High-Speed Rail Network Structural Characteristics and Evolution in China

Abstract

Based on high-speed rail (HSR) network data from 2008 to 2020, this study explores the structural characteristics and evolution of China’s HSR network from the perspective of the overall network and urban node network centrality. We show that the overall connectivity of the HSR network has improved significantly, whereas the accessibility of the HSR network has improved slightly. Furthermore, both the density and accessibility of the HSR network in different regions gradually show a decreasing trend from the east coast zone to the southwest. We also find that from the perspective of urban node network centrality, cities with high degree centrality and high betweenness centrality are densely distributed along the northern coast, eastern coast, as well as middle reaches of both the Yellow and Yangtze Rivers. Finally, the node cities have shown a significant increase in both degree centrality and betweenness centrality; thus, both the hub role and radiation capacity have improved. Our study suggests that the government should closely monitor the development of HSR networks in the western region.

1. Introduction

In 2008, China opened the first high-speed rail (HSR), Beijing–Tianjin intercity HSR. Now, China has become the country with the longest operating mileage, highest operating speed, and largest scale of HSR construction in the world, with the significant achievement of the “three 65%”: by the end of 2021, the HSR mileage in China was approximately 41,000 km, accounting for more than 65% of the total mileage worldwide [1], in terms of passenger traffic, HSR trains carry 65% of the average daily passengers in the national railroad network [1], and HSR passenger traffic in China accounts for more than 65% of the total global traffic [2]. With the continuous construction of HSRs in China, transportation convenience brought about by HSRs has benefited 272 prefecture-level cities in 31 provincial-level administrative regions, and the coverage rate of HSR cities is as high as 75%. Notably, HSR networks are not only conducive to fundamentally alleviating the tension of railroad passenger transportation in China but also play an important role in promoting the formation of transportation economic belts, deepening the structural reform on the supply side of transportation, and promoting the high-quality development of transportation [3,4,5,6,7,8]. For instance, previous studies showed that China’s HSR has promoted firms’ exports significantly and the marginal effect is 12.7%, and the HSR increases the urban built-up area by approximately 14% in China [5,8]. However, transportation does not necessarily lead to urban economic integration, and HSR service has a significantly positive effect on short-term population mobility but a negative effect on long-term migration [9,10]. Therefore, the development of HSR increases regional differences in the long term. Cities nearby core metropolises benefit from HSR development by being more tightly connected to core metropolises and other cities in the same region; however, small and medium-sized cities not belonging to any major city cluster appear to be further lagged in HSR development [11,12].

Earlier studies on social networks have clarified the importance of the centrality concept in network analysis [13]. Albert and Barabási [14] illustrated how probabilistic network models with centrality parameters can be used to improve the estimators of the actor attributes related to centrality. Newman [15] took a deeper look at betweenness centrality, and Abbasi et al. [16] showed that the betweenness centrality of an existing node was better than the degree of closeness centrality in terms of preferential attachment. In addition, Wang et al. [17] introduced several commonly used centrality indicators to characterize the node influence, Zhao et al. [18] presented the definition of the minimum dominating set of the multiplex network, and Semenov et al. [19] examined the social media network of post-Soviet space. Furthermore, social network analysis has been applied to various forms of transportation, such as aviation. For instance, Wang et al. [20] and Su et al. [21] examined the evolution of China’s aviation network, and Chung et al. [22] explored the network characteristics of the Asian international aviation market. Finally, Su et al. [23] further analyzed the scale change and spatial distribution of the main Chinese air transport network and its role in the early spread of the pandemic. Researchers have further studied the evolution of aviation networks in other countries such as Australia, the United States, and Europe [24,25,26]. Recent studies have highlighted the connectivity and accessibility of HSR networks using case studies. Many researchers have explored the impact of HSR on airlines. For instance, Ma et al. [27] and Xu et al. [28] use a theoretical model to calculate the impact of HSR on airlines, while Zhang et al. [29] use an empirical model to explore this relationship. Furthermore, Cao et al. [30] examined the accessibility of HSR networks in 44 cities in 2011, and Wang et al. [31] found that the accessibility and density of HSR networks had increased in Jiangsu Province. Moreover, Jiao et al. [32] examined the impact of China’s HSR network on the overall connectivity and nodal centrality of a city network. Finally, Guo et al. [33] focused on 20 cities in the Yangtze River Delta region of China and explored the impact of city economic networks on HSR networks. However, owing to the huge amount of data on HSR and the difficulty of obtaining it, the previous literature has focused on China’s HSR network in partial regions or a single year.

In this study, we examine the structural characteristics and evolution of China’s HSR network from the perspective of the overall network and urban node network centrality based on HSR network data from 2008 to 2020. The main findings are presented as follows: first, the overall connectivity and accessibility of the HSR network increase, whereas the cohesion of the HSR network decreases in China. Second, from a regional perspective, the density and accessibility of the HSR network show a decreasing trend from the eastern coast to the southwest, whereas the cohesion of the HSR network shows an increasing scattering trend from the middle reaches of the Yellow River to the surrounding areas. Finally, the network centrality high-value nodes are densely distributed in the northern, eastern coastal, and middle reaches of the Yellow and Yangtze River regions, and along important railroad lines. Furthermore, the hub role of node cities is further enhanced, and the radiation capacity is continuously improved.

The remainder of this paper is organized as follows: the data and methodology are explained in Section 2. Section 3 analyzes the characteristics and evolution of China’s HSR network structure. Section 4 considers node network centrality. The final section concludes the paper.

2. Data and Methodology

2.1. Sample

According to the Medium and Long-term Railway Network Plan issued by the State Council in 2008, trains with speeds of over 200 km/h are included in the scope of China’s high-speed railway. Therefore, the three types of trains counted in this paper mainly include G-Series HSR with speeds of 300–350 km/h, D-Series HSR with speeds of over 250 km/h, and C-Series HSR with speeds of over 200 km/h. According to the opening of the HSR and network structure, the data related to HSR in 2008, 2011, 2016, and 2020 are mainly used as references. The study area consists of 251 prefecture-level cities in 31 provincial-level administrative regions in China. Note that we exclude cities in Hainan province, Hong Kong, Macao, and Taiwan. According to the construction of the social network, the HSR networks in Hainan, Hong Kong, Macao, and Taiwan are not connected to the HSR network on the mainland as a whole network; therefore, we exclude cities in these areas in this study. There are two data sources for this study: (i) the basic HSR data, which are obtained from the China Statistical Yearbook [1], and (ii) the national railroad passenger train schedule, which is provided by the China Railway Customer Service Center [34].

2.2. Network Construction

A city network of passenger trains consists of nodes and edges. The set of nodes ($V=\left\{v_i:i=1,2,\dots ,n\right\}$) is defined as the cities ($v_i$) with HSR stations in their municipal districts, and the set of edges ($E=\left\{e_i:i=1,2,\dots ,m\right\}$) is the node pair whose trains run directly between the nodes ($e_i$). Two or more HSR stations in each city are considered as one node, that is, each node in this study represents a city rather than a railway station. For instance, the nodes in Beijing included data from the Beijing West Station, Beijing Station, Beijing North Station, and Beijing South Station. In this study, according to Chen et al. [35], we adopt the P-space model which is commonly used in transportation network research to construct an HSR network, taking cities as network nodes. If there are direct transportation lines between two cities, an edge is formed between them. Figure 1 presents the network evolution in 2008, 2011, 2016, and 2020 based on the actual operation of HSR passenger trains in China.

From Figure 1a,b, we can see that in 2008 and 2011, fewer cities in China opened HSR networks, mainly in the northern and eastern coastal areas. However, from Figure 1c, in 2016, the development of China’s HSR networks made a qualitative leap, and the network took shape. This is because 2014 and 2015 are the two years with the fastest development of HSR in China, and the annual increases in HSR operating mileage are 5951 and 4746 km, respectively. From 2012 to 2016, the density of the HSR network in the northern and southern coastal regions of China further increased, and the areas with the fastest network development enhancement were mainly concentrated in the southern coastal region, middle reaches of the Yellow River, middle reaches of the Yangtze River, as well as the southwest, northwest, and northeast regions, which had slower network development because fewer cities had opened HSR networks. From Figure 1d, we see that the development of China’s HSR network tends to be complex and mature in 2020, and the changes are especially evident in the southwest, northwest, and northeast regions, such as Sichuan, Ningxia, Shanxi, and Heilongjiang provinces. Meanwhile, the HSR network in the northern coastal, eastern coastal, and southern coastal regions, as well as the middle reaches of the Yellow and Yangtze Rivers, become more connected with other regions, and the network gradually tends to mature. However, as shown in Figure 1, the HSR network in the western region is not closely connected with that in the central and eastern regions. Therefore, there are significant differences in the development of HSR between eastern and western China.

3. The Characteristics and Evolution of the Global HSR Network Structure

To analyze the characteristics and evolution of China’s urban HSR network structure, this study introduces a social network approach to abstract 251 cities that have opened HSR networks in China into 251 nodes and constructs an HSR network among 251 cities in China. In this section, we use network structure tightness, urban HSR accessibility, and network cohesion to analyze the HSR network structure from overall and regional perspectives.

3.1. Network Density Analysis

The network density D measures the interconnection between nodes and reflects the overall distribution and closeness of the entire network. This reflects the degree of interconnection between nodes in the network. The formula used is given as follows:

$$D={{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n\frac{d\left(i,j\right)}{n\left(n-1\right)},$$

(1)

where D denotes the network density, n is the number of city nodes, and $d\left(i,j\right)$ is the HSR connection between cities i and j.

We then specifically analyze the changes in the overall network density of HSR in 2011, 2016, and 2020 and compare the regional differences in the eight comprehensive economic zones in 2020. As fewer cities opened HSR in 2008 and the opened cities were on different HSR lines, an HSR social network could not be constructed. The values of China’s HSR network density for 2011, 2016, and 2020 are derived from these calculations.

The overall density of China’s HSR network shows a gradual increase during 2011–2020; however, the overall structure of the transportation network needs to be strengthened. The HSR network density was 0.147 in 2011, indicating that only approximately 15% of cities in China were connected to the HSR network. The 2012–2016 period saw the comprehensive construction of China’s “Four Vertical and Four Horizontal” HSR network, during which the Hangzhou–Fuzhou–Shenzhen passenger special line, Shanghai–Wuhan–Chengdu fast passenger channel, Shanghai–Kunming HSR line, and other routes were opened, making this the most rapid stage of China’s HSR network development and enhancement. Therefore, in 2016, the HSR network density grew rapidly to 0.265, indicating that more than a quarter of the cities in China’s HSR network were connected. In 2017–2020, the blueprint of the “Eight Vertical and Eight Horizontal” HSR network took shape. The HSR network density was 0.293 in 2020, indicating that approximately 30% of the cities were connected to the network. Overall, although China’s HSR network density has gradually increased from 2011 to 2020, the overall structure of China’s HSR network is still relatively loose, and HSR connections between cities need to be further strengthened.

The report “Strategies and Policies for Coordinated Regional Development [36],” released by the Development Research Center of the State Council in June 2005, proposed development strategies for the eight comprehensive economic zones, namely the northeast (Liaoning, Jilin, and Heilongjiang), the northern coast (Beijing, Tianjin, Hebei, and Shandong), the eastern coast (Shanghai, Jiangsu, and Zhejiang), the southern coast (Fujian, Guangdong, and Hainan), the middle reaches of the Yellow River (Shaanxi, Shanxi, Henan, and Inner Mongolia), the middle reaches of the Yangtze River (Hubei, Hunan, Jiangxi, and Anhui), the southwest (Yunnan, Guizhou, Sichuan, Chongqing, and Guangxi), and the northwest (Gansu, Qinghai, Ningxia, Tibet, and Xinjiang). Therefore, we regard the eight comprehensive economic zones as subgroups of the overall network and then calculate the density between subgroups. We explore regional differences in the HSR network in 2020 (Figure 2).

From the perspective of regional network density, the HSR network density of China’s eight comprehensive economic zones varies significantly and shows a decreasing trend from the eastern coast to the southwest. First, the density of the HSR network in the eastern coastal region is 0.888, indicating that approximately 90% of the cities in the HSR network in the eastern coastal region of China are connected in the network by 2020, and the structure of the HSR network is very close. In particular, the eastern coastal region includes the three provincial-level administrative regions of Shanghai, Jiangsu, and Zhejiang, and it is subject to the connection of several HSR trunk lines, such as the Beijing–Shanghai HSR and the coastal corridor. The HSR flow between cities is very high and the density of the HSR network in this region is the highest. Second, the HSR network densities in the northeast and northern coastal areas are 0.772 and 0.732, respectively, and the structure of the HSR transportation network is tight. That is, more than three-quarters of the cities in the northeast and northern coastal regions are connected to the network by 2020. Although the northeast region is relatively small, the construction and improvement of the HSR network are more significant in the network density through the connection of railroad trunk lines, such as the Beijing–Harbin HSR, Shenyang–Harbin HSR, and Harbin–Dalian HSR. The northern coastal region includes the four provincial-level administrative regions of Beijing, Tianjin, Hebei, and Shandong, with faster economic development but smaller regional areas [1], and its HSR network is less developed than that of the eastern coastal region.

Again, the network densities in the southern coastal, northwest, and middle reaches of the Yangtze River region are all over 0.500, and the network structure is relatively tight. More than three-fifths of the cities in the HSR network in the southern coastal region are connected to the network. Specifically, the southern coastal region includes Guangdong, Fujian, and Hainan provinces. Because the HSR in Hainan province is not connected to other provinces, it is not included in the network density calculation, which may have had an impact on the calculation of network density values in the southern coastal region. Guangdong and Fujian are fast-growing economic regions in southern China, and their HSR networks are developing rapidly. The northwest region is more remote, but cities in the region that have opened the HSR have better HSR connectivity. In addition, national transportation arteries such as the Beijing–Guangzhou HSR, Shanghai–Kunming HSR, and Beijing–Kunming HSR pass through the region in the middle reaches of the Yangtze River, providing a better basis for the overall regional connection. Finally, the HSR network densities in the southwest and middle reaches of the Yellow River are 0.491 and 0.442, respectively, with a relatively loose network structure. Southwest China is a region wherein the country has focused on building HSR networks in recent years, and there is still much room for development. In the middle reaches of the Yellow River, only Henan Province has a larger population and faster economic development, and its geographical location is closer to other economically developed regions; therefore, the development of HSR is relatively advanced. Other provinces are limited by topography and economic development [1], so the development of HSR is relatively backward and needs to be further developed.

In terms of interregional connections, there are relatively few network connections among the eight comprehensive economic zones in China. First, the northern and eastern coasts play a prominent intermediary role in the overall network, with average network densities of 0.368 and 0.457, respectively. The economically developed and strategically located northern and eastern coastal regions have stronger connections to most other regions and are most closely connected to the southern coastal region. Second, the intermediary role is more prominent in the middle reaches of the Yangtze River, the middle reaches of the Yellow River, and the southern coastal regions, with mean network densities of 0.335, 0.287, and 0.260, respectively. There are fewer connections between cities in the north and south because of their regional boundaries and spatial distribution. The middle reaches of the Yangtze River are located on the central plains, with faster economic development and closer connections with other regions. The southern coastal area has a developed economy; thus, it has more connections with other regions. Third, the intermediary roles of the northeast and southwest regions are weak, with mean network density values of 0.222 and 0.202, respectively. The northeast region is not directly connected to the northwest by HSR; therefore, the intergroup density between the northeast and northwest regions is 0. Fourth, the weakest intermediary is in the northwestern region, with a mean network density of 0.149. The northwest region has the weakest connection with other regions because of distance and geographical barriers.

3.2. Accessibility Evaluation

The average path length L measures the average number of shortest paths between all node pairs. This reflects the reachability of the network and is an important indicator of network performance. The calculation formula is given as follows:

$$L=\frac{1}{n\left(n-1\right)}{{\displaystyle \sum }}_{i\ne j}d\left(v_i,v_j\right),$$

(2)

where $d\left(v_i,v_j\right)$ is the shortest path length between nodes and n is the number of city nodes in the network. In general, a shorter average path length indicates that passengers can reach their destinations with fewer interchanges through other nodes, whereas a larger clustering coefficient implies fewer interchanges with a higher probability in the network. We then obtain the accessibility values of China’s HSR network in 2011, 2016, and 2020.

The accessibility of China’s HSR network increases significantly during the 2011–2020 period, and it shows significant phase characteristics. Overall, the average path length shows a decreasing trend with the rapid development of HSR in the last decade, and network accessibility has decreased from 1.979 in 2011 to 1.800 in 2020, representing a decrease of 9.04%. Put differently, connecting all city pairs required an average of 0.979 train interchanges in 2011, decreasing to 0.8 by 2020, indicating a significant improvement in urban accessibility in China. Moreover, HSR accessibility decreased slightly between 2017 and 2020 because, after 2017, the HSR network gradually covered the whole country, but the cities with existing HSR networks and the newly opened HSR cities in the northeast, northwest, and southwest regions were not well connected, which inhibited urban HSR accessibility.

We further explore the regional differences in the accessibility of HSR networks in 2020 (Figure 3).

From the viewpoint of network accessibility in different regions, the overall accessibility of HSR in China’s eight comprehensive economic zones shows a decreasing trend from east to southwest. First, the eastern coast and northwest region have the strongest network accessibility, with average path lengths of 1.112 and 1.167, respectively, indicating that all cities within the eastern coast need only 0.112 interchanges on average, and regional accessibility is the strongest. Note that in the “Eight Vertical and Eight Horizontal” HSR network, the Land Bridge Passage and the Qingdao–Yinchuan Passage pass through the interior of the northwest region, and these two HSR lines connect the cities in the northwest region that have jointly opened HSR networks. The northeast and northern coastal regions had better regional accessibility, with network accessibility values of 1.228 and 1.268, respectively. Once again, the network accessibility of the southern coastal and middle Yangtze River regions is weak, at 1.387 and 1.496, respectively. The accessibility of HSR is slightly weaker than that of the previous four regions but relatively better. Finally, the accessibility values of the middle reaches of the Yellow River and the southwest region are 1.516 and 1.541, respectively, and the average number of inter-city transfers required between these two regions is greater than 0.500.

In terms of interregional network accessibility averages, the regional differences are not significant. The eastern coastal region, with an average path length of 1.451, has the most convenient connections with other regions. Next, the average accessibility values of the northwest, north coast, and northeast regions are slightly weaker than that of the east coast, with average path lengths of 1.505, 1.506, and 1.530, respectively. Again, the middle reaches of the Yangtze and Yellow Rivers are less accessible on average, with average path lengths of 1.610 and 1.655, respectively. Finally, the southern coastal and southwestern regions have the weakest average accessibility, with average path lengths of 1.715 and 1.762, respectively. Cities in the northwestern region with HSR networks are not directly connected to cities in the northeastern region by HSR; therefore, there is no accessibility value between the two regions.

3.3. Network Cohesion

The clustering coefficient $C\left(v_i\right)$ is a transfer function that reflects the local cohesion of the nodes of the network. The local clustering coefficient C is the average of the clustering coefficients of all nodes, and it measures the degree of clustering in the vicinity of each node in the graph. It is a coefficient that reflects the degree of aggregation of the entire network, indicating the local cohesiveness of the network. The local clustering coefficients of the nodes are given by the ratio of the connectivity between nodes in the neighborhood divided by the number of possible connected edges between them:

$$C=\frac{1}{n}{{\displaystyle \sum }}_{v_i\in V}C\left(v_i\right)=\frac{1}{n}\frac{2\left|\left\{a_{ij}:v_i,v_j\in N_i,a_{ij}\in A\right\}\right|}{k_i\left(k_i-1\right)},$$

(3)

where $N_i=\left\{v_j:a_{ij}\in A\right\}$ is the set of nodes immediately adjacent to the node, $k\left(i\right)$ is the number of nodes, and $a_{ij}$ is the node directly connected to the node. Thereafter, we obtain the cohesion of China’s HSR network in 2011, 2016, and 2020.

The cohesiveness of China’s HSR network decreases significantly between 2011 and 2020 and shows significant phase characteristics. In 2011, there were fewer cities with HSR networks in China; therefore, the cohesiveness of the network mainly focused on the cohesiveness of individual city nodes. With the construction of “Four Vertical and Four Horizontal” HSR lines, the number of core city nodes increased and the clustering coefficient decreased significantly, from 0.909 in 2011 to 0.677 in 2016. After 2016, China’s HSR construction gradually slowed down, and the network construction gradually shifted from increasing urban nodes to the connection between nodes; thus, the value of the local clustering coefficient increased slightly, indicating that China’s HSR network was increasingly developed, and individual urban nodes could become nearby cores. An increase in the agglomeration of city nodes indicates that the cohesiveness of China’s HSR network is gradually increasing and that an increasing number of cities can become core nodes.

To explore regional differences in the cohesiveness of the HSR network, the cohesiveness values of China’s regional HSR network in 2020 are further calculated by taking the eight comprehensive economic zones as the unit (Figure 4).

In terms of network cohesiveness across the different regions, the cohesiveness of China’s eight comprehensive economic zones in the HSR network shows a trend of increased scattering from the middle reaches of the Yellow River to the surrounding areas. Similar to network accessibility, cohesiveness is generally high in different regions. First, the eastern coastal region has the highest network clustering coefficient of 0.919, indicating high internal network cohesion in the region. Second, the clustering coefficients of the middle reaches of the Yangtze and Yellow Rivers are 0.755 and 0.734, respectively, indicating that there is still room for the development of the degree of HSR clustering within these two regions. Finally, the western regions have network clustering coefficient values exceeding 0.800, indicating a high degree of intra-regional cohesion in the HSR network.

In terms of inter-regional network cohesion, with an increase in geographical distance, the degree of network cohesion among the different regions in China gradually decreases. The mean values of the clustering coefficients in the northeast, east coast, and northwest regions rank relatively high among the eight comprehensive economic zones, indicating a high degree of HSR network clustering in these regions. Although fewer cities in the northeast and northwest regions have opened HSR, inter-city cohesion is high; the eastern coastal region has a more developed HSR network overall, and the cohesion is higher. However, the mean values of the clustering coefficients of the northern coastal, southern coastal, southwestern, middle Yangtze River, and middle Yellow River regions are lower than 0.800, indicating that the degree of cohesion of the HSR networks in these regions is low.

Finally,

Table 1. The overall density, accessibility, and cohesion of the HSR network.

Year	2011	2016	2020
Density	0.147	0.265	0.293
Average path length	1.979	1.708	1.800
Clustering coefficient	0.909	0.677	0.682

summarizes the HSR network density in 2011, 2016, and 2020.

4. City Node Network Centrality

We use degree centrality and betweenness centrality to analyze the hub role and radiation capacity of China’s major city nodes in the HSR network from 2011 to 2020.

4.1. Measures

The degree centrality, $C_D\left(v_i\right)$, measures the ability of a single node to communicate with other nodes, and it refers to the number of nodes connected to other nodes. It characterizes the importance of a node in the region; the greater the degree centrality of a node, the greater its connectivity. The calculation formula is as follows:

$$C_D\left(v_i\right)=\frac{{{\displaystyle \sum }}_{j=1}^n{a}_{ij}\left(i\ne j\right)}{n-1},$$

(4)

where $a_{ij}$ is the node directly connected to node i and n is the number of city nodes in the network.

The betweenness centrality, $C_B\left(v_i\right)$, measures the ability of a node to become an intermediary for other nodes, quantifies the control of a node over connections between other nodes in the network, and measures the transferability of individual nodes in the network. This is calculated as follows:

$$C_B\left(v_i\right)=\frac{{{\displaystyle \sum }}_{j<k}\frac{g_{jk}\left(i\right)}{g_{jk}}}{\frac{1}{2}\left(n-1\right)\left(n-2\right)},$$

(5)

where $g_{jk}$ is the number of paths that exist between city j and city k, and $\frac{g_{jk}\left(i\right)}{g_{jk}}$ indicates the probability that city i is on the path between city j and city k.

4.2. The Analysis

We observe the distribution of cities with different centralities in the eight comprehensive economic zones on the map according to the specific values of the degree centrality of the opening of HSR in Chinese cities in 2020. Figure 5 shows the scattered distribution of cities with an HSR degree centrality in China. To analyze the distribution of centrality of different cities in China more clearly, only the cities to which the premium stations and first-class stations belong are identified in the scatter diagram.

As shown in Figure 5, cities with a high degree of centrality are concentrated in the northern and eastern coastal areas, and most of them are located along the “Eight Vertical and Eight Horizontal” important railway lines of China’s HSR network, such as the Land Bridge Passage, Longhai Line, and Shanghai–Kunming Passage. First, Beijing is the only city with a degree centrality over 200, with a value as high as 208, indicating that Beijing has the strongest hub role in China’s HSR network. Cities with a degree centrality greater than 150 and less than 200 are Shanghai, Zhengzhou, Nanjing, Changsha, Wuhan, Hangzhou, and Wuxi, which are concentrated on the eastern coast, as well as the middle reaches of the Yellow and Yangtze Rivers, and they have a very significant hub role in the HSR network. Second, cities with a degree centrality greater than 100 and less than 150 have a significant hub role in the network; they are still mainly concentrated in the abovementioned regions, and a few, such as Guangzhou, Chongqing, Chengdu, and Shenzhen, are distributed in the southwestern and southern coastal areas.

Again, the number of cities with a degree centrality greater than 50 and less than 100 is the largest, accounting for 39.4% of all cities, but the distribution is relatively scattered, mainly in the northeast, northwest, and southwest regions, and mostly located in traffic arteries. Owing to topographic factors, distance, and other reasons, relatively few cities in these regions have opened HSR networks, and the period is relatively short, hence there is still much room for the development of the city’s hub role in the HSR network. Finally, the number of cities with a degree centrality of less than 50 is high, accounting for 33.9% of all the cities. In general, at present, China’s core cities are highly centralized, and most cities with a low degree of centralization are distributed around developed cities in various regions and enter the HSR network through their connection to large cities.

Based on the specific values derived from the opening of China’s HSR in 2020, Figure 6 shows the scattered distribution of cities with HSR betweenness centrality in China.

Figure 6 shows that cities with high betweenness centrality have a strong radiation capacity in China’s HSR network and are densely distributed along the eastern and northern coasts, as well as the middle reaches of the Yangtze and Yellow Rivers, which are the most important node cities on the railroad lines. Beijing has the highest betweenness centrality in China, with a value of 4767. Second, most cities with betweenness centrality values greater than 500 and less than 1000 are located in the northern, eastern coastal, and middle reaches of the Yellow and Yangtze Rivers, whereas a few cities, such as Lanzhou and Chengdu, are distributed in the northwest and southwest regions. These are the larger cities in the region; other cities in the region mainly transit through these transit hubs and have a strong radiation capacity in the HSR network. Third, the largest number of cities have betweenness centrality values greater than 100 and less than 500, accounting for 39.0% of all cities, among which Shenyang and Jinzhou, located in the northeast, are important cities on the Beijing–Harbin line, and are the necessary places for cities in the northeast to enter Beijing and other cities. Fourth, the number of cities with a betweenness centrality of less than 100 is high, accounting for 53.3% of all cities, and the distribution is relatively scattered, mainly located in the northeast, northwest, southwest, and southern coastal regions. Owing to differences in geographical location, the cities in these regions cannot connect and penetrate the overall network as hubs.

To analyze the changes in the centrality of major cities in China more specifically, the top 20 cities are ranked based on degree centrality and betweenness centrality in 2020.

Table 2. Top 20 cities in terms of centrality in 2020.

${\mathit{C}}_{\mathit{D}}\left({\mathit{v}}_{\mathit{i}}\right)$				${\mathit{C}}_{\mathit{B}}\left({\mathit{v}}_{\mathit{i}}\right)$
	City	2020	2011		City	2020	2011
1	Beijing ─	204	22	1	Beijing ─	4767	35
2	Shanghai ─	191	22	2	Zhengzhou ↑	1695	6
3	Zhengzhou ↑	189	4	3	Xi’an ↑	1684	6
4	Nanjing ↓	173	22	4	Chengdu ↑	1540	0
5	Changsha ↑	165	16	5	Shanghai ↓	1506	35
6	Wuhan ↓	164	16	6	Guangzhou ↓	1409	20
7	Hangzhou ─	162	14	7	Shijiazhuang ↑	1078	6
8	Suzhou ─	154	22	8	Lanzhou ↑	997	-
9	Guangzhou ↓	148	13	9	Nanjing ─	793	35
10	Changzhou ↑	146	-	10	Changsha ↑	737	25
11	Shijiazhuang ─	146	4	11	Wuhan ↓	714	25
12	Wuxi ─	146	22	12	Ji’nan ↑	710	24
13	Hefei ↑	146	18	13	Changchun ↑	704	1
14	Xi’an ↑	144	4	14	Chongqing ↑	642	-
15	Xinyang ↑	141	-	15	Suzhou ↑	641	34
16	Xuzhou ↓	141	-	16	Hangzhou ↓	634	22
17	Chongqing ↑	141	-	17	Tianjin ↓	575	34
18	Ji’nan ↓	137	15	18	Wuxi ↑	540	34
19	Zhenjiang ─	137	22	19	Changzhou ─	516	-
20	Nanchang ↑	136	1	20	Guiyang ─	507	-

shows the changes in the centrality values of these cities over the different years. Among them, “─, ↑, ↓” after the city name indicates the change in the city’s ranking after comparing 2011, meaning the same, up, and down, respectively. A “-” in the place of the centrality value means that the city has not yet opened an HSR network that year.

Furthermore, Figure 7 shows the geographical location of the Top 20 cities in terms of centrality in China.

From the evolution of network centrality, the degree and betweenness centralities of the top 20 cities in the centrality ranking from 2011 to 2020 show a significant increasing trend. Among them, the top-ranked cities in 2020 are located on the Longhai Line, Shanghai–Kunming corridor, and other traffic arteries, which also constitute an important part of China’s “Eight Vertical and Eight Horizontal” HSR network, mostly located in the northern, eastern, and southern coastal areas. First, cities with rising rankings are Zhengzhou, Changsha, Chongqing, and Nanchang. These cities are the most important provincial capitals in the middle reaches of the Yellow and Yangtze Rivers. Although most of them opened the HSR after 2011, they developed very rapidly. Nanjing, Wuhan, Guangzhou, Xuzhou, and Ji’nan rank the lowest. Most of these cities are provincial capitals in economically developed regions, with many years of operating HSR and steady development of HSR construction, but relatively declining in ranking as other cities develop faster. Finally, cities with unchanged rankings are Beijing, Shanghai, Hangzhou, Shijiazhuang, Wuxi, and Zhenjiang, mainly located in the northern and eastern coastal regions. These cities developed their HSR networks early and have been growing steadily over the past decade, with their rankings remaining unchanged.

Compared with degree centrality, the ranking of betweenness centrality is more variable, and the values significantly differ between cities. The top-ranking cities in terms of betweenness centrality in 2020 are mostly provincial capitals or cities located at the intersection of national railroad trunk line transportation corridors. First, cities with rising rankings include Zhengzhou, Xi’an, Chengdu, Shijiazhuang, Lanzhou, Changchun, Chongqing, and Suzhou. These cities are scattered across the middle reaches of the Yellow and Yangtze Rivers, as well as the southwest and northeast, and they are the most important hub cities in their respective regions. Among these, the city with the fastest increasing ranking is Lanzhou, which is an important hub city in China’s western provinces, and the main HSR lines passing through Lanzhou are the Xulan HSR line, Lanzhou–Chongqing HSR line, and Lanzhou–Urumqi passenger line, all of which are important components of the “Eight Horizontal” HSR network in China. Changchun in the northeast region occupies a position similar to Lanzhou and is located in the center of the northeast region. Second, cities with decreasing rankings are Shanghai, Guangzhou, Wuhan, and Hangzhou, all of which are economically developed cities in China with relatively developed HSR construction. Their rankings relatively decrease with the development of other cities, indicating that the radiation capacity of these cities in the HSR network is relatively decreasing. Third, cities with unchanged rankings are Beijing, Nanjing, Changzhou, and Guiyang, indicating that the radiating capacity of these cities in the HSR network remains unchanged during the decade.

To compare and analyze the hub and radiation roles of China’s major cities in the HSR network in 2020, the centrality of each city in the quadrant diagram is depicted based on the cities where the premium and first-class stations are located (Figure 8). The X−axis is the degree centrality, and the Y-axis represents the betweenness centrality. Based on the centrality values of different cities in 2020, the degree centrality and betweenness centrality (100, 100) are selected as the coordinate origins. As shown in Figure 8, cities in different quadrants are mainly divided into three categories: (i) cities in the first quadrant have high degree centrality and high betweenness centrality, indicating that these cities have a wide radiation range of HSR and occupy an important hub position; (ii) cities in the second quadrant have low degree centrality but high betweenness centrality, indicating that these cities have an important hub role; and (iii) cities in the third quadrant have low degree centrality and betweenness centrality, indicating that these cities are weak in both HSR radiation and hub functions.

The cities in the first quadrant can be further divided into three categories: (i) cities with relatively high degree and betweenness centralities (i.e., $C_D\left(v_i\right)>180$ and $C_B\left(v_i\right)>1500$), which are the most important hub cities in the HSR network with strong radiation capacity, such as Beijing, Shanghai, and Zhengzhou; (ii) cities with intermediate degree and betweenness centralities (i.e., $140<C_D\left(v_i\right)<180$ and $500<C_B\left(v_i\right)<1500$), but still more important, such as Nanjing, Wuhan, Changsha, and Guangzhou, which have more developed transportation networks and can play a better connecting role; and (iii) cities with relatively low degree and betweenness centralities (i.e., $100<C_D\left(v_i\right)<140$ and $100<C_B\left(v_i\right)<500$), such as Chengdu, Nanchang, Ji’nan, and Fuzhou. These cities have convenient transportation and are well connected to other cities.

The cities in the second quadrant are less central but more intermediate, with degree centrality greater than 80 and less than 100 and betweenness centrality greater than 100 and less than 500, such as Shenyang, Jinzhou, Lanzhou, Changchun, Taiyuan, Nanning, and Qinhuangdao. These cities play a significant intermediary role and are important transportation hubs in various regions; however, their radiation capacity is weak. In addition, Lanzhou is the most important hub city in the northwest region, Qinhuangdao is a necessary place for the northeast region to enter customs, and Liupanshui and Nanning are important transportation hubs in the southwest region.

The cities in the third quadrant can be further divided into two categories: (i) cities with degree centrality greater than 50 and less than 80 and betweenness centrality greater than 50 and less than 100, such as Quanzhou, Harbin, Dalian, and Yantai. These cities have been open for a short period, and their radiation capacity and hub role still have more room for development; and (ii) cities with degree centrality greater than 30 and less than 50 and betweenness centrality greater than 5 and less than 50, such as Shantou, Daqing, and Yinchuan. These cities are generally located in the northeast and northwest regions, with a few located in the middle reaches of the Yellow River, southern coast, and southwest regions.

Finally, the cities with extremely low degree and betweenness centralities (i.e., $0<C_D\left(v_i\right)<30$ and $0<C_B\left(v_i\right)<5$), such as Chaoyang, Fuxin, and Mudanjiang, could not be represented on the quadrant map. Most of these cities are located in the northeast and northwest regions and are relatively backward in terms of economic development. Owing to the “lag” in the opening of HSR, the positive impact of the opening of HSR on small cities around big cities will be gradually reflected in future development.

5. Conclusions

The rapid development of HSR significantly affects the accessibility and connectivity of cities in the transportation network, thereby influencing the location advantages of cities and their positions in the urban relationship network. In this study, we use three overall network indicators (i.e., network density, average path length, and clustering coefficient) and two node centrality indicators (i.e., degree centrality and betweenness centrality) to analyze the overall situation of the HSR network and city nodes among 251 cities in China in the context of the “Eight Vertical and Eight Horizontal” HSR networks. Based on the eight comprehensive economic zones, we explore the structural characteristics and evolution of the HSR network from 2008 to 2020.

The main conclusions of this study are presented as follows: first, with increasing values of network density, the overall HSR network density in China shows a gradually increasing trend, but the overall structure of the transportation network needs to be strengthened. From the perspective of network density in different regions, the current density of the HSR network in China’s eight comprehensive economic regions shows a decreasing trend from the eastern coast to the southwest; from the perspective of inter-regional network connection, the northern and eastern coasts in the overall network are the most prominent. Second, with the decline in the average path length, the accessibility of China’s HSR network substantially increases but shows significant phase characteristics. From the viewpoint of network accessibility in different regions, the overall regional HSR accessibility in China decreases from the eastern coast to the southwest; from the viewpoint of inter-regional network accessibility, the accessibility gap in different regions is not significant. Third, with a decline in the clustering coefficient, the cohesiveness of China’s HSR network decreases more significantly but shows considerable stage characteristics. From the viewpoint of network cohesion in different regions, the current regional network cohesion shows a trend of increasing scattering from the middle reaches of the Yellow River to the surrounding areas; from the viewpoint of inter-regional network cohesion, the overall cohesion is high but the value changes are not significant. Fourth, the evolution of China’s HSR network has gradually changed the hub position and radiation capacity of cities in the network, and cities with high centrality rankings have gradually shifted from the core hubs of the transportation network to densely populated and economically developed areas. Fifth, cities such as Beijing, Shanghai, Zhengzhou, Wuhan, and Hangzhou rank high in degree centrality, and they have a wide range of hubs in the HSR network. Cities such as Beijing, Zhengzhou, Lanzhou, and Chengdu have high betweenness centrality and a strong radiation capacity in China’s HSR network, the vast majority of which are located on the main railroad lines, such as the Longhai Line and Shanghai–Kunming Passage, which are spatially coupled with the locations of regional railroad bureaus.

The findings of this study are important for identifying the city hierarchy in China’s HSR network. The continuous construction of HSR networks has improved the connectivity of cities along these lines, especially those that are densely populated and economically developed. Therefore, as the development of China’s HSR network has increased, cities at the center of the network have gradually shifted from core hubs in the economic network to densely populated and economically developed cities. Cities that have risen in the ranking of HSR network centrality should give full play to their hub role, continuously expand their radiation range, and promote the leapfrog development of the economy and society. China’s HSR network is still under further construction, and this study provides a platform for assessing the impact of HSR on urban development to monitor the long-term progress of HSR development. Policymakers should focus on HSR development in the western region to further enhance the role of HSR construction in promoting regional economic development.

In this study, we use network structure tightness, urban HSR accessibility, and network cohesion to analyze the HSR network structure from overall and regional perspectives. These are standard metrics in the literature. However, other metrics such as eigenvector centrality, small-world characteristics, and clique networks could be further used. This remains for future research.