Gray Correlation Entropy-Based Influential Nodes Identification and Destruction Resistance of Rail-Water Intermodal Coal Transportation Network.

Evaluating the importance of nodes in coal transportation networks and identifying influential nodes is a crucial study in the field of network science, vital for ensuring the stable operation of such complex networks. However, most existing studies focus on the performance analysis of single-medium networks, lacking research on combined transportation, which is not applicable to China's coal transportation model. To address this issue, this paper first establishes a static topological structure of China's coal-iron-water combined transportation network based on complex network theory, constructing a node importance evaluation index system through four centrality indicators. Subsequently, an enhanced TOPSIS method (GRE-TOPSIS) is proposed based on the Grey Relational Entropy Weight (GRE) to identify key nodes in the complex network from local and positional information dimensions. Compared to previous studies, this research emphasizes composite networks, breaking through the limitations of single-medium network research, and combines gray relational analysis with entropy weighting, enhancing the objectivity of the TOPSIS method. In the simulation section of this paper, we establish the model of China's coal-iron-water combined transportation network and use the algorithm to comprehensively rank and identify key nodes in 84 nodes, verifying its performance. Network efficiency and three other parameters are used as measures of network performance. Through simulated deliberate and random attacks on the network, the changing trends in network performance are analyzed. The results show that in random attacks, the performance drops to around 50% after damaging nearly 40 ordinary nodes. In contrast, targeting close to 16 key nodes in deliberate attacks achieves a similar effect. Once key nodes are well protected, the network exhibits a certain resistance to damage. [ABSTRACT FROM AUTHOR]