Locating influential nodes in hypergraphs via fuzzy collective influence

Identifying the most influential nodes has become a crucial topic in network science for applications such as viral marketing, rumor suppression, and disease control. However, traditional research on influential node identification focuses mainly on pairwise interactions rather than higher-order interactions between individuals. To solve this problem, we propose s-distance-based fuzzy centrality methods (HDF and EHDF) that are customized for hypergraphs, which can characterize higher-order interactions between nodes via hyperedges. The methods we proposed assume that the influence of a node is dependent on neighboring nodes with a certain s-distance. Extensive experiments on 6 empirical hypergraphs indicate that HDF and EHDF can better identify influential nodes than the baseline methods. Furthermore, our methods demonstrate significant effectiveness in identifying the most influential nodes, achieving a maximum improvement of 411.37% compared to the best state-of-the-art baseline. Our proposed theoretical framework for identifying influential nodes could provide insights into the utilization of higher-order structures for tasks such as vital node identification, influence maximization, and network dismantling.