Distance-parameterized h-index gravity model for influential node identification in complex networks

Abstract

Identifying influential nodes in complex networks through gravity-based models remains challenging due to the complex interplay between node quality and distance metrics. We propose a novel physics-inspired framework that uniquely integrates these parameters by treating inter-node distance as a dynamic factor in determining node quality. This approach extends the traditional h-index to a distance-parameterized neighborhood h-index, where node influence is quantified through iterative distance-based traversal. The framework introduces a saturation distance parameter to optimize the interaction range, addressing a fundamental limitation in existing gravity-based models. We validated our method on eight real-world networks using the Susceptible-Infected-Recovered (SIR) epidemic model. Results demonstrate superior performance in three aspects: higher correlation with SIR spreading outcomes, enhanced monotonicity in influence ranking, and further improved node distinguishability compared to nine conventional methods. This gravitational framework provides a more accurate and computationally efficient approach for identifying critical nodes in epidemic control and information diffusion.