Identification of vital nodes based on global and local features in hypergraphs

Abstract Hypergraphs, which encapsulate interactions of higher-order beyond mere pairwise connections, are essential for representing polyadic relationships within complex systems. Consequently, an increasing number of researchers are focusing on the centrality problem in hypergraphs. Specifically, researchers are tackling the challenge of utilizing higher-order structures to effectively define centrality metrics. This paper presents a novel approach, LGK, derived from the K-shell decomposition method, which incorporates both global and local perspectives. Empirical evaluations indicate that the LGK method provides several advantages, including reduced time complexity and improved accuracy in identifying critical nodes in hypergraphs.