**1. Introduction**

Railways are a basic element of transportation systems and have played a key role in social and economic development in many countries since the 19th century. With the recent rapid development of urbanization in China, by the end of 2016, the length of the railway network had reached 1.24 × 10<sup>5</sup> km, and the length of China's high-speed rail (HSR) network was nearly 66 times that of the United States (United States: 362 km) [1]. China's first HSR route (Shenyang–Qinhuangdao), on which trains operate at a speed of 200 km/h, opened in 2003, almost 50 years after the world's first HSR route in Japan in 1964. By July 2013, however, China had the largest HSR network in the world (at 9760 km), accounting for 46% of the world's total [2]. At the same time, China's GDP (USD 11.20 trillion) is only three-fifths that of the United States (USD 18.62 trillion) [1], which implies a potential mismatch between railway investment and economic development and highlights the significance of having an efficient and comprehensive railway system. Evaluating the railway network distribution and its impact on social and economic development is an important area of research in economic geography and regional

economics [3,4]. Accessibility has long been a central issue in transport geography and is a commonly used indicator in the field of transportation network analysis, transport planning, and land use [5,6].

Accessibility is a popular measure for assessing the overall spatial structure of a transportation network [7]. In 1959, Hansen was the first to define accessibility as the size of the interactions between nodes in a transportation network, and he suggested a method to measure it in metropolitan areas [8]. In 1979, Morris stated that accessibility is the means to reach a given activity site from a certain place by a specific transportation system [9]. Since the formation of these definitions, accessibility has been a central theme in transportation studies, and its measurement can be divided into three groups based on function: spatial separation, cumulative opportunity, and spatial interaction measures [10]. The first group involves calculating the topological length, the shortest distance, time, or cost between two nodes [11,12], and only measures the connectivity of the transportation network. The second group focuses on the proximity of cities to development opportunities and involves estimating the size of the population or the scale of the economic activities that can be reached from a node within a certain period of time [13,14]. The third group comprises what are called potential values [15,16].

The advantages and disadvantages of the three groups are as follows. The methods of the first group take the cost of the individual flows in the transportation network into account, it do not consider the distance attenuation and the magnitude of the force at each point. The methods of the second group essentially measure accessibility by evaluating the convenience of a certain point of travel, without considering the interaction between the measurement point and the attraction point and the attenuation of its spatial e ffect with distance. The methods of the third group combine the spatial e ffect, distance, and gravitational scale of each attraction point in space to measure the accessibility—the larger the force between an attraction point and the measurement point, the smaller the distance between them and the higher the accessibility level.

In summary, scholars have developed research methods and applications for railway accessibility, laying a methodological foundation for the study of railway network distribution. The above methods are used to analyze the spatial e ffects of transportation accessibility or transportation conditions from di fferent perspectives. However, although many scholars have macroscopically analyzed railway distribution, a method that systematically and comprehensively evaluates the railway network distribution combined with the social economy is still lacking. This is need to further refine the system mechanism of the railway network and shape the regional spatial structure.

Therefore, based on the passenger railway networks, this study constructs a railway network distribution index including assessment of the railway network density, railway network proximity, the shortest travel time, train frequency, and social-economic indicators, to explore the characteristics of China's railway network distribution in 2015. This method could be used to optimize railway network structure and as a macro-level decision-making reference for evaluating major railway projects.

#### **2. Materials and Methods**

#### *2.1. Research Area and Data Sources*

In China, the administrative divisions are divided into provincial administrative districts, prefecture-level administrative districts, county-level administrative districts, and the town-level administrative districts. The county-level administrative districts include city-governed districts, county-level cities, counties, autonomous counties, flags, autonomous flags, special zones, and forest areas [17]. In this study, county-level administrative districts are used as the basic statistical unit, and city-governed districts are merged into one.

There are many distribution structures of urban agglomerations according to di fferent criteria and principles. In China, the main urban agglomerations structures are Shimou Yao's "6 + 7" plan [18], Chaolin Gu's "3 + 3 + 7 + 17" plan [19], and Chuanglin Fang's "5 + 9 + 6" plan [20]. In this paper, Chuanglin Fang's "5 + 9 + 6" plan is used to discuss the railway network distribution with regard to urban agglomeration, because this plan takes China's major function-oriented zoning [21] and

national urban system planning for 2006–2020 into account [22] and can describe urban agglomeration comprehensively. Focused on the new urbanization policy, this plan scientifically cultivates large, medium and small scale and gradient urban agglomerations, building five national-level urban agglomerations (Yangtze River Delta, Pearl River Delta, Beijing-Tianjin-Hebei, Triangle of Central China, and Chengyu), nine regional-level urban agglomerations (Harbin-Changchun, Shandong Peninsula, Liaozhongnan, West side of the Straits, Central Plains, Guanzhong Plain, Jianghuai, Beibu Gulf, and Tianshan North Slop), and six local-level urban agglomerations (Hubaoeyu, Jinzhong, Ningxia along the Yellow River, Lanxi, Dianzhong, and Qianzhong), promotes the coordinated development of urban agglomerations at di fferent levels, and forms a new system of "5 + 9 + 6" spatial structure of China's urban agglomerations. This plan provides a scientific prescription for rational construction of urban agglomerations, plays the high-end think tank of the development of the national urban agglomerations, promotes the urban agglomerations as the main body for the new urbanization, and also makes an important decision-making support for the construction of the urban agglomerations.

Due to China's accelerated economic and social development, the country is divided into four major economic regions: the eastern region, which includes Beijing City, Tianjin City, Hebei Province, Shanghai City, Jiangsu Province, Zhejiang Province, Fujian Province, Shandong Province, Guangdong Province, and Hainan Province; the northeast region, which includes Liaoning Province, Jilin Province, and Heilongjiang Province; the central region, which includes Shanxi Province, Anhui Province, Jiangxi Province, Henan Province, Hubei Province, and Hunan Province; and the western region, which includes Inner Mongolia, Guangxi, Chongqing City, Sichuan Province, Guizhou Province, Yunnan Province, Tibet, Shanxi Province, Gansu Province, Qinghai Province, Ningxia, and Xinjiang [23]. The main features of economic and social development in the various regions are the development of the western region, the revitalization of the northeast region, the rise of the central region, and the leading development in the eastern region.

The specific data sources, shown in Table 1, included (1) land area, population, GDP, gross industrial value above designated size, and fixed asset investment by county-level administrative districts of China for 2015, obtained from the China County Statistical Yearbook and the China City Statistical Yearbook [24,25]; and (2) 2015 vector data of the railway line network, railway stations, and train frequency, acquired from the website of https://www.amap.com/ and the Railway Customer Service Center of China using web crawler technology. Specifically, land area, population, GDP, gross industrial value above designated size, fixed asset investment, and train frequency data are spatialized and divided into each county-level administrative districts of China; the railway line network and railway station data have gone through error analysis and correction, format conversion, projection conversion, scale consistency and other processing, being prepared for the subsequent county-level data overlay analysis.


**Table 1.** Data sources for the railway network distribution of China in 2015.
