A Unified Weighted K-Shell Framework With Dynamic Decomposition for Influential Node Identification in Complex Networks

Abstract

Identifying influential nodes in complex networks is a fundamental problem in network science, with applications in epidemic control, information diffusion, and rumor spreading. K-shell decomposition is widely used due to its global perspective and linear time complexity. However, most K-shell based approaches are designed for unweighted networks, while many real-world systems such as transportation, communication, and social networks are inherently weighted. Existing weighted extensions often suffer from low accuracy, limited resolution, or high computational cost. To address these limitations, we propose a unified K-shell based benchmark of nine centrality indices tailored to weighted networks. The core contribution is a novel measure, Dynamic Weighted K-Shell (DWKS). Instead of relying on static edge weights, DWKS applies a dynamic decomposition of weights, enabling more accurate identification of dense and influential structures. DWKS is further used to replace the classical weighted K-shell (KSW) in two existing methods, Generalized Degree Decomposition (GDD) and WKS2015, yielding two enhanced variants, DGDD and NWKS2015. In addition, two base methods, KSWExt and DWKSExt, are introduced to extend KSW and DWKS to structurally weighted unweighted networks. The proposed methods are evaluated using the SIR spreading model on nine weighted networks, including USAir97 and Email, as well as twelve unweighted networks. Results show that DWKS achieves the highest accuracy, precision, and resolution among all nine weighted K-shell based indices. Notably, DWKS achieves an average per-network relative improvement of 13.6% over KSW in terms of Tau correlation, confirming the effectiveness of the proposed benchmark for influential node identification.