Zhao Xinyun, Zhang Yongheng, Zhai Qingying, Zhang Jinrui, Qi Lanlan
Electronic Engineering Institute, National University of Defense Technology, Hefei 230037, China.
Institute of Mathematics, Hefei University of Technology, Hefei 230601, China.
Entropy (Basel). 2024 Dec 9;26(12):1075. doi: 10.3390/e26121075.
Correctly identifying influential nodes in a complex network and implementing targeted protection measures can significantly enhance the overall security of the network. Currently, indicators such as degree centrality, closeness centrality, betweenness centrality, H-index, and K-shell are commonly used to measure node influence. Although these indicators can identify critical nodes to some extent, they often consider node attributes from a narrow perspective and have certain limitations. Therefore, evaluating the importance of nodes using most existing indicators remains incomplete. In this paper, we propose the multi-attribute CRITIC-TOPSIS network decision indicator, or MCTNDI, which integrates closeness centrality, betweenness centrality, H-index, and network constraint coefficients to identify critical nodes in a network. This indicator combines information from multiple perspectives, including local neighborhood importance, network topological location, path centrality, and node mutual information, thereby solving the issue of the one-sided perspective of single indicators and providing a more comprehensive measure of node importance. Additionally, MCTNDI is validated through the analysis of several real-world networks, including the Contiguous USA network, Dolphins network, USAir97 network, and Tech-routers-rf network. The validation is conducted from four aspects: the results of simulated network attacks, the distribution of node importance, the monotonicity of rankings, and the similarity of indicators, illustrating MCTNDI's effectiveness in real networks.
正确识别复杂网络中的有影响力节点并实施针对性保护措施，可显著提高网络的整体安全性。目前，度中心性、接近中心性、中介中心性、H指数和K壳等指标常用于衡量节点影响力。尽管这些指标能在一定程度上识别关键节点，但它们往往从狭隘的角度考虑节点属性，存在一定局限性。因此，使用大多数现有指标评估节点重要性仍不完整。在本文中，我们提出了多属性CRITIC-TOPSIS网络决策指标（MCTNDI），它整合了接近中心性、中介中心性、H指数和网络约束系数来识别网络中的关键节点。该指标结合了来自多个视角的信息，包括局部邻域重要性、网络拓扑位置、路径中心性和节点互信息，从而解决了单一指标视角片面的问题，并提供了更全面的节点重要性度量。此外，通过对几个真实网络的分析对MCTNDI进行了验证，包括美国 contiguous 网络、海豚网络、USAir97网络和技术路由器射频网络。验证从模拟网络攻击结果、节点重要性分布、排名单调性和指标相似性四个方面进行，说明了MCTNDI在真实网络中的有效性。
