Finding influential nodes in complex networks by integrating nodal intrinsic and extrinsic centrality

Finding influential nodes in complex networks holds significant application in understanding network structure, optimizing information dissemination, and enhancing network robustness. The effective capture of key characteristics of high-influence nodes has piqued the interest of numerous researchers. However, to balance the complexity and validity, existing metrics fall short of capturing the crux that determines node influence with low complexity. Recently, certain local indices (such as degree, k-shell, H-index etc.) have been appropriately expanded and combined, successfully identifying the influence of nodes within the network. Notably, methods such as WKS, WNC, WKSD, and HIC stand out. Inspired by these approaches, our research suggests that a node's influence is manifested in both intrinsic and extrinsic centrality. We introduce a method, termed WDKS, to pinpoint influential nodes within complex networks. In WDKS, the product of degree and k-shell is regarded as the intrinsic influence of nodes, whereas the centrality of nodes' neighborhood exerts an additional effect on it via the virtue of potential edge weights. This measurement approach endows WDKS with a linear computational complexity of O(m), rendering it resilient to the scale of datasets. To validate the identification efficacy of WDKS, we employed the SIR model for simulation and comparative analysis on 12 real-world social and natural network datasets. The findings reveal that WDKS outperforms nine other established metrics in terms of node influence ranking, high-influence nodes identification, ranking monotonicity, and spreading capability. Furthermore, as WDKS doesn't necessitate parameter adjustments based on diverse network structures, it exhibits excellent robustness and versatility.