Li Shaobao, Quan Yiran, Luo Xiaoyuan, Wang Juan
School of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China.
Sci Rep. 2025 Apr 3;15(1):11440. doi: 10.1038/s41598-025-94193-w.
dentifying critical nodes in complex networks presents a significant challenge that has garnered extensive research attention. Previous studies often overlook the importance of spatial information, thereby limiting the accurate identification of key nodes. To address this gap, we introduce an advanced centrality model, termed Degree-k-shell-Betweenness Centrality (DKBC), which is grounded in the principle of gravity. The DKBC model integrates the centrality attributes of node degree, spatial positioning, and intermediate degree, resulting in improved accuracy for key node identification in complex networks. This innovative approach outperforms traditional gravity-based methods in terms of effectiveness. We validated the diffusion capacity of the proposed model using the Susceptible-Infected-Recovered (SIR) epidemic model and the Independent Cascade (IC) model, assessing correlation through the Kendall coefficient τ. A comparative analysis with benchmark algorithms highlights the superior performance of the DKBC model. Empirical validation across twelve real-world networks demonstrates the model's exceptional accuracy in identifying key nodes. This study significantly advances the field by illustrating the effectiveness of incorporating spatial information into centrality measures to enhance both network analysis and practical applications.
识别复杂网络中的关键节点是一项重大挑战，已引起广泛的研究关注。以往的研究往往忽视了空间信息的重要性，从而限制了关键节点的准确识别。为了弥补这一差距，我们引入了一种先进的中心性模型，称为度-k壳-介数中心性（DKBC），它基于引力原理。DKBC模型整合了节点度、空间定位和中间度的中心性属性，提高了复杂网络中关键节点识别的准确性。这种创新方法在有效性方面优于传统的基于引力的方法。我们使用易感-感染-恢复（SIR）流行病模型和独立级联（IC）模型验证了所提出模型的扩散能力，并通过肯德尔系数τ评估相关性。与基准算法的比较分析突出了DKBC模型的优越性能。对十二个真实网络的实证验证表明该模型在识别关键节点方面具有卓越的准确性。本研究通过说明将空间信息纳入中心性度量以增强网络分析和实际应用的有效性，显著推进了该领域的发展。
