**3. Results**

#### *3.1. Spatial Pattern of Railway Network Density*

China's railways, which are divided into ordinary and high-speed railways, currently provide important support for regional external relations. Figure 2 shows the distribution pattern of the railway network density based on the county-level administrative regions of China and reflect the ability of railway facilities to support the development of a county.

The following features of the distribution pattern of the railway network density are noteworthy: (1) The total length of railways in China is 77,800 km, and the total railway network density is 0.0082 km/km2. According to medium- and long-term railway network planning (2016-2030), by 2025, the railway network needs to reach about 175,000 km, of which the high-speed railway will account for about 38,000 km. (2) Railway connections are not found in 44.79% of counties. The lengths of railways are relatively short in some counties, so their densities are also low. For example, the railway network density between 0 and 0.01 km/km<sup>2</sup> in 195 counties (8.83% of all counties), and such counties have low support capacity for development. The railway network density is between 0.01 and 0.03 km/km<sup>2</sup> in 617 counties (27.94% of total counties); between 0.03 and 0.05 km/km<sup>2</sup> in 253 counties (11.46%). Only 6.97% of counties have railway network densities higher than 0.05 km/km2, and the railway contributes significantly to the development of these counties. (3) Railway network density is high in the central and eastern parts of China, while it is relatively low in the western part of China. In eastern China, in particular, the railway network density of the south is lower than that of the north. (4) Some regions of the railway network are particularly dense, including the Beijing-Tianjin region, the Yangtze River Delta region, and the Zhengzhou, Wuhan, and Chengdu Economic Zone. These areas have high spatial coupling with economic agglomeration and an urban system [36]; thus, railway networks have a significant ability to support the socioeconomic development of China's dense urban areas.

Generally speaking, the development of China's railway network has supported the rapid urbanization process to a certain extent, it based on the considerable population and economic scale, the construction of the railway network needs to be strengthened further to realize national railway connectivity, high-speed railways between provincial capitals, the rapid arrival of intercity railways, and the distribution of basic coverage to all counties by 2030 [37].

**Figure 2.** The spatial pattern of China's railway network density in 2015.

#### *3.2. Spatial Pattern of Railway Network Proximity*

The railway network proximity can reflect the external accessibility and convenience of travel of a county. The spatial pattern of railway network proximity at the county level is shown in Figure 3, and has the following main characteristics: (1) The railway network proximity is 0 in 369 counties (16.71% of all counties), indicating a lack of accessibility. The number of counties with a railway network proximity of 0–0.5, and thus a lower supporting capacity for development, is 486 (22.01% of the total). The railway network proximity of 168 counties is in the range 0.5–1.0 (7.61% of all counties), suggesting a positive effect of the railway network on the development of these counties. The highest railway network proximity is found in 53.67% of the counties in China, which indicates that the railway network plays an important role in the development of these counties. (2) The railway network proximity is high in the central and eastern parts of China, it relatively low in western China, which indicates that railway network proximity has a stronger supporting capacity in eastern counties than in western counties. (3) In eastern China, there is a clear spatial difference in railway network proximity between the north and the south. For example, the northeastern region, Inner Mongolia, the capitals of Ningxia and Qinghai provinces, Beijing-Tianjin-Hebei, the Yangtze River Delta, Wuhan, and Chongqing have a high railway network proximity, while the southern region has a low railway network proximity and presents a strip distribution.

**Figure 3.** The spatial pattern of China's railway network proximity in 2015.

#### *3.3. Spatial Pattern of the Shortest Travel Time*

The shortest travel time shows the external connectivity of the railway network and is an important indicator to measure the regional railway network structure and external geographical connections. The spatial pattern of the shortest travel time at the county level is shown in Figure 4, and has the following main characteristics: (1) The shortest travel time is less than 9 h in 304 counties (13.77%), indicating that these counties have the highest degree of ease of external connection. The shortest travel time is 9–12 h in 594 counties (26.90%; higher degree of ease of external connection); 12–15 h in 166 counties (7.52%; lower degree of ease of external connection); and greater than 15 h in 1144 counties (51.81%; lowest degree of ease of external connection). (2) The shortest travel time has significant spatial differences throughout the country, characterized by a gradual rise from the coast to inland, and a concentration of areas with the shortest travel time in the eastern region. (3) Hachang agglomeration, Beijing-Tianjin-Hebei, the Yangtze River Delta (Shanghai, Nanjing, Hefei, and Hangzhou), the Pearl River Delta, Wuhan, Nanchang, and Changsha have the shortest travel time, and cover a wide area.

Generally speaking, based on the shortest travel time, the convenience of the railway network in China is generally low. On the one hand, this is due to restrictions placed on the construction of railways by the natural terrain; on the other hand, because the national railway system is not perfect, it is still necessary to strengthen the railway links and exchanges within the inter-regional and urban agglomerations.

**Figure 4.** Spatial pattern of the shortest travel time by railway of China in 2015.

#### *3.4. Spatial Pattern of Railway Network Distribution*

The railway network density, railway network proximity, and the shortest travel time reflect the contribution of the railway network to each county's development, and demonstrate the counties' future development potential. Integrating these three indicators and combining train frequency, population, GDP, gross industrial value above designated size, and fixed asset investment, the spatial pattern of the railway network in China was determined by setting the weight of each factor using the AHP method, as shown in Figure 5. The weights of each indicator obtained by the AHP method were 0.1569, 0.2273, 0.3268, 0.1077, 0.0242, 0.0734, 0.0498, and 0.0340, respectively, and the consistency ratio was found to be CR = 0.03 < 0.1 which was through the consistency test. Hence, the normalized eigenvectors can be used as weight vectors.

The railway network distribution index is divided into five levels, namely, 0–0.01, lacking railway network distribution; 0.01–0.20, relatively lacking in railway network distribution; 0.20–0.35, moderate railway network distribution; 0.35–0.45, good railway network distribution; and >0.45, perfect railway network distribution. The following are the main observations of the railway network distribution in China: (1) 660 counties (29.89%) have a perfect railway network distribution, which provides the strongest support for future development; 423 counties (19.16%) have a good railway network distribution, indicating strong support for future development; 99 counties (4.48%) have moderate railway network distribution, and railway facilities in these areas have general support capacity but have strong development potential and opportunities; and 1026 counties (46.47%) lack railway network distribution and do not provide enough support for future development. (2) The railway network distribution index shows a pattern of decline from coastal counties toward the interior of the country, with the highest railway network distribution indices in coastal counties and the lowest indices in western counties and parts of central counties. (3) The railway network distribution index is significantly higher in central and eastern counties than in western counties, for example, Beijing-Tianjin-Hebei, the Yangtze River Delta, the Pearl River Delta, Chengdu-Chongqing, the Wuhan metropolitan area, the North Gulf Area, Shandong Peninsula, and Hachang District have higher railway network distributions than other areas of China, and also have strong development support.

Generally speaking, the railway network distribution of China is relatively e ffective, especially in the eastern region, where a relatively complete railway connection network exists, while the western region has a relatively inadequate network distribution. In the future, it might be advisable to strengthen the connections between large cities 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 central and western areas also could focus on strengthening the construction of railway facilities to promote the movement of people and industries between the east and west regions, thereby increasing the urban vitality of the western region.

**Figure 5.** Spatial pattern of the railway network of China in 2015.

The distribution of railway network and economic development are mutually influential. The construction of railway infrastructure would promote the economic development of the region. Similarly, the economic development would also a ffect the operation and development of the railway infrastructure of the region. In this study, it is reasonable to take population and economic factors as indicators that reflect the characteristics of railway network distribution. Many scholars have studied the relationship between transportation infrastructure network and economic development, which was the 'chicken and egg' problem. For example, Xie and Levinson (2009) provided an overview of transportation networks following five main streams: network growth in transport geography; tra ffic flow, transportation planning, and network growth; statistical analyses of network growth; economics of network growth; and network science [38]. The review pointed out the positive interaction between economic development and transportation network construction. Levinson (2007) examined the changes that occurred in the rail network and density of population in London during the 19th and 20th centuries, and the research found that there was a positive feedback e ffect between population density and network density [39].
