Key Nodes Identification Method in Scale-Free Network Based on Structural Holes

Scale-free networks exhibit high heterogeneity, enhancing robustness against random attacks but creating vulnerability to targeted assaults. While current key node identification methods (e.g., degree centrality, betweenness centrality) often neglect structural hole nodes or suffer from high computational costs, this can lead to biased prioritization of key nodes. This study proposes a novel hybrid method that integrates structural holes importance indices with Mixed Degree Decomposition (MDD) to optimize node importance evaluation. It introduces two innovations: Dynamic multi-hop bridge detection, extending beyond the 2-hop limitation of E-Burt to quantify long-range bridging influence efficiently; and a weighted fusion model balancing coreness (via MDD) and bridging roles (via structural holes) with linear time complexity.Experiments on synthetic (Barabási-Albert), social (dolphin), infrastructure(Western U.S. power grid), and collaboration (co-authorship) networks demonstrate superiority. In deliberate attack simulations, the proposed algorithm triggers structural collapse (Structural Largest Connected Component $\mathrm {SLCC}\le 0.03$ ) with only 17.1% node removal, outperforming degree centrality (18.5% node removal required), E-Burt algorithm (21.5% higher node removal required), MDD (28.6% node removal required), and Tensor-Centric Hybrid (23.6% node removal required). The proposed algorithm achieves higher accuracy in structural hole-aware ranking compared to benchmarks while maintaining ${ O}\left ({{ m+n.logn }}\right)$ complexity. It achieves an effective balance between computational complexity and identification accuracy for critical infrastructure and collaboration network analyses.