Beyond Pairwise Interactions: Unveiling the Role of Higher-Order Interactions via Stepwise Reduction

Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order interactions. Hypergraph, as a mathematical tool, can effectively characterize higher-order interactions, where nodes denote entities and hyperedges represent interactions among multiple entities. Meanwhile, all higher-order interactions can also be projected into a number of lower-order interactions or even some pairwise interactions. Whether it is necessary to consider all higher-order interactions, and whether it is with little loss to replace them by lower-order or even pairwise interactions, remain a controversial issue. If the role of higher-order interactions is insignificant, the complexity of computation and the difficulty of analysis can be drastically reduced by projecting higher-order interactions into lower-order or pairwise interactions. We use link prediction, a fundamental problem in network science, as the entry point. Specifically, we evaluate the impact of higher-order interactions on link predictive accuracy to explore the necessity of these structures. We propose a method to decompose the higher-order structures in a stepwise way, thereby allowing to systematically explore the impacts of structures at different orders on link prediction. The results indicate that in some networks, incorporating higher-order interactions significantly enhances the accuracy of link prediction, while in others, the effect is insignificant. Therefore, we think that 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 both necessary and valuable.