**5. Conclusions**

Based on indicators of the railway network density, railway network proximity, the shortest travel time, train frequency, and also social-economic indicators, this study took advantage of a railway network distribution index to investigate the railway network distribution pattern in China in 2015. The results of this study could guide the optimization of the railway network structure and provide a basis for macro decision-making for the planning and evaluation of major railway infrastructure construction.

The findings were as follows: (1) In 2015, railway network density was relatively low in almost half of the counties of China. The railway network density was high in the central and eastern parts of China and relatively low in western China, and there were multiple dense railway network areas. The railway network proximity was high in nearly half of the counties in China, as was evident in the strip distribution. Based on the shortest travel time, the convenience of most counties in terms of external connections to the rest of China is generally low, with the convenience gradually rising from coastal to inland areas; the areas with the shortest travel time were mainly concentrated in the eastern region. (2) In 2015, the railway network distribution in nearly one-third of the counties of China was ideal. The distribution was grouped into two major zones with multiple dense areas. It might be advisable to strengthen the connections between large and small cities in the eastern region, so that large cities can drive the development of small cities around them. The major urban agglomerations in the midwest also could focus on several aspects such as strengthening the construction of railway facilities, promoting the movement of people and industries between the east and west regions, and increasing the urban vitality of the western region.

This study revealed the distribution pattern of the railway network in China and has significance for the optimization of the railway network structure and the development of urbanization in China. Based on the railway network distribution indicators, the national railway network is divided into five levels: insufficient railway network distribution, relatively insufficient railway network distribution, moderate railway network distribution, good railway network distribution, and perfect railway network distribution. Utilizing the advantages of the railway should be considered when planning economic development and industry activities. The five national-level urban agglomerations—Beijing-Tianjin-Hebei, the Yangtze River Delta, the Pearl River Delta, Triangle of Central China, and Chengdu-Chongqing—have moderate railway infrastructures, and local governments may harness the advantages of other transportation facilities in these regions, such as roads, aviation, and ports, to compensate for the inadequacy of the railway network, and actively participate in international economic competition to enhance China's urbanization. There are four regional-level agglomerations that have good railway network distribution—Liaozhongnan, Jianghuai, Harbin-Changchun, and Central Plains—Where the governmen<sup>t</sup> may take full advantage of the railway network and promote regional integration. The railway network distribution of other regional-level urban agglomerations and local-level urban agglomerations is moderate or relatively lacking. In the future, the local governmen<sup>t</sup> could plan for the reasonable construction of railway facilities and combine them with other modes of transportation to match the development of the population and economy.

**Author Contributions:** You Li conceptualized this research and contributed extensively to data curation and formal analysis; Minmin Li contributed to the methodology, investigation, and writing of this research; Renzhong Guo and Biao He gave ideas to validate the conceptualization and methodology; Yong Fan provided many suggestions for improving and modifying this article.

**Funding:** This research was funded by the China Postdoctoral Science Foundation, gran<sup>t</sup> number: 2018M633108, 2018M643150 and the Natural Science Foundation of China, gran<sup>t</sup> number: 41701187.

**Acknowledgments:** The authors are grateful for the "Connection value of transportation network based on breaking points model", "Research on Pole-like Furniture Recognition in Mobile Laser Scanning Data Considering the Topological Structure Between Components" and "Research on Spatial Structure and Evolution Model of Urban System based on Entropy Theory" projects of Shenzhen University. We also would like to thank Jian Sun, who works at Jilin University and gave many suggestions for improving this article.

**Conflicts of Interest:** The authors declare no conflict of interest.
