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

Scale-free networks exhibit high heterogeneity, which enhances robustness against random attacks but creates vulnerability to targeted assaults. Current key node identification methods often neglect the structural hole nodes, leading to biased prioritization of key nodes. This study proposes a structural hole-driven method that integrates structural holes importance indices with Mixed Degree Decomposition to optimize node importance evaluation. Experiments were conducted on multi-scale networks, including synthetic Barabási-Albert networks, a real-word dolphin social network, a large-scale power grid(Western U.S. power grid), and a collaboration networks(co-authorship network). The method outperforms algorithms (degree centrality, betweenness centrality, E-Bur, Mixed Degree Decomposition, and Tensor-Centric Hybrid Method) in structural hole-aware accuracy, ranking comprehensiveness, and computational efficiency. Deliberate attack simulations demonstrate its superior effectiveness: progressively removing top-ranked nodes disrupts connectivity faster, achieving structural collapse (Structural Largest Connected Component SLCC ≤ 0.03) with only 17.1% node removal, surpassing degree centrality (29.0% node removal required), betweenness centrality (18.5% node removal required), E-Burt algorithm (21.5% higher node removal required), Mixed Degree Decomposition (28.6% node removal required), and Tensor-Centric Hybrid (23.6% node removal required). The proposed algorithm achieves an effective balance between computational complexity and high identification accuracy for critical infrastructure and collaboration network analyses.