基于多层复杂网络的中欧班列运输网络关键节点识别研究

若运输网络中的重要节点发生故障，中欧班列的运输效率和货物流动会受到严重制约。 本文提出一种基于改进TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution) 法及灰色关联分析的多层网络节点重要性评价方法。首先，以中欧班列运输网络结构特征为基础，构建中欧班列多层网络；其次，选取度中心性、介数中心性及接近中心性等多个评价指标，运用改进TOPSIS法计算节点单层网络重要度评价值，采取灰色关联分析融合得到节点综合重要度评价值；最后，利用多层网络SIR(Susceptible Infected Recovered Model)模型验证方法的有效性。 结果表明：本文识别出的关键节点包含中欧班列主要线路的起讫城市、境内外重要口岸和中欧班列集结中心，结果与实际情况较为契合；采用排序前10%重要节点作为初始感染节点，SIR网络感染率在 20 次迭代后达到 97.8%，本文提出方法的网络节点感染率及传播速率均高于 BC (Betweenness Centrality)算法、DC(Degree Centrality)算法和PageRank算法等传统单一网络排序方法，即识别的关键节点对全局网络的影响更为普遍和高效。此外，根据排序结果从国家层面提出相应的政策建议，有助于提高中欧班列运输网络的鲁棒性。

Key Node Identification of China Railway Express Transportation Network Based on Multi-layer Complex Network

The transportation efficiency and the associated freight flow of the China Railway Express will be severely restricted, once an important node in the transportation network fails. This paper proposes a multi-layer network node importance evaluation method based on an improved TOPSIS method and grey relational analysis. First, based on the structural characteristics of the China Railway Express transportation network, a multi-layer network is constructed. Secondly, we select evaluation indexes including degree centrality, betweenness centrality, and proximity centrality, and then apply the improved TOPSIS method to calculate the evaluation value of node importance in the single-layer network and adopt the gray relational analysis to obtain the comprehensive importance value. Finally, we use the multilayer network SIR model to verify the effectiveness of the method. The results show that: (1) the key nodes identified in this paper include the origin and destination of the main routes of the China Railway Express, important domestic and foreign ports, and the assembly centers, which indicates that the results are more in line with the actual situation; (2) the SIR network infection rate reaches 97.8% after 20 iterations by using the top 10% important nodes as the initially infected nodes. The network node infection rate and propagation rate of the method proposed in this paper are higher than those of traditional single network ranking methods such as the BC algorithm, DC algorithm, and PageRank algorithm. The impact of key nodes on the global network is more pervasive and efficient. In addition, this paper puts forward corresponding policy suggestions from the national level according to the ranking results, which can help to improve the robustness of the China Railway Express transportation network.