Unveiling the role of higher-order interactions via stepwise reduction
J. G. Bian, Tao Tang, Yilin Bi
Abstract
Abstract Complex systems usually feature interactions not only between pairwise entities but also among three or more entities. Hypergraph can effectively characterize these higher-order interactions. Meanwhile, all higher-order interactions can also be projected onto a number of lower-order interactions. Determining whether all higher-order interactions must be considered or if they can be approximated by lower-order interactions with minimal loss remains an open question. We propose a method to decompose higher-order structures in a stepwise way, thereby allowing to explore the impacts of hyperedges of any order. Experiments suggest that in some networks, incorporating higher-order interactions significantly enhances the accuracy of link prediction, while in others, the effect is insignificant. Therefore, the role of higher-order interactions varies in different types of networks. Overall, since the improvement in predictive accuracy provided by higher-order interactions is significant in some networks, we believe that the study of higher-order interactions is valuable.