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Understanding the structure of the Chinese railway network (CRN) is crucial for maintaining its efficiency and planning its future development. To advance our knowledge of CRN, we modeled CRN as a complex weighted network and explored the structural characteristics of the network via statistical evaluations and spatial analysis. Our results show CRN as a small-world network whose train flow obeys power-law decaying, demonstrating that CRN is a mature transportation infrastructure with a scale-free structure. CRN also shows significant spatial heterogeneity and hierarchy in its regionally uneven train flow distribution. We then examined the nodal centralities of CRN using four topological measures: degree, strength, betweenness, and closeness. Nodal degree is positively correlated with strength, betweenness, and closeness. Unlike the common feature of a scale-free network, the most connected nodes in CRN are not necessarily the most central due to underlying geographical, political, and socioeconomic factors. We proposed an integrated measure based on the four centrality measures to identify the global role of each node and the multilayer structure of CRN and confirm that stable connections hold between different layers of CRN.

Characterizing the Structure of the Railway Network in China: A Complex Weighted Network Approach