Beyond Pairwise Interactions: Unveiling the Role of Higher-Order Interactions via Stepwise Reduction (2411.05685v1)

Abstract: 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.