Identifying Vital Nodes by Local G-Core on Symmetric Networks

The H-index is a widely recognized centrality measure for nodes in symmetric networks, defined as the maximum number of neighbors with degrees equal to or greater than the node’s own degree. However, this metric underestimates the structural influence of "weak nodes" – low-degree nodes connected to high-degree hubs – that often serve as critical connectors in network topology. To address this limitation, we propose the Hα-index, which generalizes the H-index by considering the maximum number of neighbors with degrees at least α times the node’s degree, where α≥1. Based on this refinement, we introduce two novel centrality measures: g-core and local g-core, derived through iterative application of the Hα-index to a node’s neighbors. Extensive experiments on fifteen real-world networks demonstrate the efficiency of our methods. Notably, the local g-core achieves 45%-105% higher Kendall Tau correlation coefficients compared to the traditional H-index and coreness on three benchmark networks, highlighting its superior performance in capturing node influence.