###### Abstract  
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. disgies engineering; rail-water intermodal transport; complex network; influential nodes identification; network performance +
Footnote †: journal: Applied Sciences  
Under the combined influence of coal supply and demand patterns, coal transportation patterns, economic layout, geographical environment, etc., China has formed a complex coal transportation network consisting of various transportation modes such as railways, highways, and waterways [7]. With the development of the national economy, the supply and demand of coal have grown rapidly, the size of the Coal Transportation Network (CTN) continues to expand, and the risks and uncertainties the network faces increase with its structural complexity and growing scale. In practical applications, the coal transportation supply chain, a complex network system comprising numerous routes, aims to meet coal demand. Its regular operation can be affected by various uncertainties. Hence, investigating supply chain vulnerability is of great theoretical significance and practical value to ensure the efficient operation of the supply chain and enhance its overall resilience [8]. Essentially, Rail-Water combined Coal Transportation Networks (RWCTN) belong to transportation networks. Complex network theory as an efficient tool has been used to study the importance evaluation of nodes in transportation networks of different modes. [PERSON] et al. [9] built a new index based on betweenness centrality, closeness centrality, and weighted node degree to evaluate the importance of nodes in Rail Transportation Networks (RTN). However, current research lacks comprehensive consideration of key node identification combining waterway and land transportation networks and mainly focuses on the impact of road network node units on the entire network in emergencies or vulnerability analysis of nodes in coal-iron-water combined transportation networks. Therefore, most of the centrality-based methods for ranking influential nodes are proposed from a certain point of view, which more or less have restrictions and merely can be carried out on some specific networks [5].