Identifying important nodes of hypergraph: An improved PageRank algorithm

Abstract Hypergraphs can accurately capture complex higher-order relationships, but it is challenging to identify their important nodes. In this paper, an improved PageRank (ImPageRank) algorithm is designed to identify important nodes in a directed hypergraph. The algorithm introduces the Jaccard similarity of directed hypergraphs. By comparing the numbers of common neighbors between nodes with the total number of their neighbors, the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected, and can reflect the potential correlation between nodes. An improved susceptible–infected (SI) model in directed hypergraph is proposed, which considers nonlinear propagation mode and more realistic propagation mechanism. In addition, some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs. Finally, the ImPageRank algorithm is used to evaluate the performance of the SI model, network robustness and monotonicity. Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.