed method over other existing methods.