Exploring node importance evolution of weighted complex networks in urban rail transit

With the development of complex networks in urban rail transit (URT), the topological structure changes accordingly and node importance also redistributes dynamically. However, many deficiencies exist in the single measure or unweighted network or static network when ranking node importance. Most importantly, the evolution mechanism of node importance with the network development is seldom studied. In view of this, in this paper, six unweighted and weighted complex networks are firstly modeled in the evolution of URT networks. One of Multiple Attribute Decision Making (MADM) methods is proposed, that is WTOPSIS (The Weighted Technique for Order of Preference by Similarity to Ideal Solution) algorithm combining Coefficient of Variation method and TOPSIS. Then four local and global centralities are aggregated and utilized in WTOPSIS to rank the node importance in those six networks. On the basis, the intersection degrees among the ranking sets are calculated to evaluate the similarities of ranking results. Furthermore, the factors contributing to the evolution of node importance are discussed quantitatively and qualitatively with examples. Finally, the feasibility of the method is verified by the Shenzhen Metro system in 2016. Results show that WTOPSIS algorithm outperforms the single attribute in ranking node importance, which makes up for the shortcomings in existing studies. Besides, for different stations in URT network development, node importance evolution is affected differently by the changes of topological structure and passenger flow. It is necessary to combine with the actual situations for the specific analysis. This study reveals the evolution mechanism of the node importance in the development of URT networks and it also has great theoretical and practical significance.