Identification of key nodes in urban bus-metro network: A NK-shell algorithm based neighborhood KS

Key nodes significantly influence the connectivity and functionality of urban public transit networks. To address the limitations of insufficient resolution and accuracy in existing methods for key node identification in complex networks, this paper proposes the NK-shell algorithm, a novel approach based on the neighborhood K-shell (KS) values. The algorithm integrates global network structure with local features of first- and second-order neighboring nodes, enabling a multidimensional evaluation of node importance. To validate its effectiveness, six key node identification methods, θ, Cnc+, CC, BC, K-shell, and NK-shell, are comparatively evaluated in six real-world networks using the Susceptible-Infected-Recovered (SIR) model. In addition, ablation experiments are conducted to compare the impact of incorporating different orders of neighborhood information. The results demonstrate that the NK-shell algorithm outperforms the others in terms of monotonicity, accuracy, precision, and ranking resolution, significantly distinguishing the importance levels of different nodes. It effectively overcomes the resolution limitations of traditional K-shell methods in distinguishing nodes within the same shell, thereby enhancing the comprehensiveness and applicability of node importance evaluation.