A gravity-inspired hierarchical approach considering time spreading for key node identification in complex networks

Due to the significant heterogeneity inherent in complex networks, only a small fraction of nodes plays critical roles in governing network functionality and dynamics. Identifying key nodes in such networks is therefore a fundamental challenge, with wide-ranging applications in information diffusion, network dynamics analysis, and epidemic control. Traditional centrality-based metrics typically quantify node importance based on a single topological feature, while recent advances still struggle to effectively capture the combined influence of nodes across multiple structural scales. To address these limitations, this paper proposes a Gravity-Inspired Hierarchical Centrality (GIHC) metric for key node identification in complex networks. This metric quantifies the importance of nodes based on spreading efficiency, taking into account time spreading and temporal constraints. Leveraging the high structural awareness of shortest-path-based and semi-local neighborhood indices, GIHC uniquely integrates the influence of semi-local connections into the estimation of node importance. Inspired by the law of gravity, the GIHC models node interactions as gravitational forces, enabling a more accurate reflection of structural influence within the network. Furthermore, GIHC incorporates global hierarchical information alongside semi-local neighborhood propagation capabilities, forming a hybrid centrality metric that captures both hierarchical organization and mesoscopic influence patterns. Extensive experiments conducted on real-world networks demonstrate that GIHC achieves improved scalability and enhanced ranking accuracy compared to existing centrality metrics. Moreover, GIHC consistently outperforms competing algorithms in epidemic spreading simulations and ranking consistency evaluations, effectively capturing the hierarchical semi-local spreading capabilities of key nodes.