Journal of Advanced Transportation
Volume 2019 (2019), Article ID 1493206, 16 pages
https://doi.org/10.1155/2019/1493206

Research Article

Exploring the Node Importance and Its Influencing Factors in the Railway Freight Transportation Network in China

Qipeng Sun,1,2 Xiaozhuang Guo,1,2 Wenjing Jiang,¹ Haiying Ding,³ Tingzhen Li,1,2 and Xingbo Xu¹

¹School of Economics and Management, Chang’an University, Xi’an, China
²Integrated Transportation Economics and Management Research Center, Chang'an University, Xi’an, China
³Shaanxi College of Communication Technology, Xi’an, China

Correspondence should be addressed to Xiaozhuang Guo; 13201581776@163.com

Received 24 October 2018; Revised 8 February 2019; Accepted 11 March 2019; Published 26 March 2019

Academic Editor: Luigi Dell'Olio

Copyright © 2019 Qipeng Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Node importance is a key factor affecting the overall operation efficiency of a railway freight transportation network (RFTN) that can be measured with the indicators of Hub and PageRank. Based on complex network theory and the national railway cargo exchange data of China’s provinces, this study constructs an RFTN model with the 31 provinces as the nodes and measures the values of Hub and PageRank for the 31 provinces. Then, the time evolution law of the importance of the provincial nodes is analyzed comprehensively, and, using a regression model, the influencing factors of the importance of the provincial nodes are identified. The results show the following. (1) The uneven distribution of natural resources will affect the spatial changes in the importance of RFTN nodes. The Hub values tended to cluster around the average, and the economic structure of the output-oriented provinces improved as a whole. At the same time, the PageRank values of many provinces in the central and western regions significantly increased, and those provinces exhibited more frequent exchanges of goods with other provinces and closer economic ties with other regions. (2) The traffic fixed asset investments and the population density have the most obvious influences on the importance of the provincial nodes with a positive effect. In contrast, the railway freight concentration (RFC) coefficient, geographical location (longitude and latitude), and coastal region all have negative effects on the importance of provincial nodes. The results of this study provide scientific decision-making support for the reasonable establishment and distribution of RFTN hubs in China.

1. Introduction

The transportation network, which constitutes one of the three major networks (transportation, energy, and information) created by human society, lays an important foundation for the development of modern human civilization [1] and plays vital roles in the movement of people, the exchange of goods, and the regional development of the economy. The distributions of both natural resources and socioeconomic elements are unbalanced and therefore form unique regional economic and spatial structures. This imbalance and unique regional economic and spatial structures promote the production and transportation of goods between regions [2]. The transportation of goods is a manifestation of the flow of elements such as resources and products, thereby reflecting the economic relationship or functional division between geographic units in addition to the strength of the interactions between regional economic activities and trade. China possesses a vast territory in which the distributions of natural resources and socioeconomic elements are extremely unbalanced. Therefore, railway cargo transport in China facilitates a large span of economic relations and mutual exchanges through transport tasks [3]. By the end of 2017, China boasted a total railway operating mileage of 127,000 kilometers, and a total of 3.689 billion tons of freight were hauled in 2017. Railway cargo transport thus plays an extremely important role in China's economic development [4].

The development of a railway freight transportation network (RFTN) constitutes a significant public policy objective intended to support long-term sustainable economic growth and regional cohesion and competitiveness throughout the country. Moreover, the economic ties between regions are generally considered to be interdependent, and the intensities of their connections present complex interaction rules in association with the traffic infrastructure and the levels of traffic and transport activities [5]. Consequently, the construction of an RFTN should be based on China's long-term development strategy and the interaction laws of regional economic relations and the RFTN should be designed according to the overall optimal network efficiency. For this purpose, the layout of freight terminals is highly critical; that is, it represents an important node setting in the network. However, in the actual operation of China's railway cargo transportation hub, more consideration is given to the administrative regionalization, mainly based on the direct technical and economic feasibility, whereas less emphasis is placed on the impacts of the regional economic connection strength and network efficiency. As a result, numerous problems, such as a poor distribution of goods and poor economies of scale, are encountered, thereby reducing the overall efficiency of the RFTN.

“In the presence of transport hubs, which typically constitute the components (main nodes) of wider transport corridors, the relationship between increasing returns in production and falling transport costs has been found to generate persistent lock-in effects due to self-reinforcing agglomeration up to a certain threshold, beyond which these effects vanish and a new productive specialization pattern emerges [6–8]” (the content inside the quotes comes from Tsekeris [9]). The hub location problem is regarded as a relatively new extension of the traditional facility location problems and is typically treated within the generalized context of the network design problem. Hubs are facilities that serve the consolidation, connection, and interchange of freight flows among origin-destination markets and are typically modeled as points in space. In hub-based logistics networks, economies of scale allow for cost savings stemming from the consolidation of interhub flows [10]. However, the existing literature does not sufficiently consider railway freight transportation hubs from a network perspective. Instead, scholars have paid more attention to the multimodal transport organization level in hub problems [11–13] and the optimization of hub locations at the strategic decision-making level in addition to optimization algorithms [14, 15]. These studies provide an important reference for the study of railway freight transport hubs, but they were not conducted from a network perspective. It is consequently difficult to consider the interactions of cargo flows among network nodes, and establishing freight hubs based on these interactions to maximize the overall network efficiency is problematic.

The rise and perfection of complex network theory and related methods have provided powerful tools for the analysis of the node characteristics of transportation networks from a network perspective, and, thus, those tools can better express the interactive relationships among the nodes in the network. This theory has been applied with increasing frequency in the transportation system [16–18]; for example, complex network theory has been employed in research on aviation networks both nationally (in India and China) and globally [19–26] in addition to studies on the complex subway system networks in Boston, Beijing, and Kuala Lumpur [27–29], the characteristics of complex urban road networks [30–32] and complex global shipping networks [33–35], the topological nature of the Indian railway network [36, 37], and the topological features of China's railway network [38, 39].

Node importance analysis is an important component of the analysis of complex network characteristics. Guimerà et al. [21] compared the importance of global air transport network nodes (cities and airports) with topological statistical properties, such as the degree of adoption and intermediary centrality. Oum et al. [40] studied the importance of air cargo network nodes, Ducruet et al. [41] and Li et al. [17] studied the importance of shipping network nodes, and Wang and Cullinane [42] studied the status of port centers in the maritime container transport network and its influencing factors. These studies showed that research on the node importance can provide more valuable solutions for freight hub problems from a network perspective. However, few studies have been performed on the importance and influencing factors of the RFTN. This may be related to the complexity of the RFTNs in specific regions. With the rapid development of China's economy and the continuous improvement of the railway infrastructure therein, China's RFTN encompasses an enormous scale with a relatively large intensity of freight exchanges between hubs, and thus the network characteristics are more complex than those of other countries. Hence, this study on the importance of China's RFTN nodes using complex network theory incorporates the theoretical and practical considerations needed to adequately reflect the real situation and is more representative than previous studies.

Based on the above analysis, this study selects China’s RFTN as the research object, examines the node importance index in complex network theory to measure the importance of the Chinese RFTN nodes, and analyzes the evolution law of the importance of the Chinese RFTN nodes; by screening the relevant factors, a regression model is established to identify the size and direction of the factors affecting the importance of RFTN nodes. The research results provide a theoretical basis for the effective planning and layout of the China Railway Freight Network Hub.

The other sections of this thesis are structured as follows. Section 2 provides the method for constructing an RFTN and the method for calculating the importance of the RFTN nodes, analyzes the influencing factors on the RFTN nodes, and describes the source of the research data. Section 3 presents the calculation results, which are then analyzed and discussed. Finally, Section 4 presents the conclusions derived from the findings of this thesis.

2. Methodology and Data

2.1. The Methodology and Data for Constructing an RFTN

In this study, the geographical location of each provincial capital in China is coded to build an RFTN. As a result, China’s RFTN is defined as a directional weighted network . The node set is defined as , where is the number of nodes and each node is a province of China. Specifically, we define the capital of each province to represent the province. Here, we regard the provinces as nodes in China's RFTN because the railway freight transport nodes in China are generally set up according to administrative divisions. The economic development level and policy orientation of each province will directly affect the importance of the nodes, and the edges represent the interactions of transport between the provinces. Selecting provinces as nodes is beneficial to distinguishing the administrative advantages of the provinces and obtaining more effective resources and means for improving the importance of the nodes, making the analysis results of the papers more useful. China's railway transportation data is also based on provincial statistics, and the selection of provinces as the nodes is also conducive to improving the accuracy of the paper’s calculation results. The edge set is defined as , where is the number of edges and the edge is an interaction of transport between provinces. The weight of an edge is the amount of transportation between the provinces, the direction of the edge in the network represents the direction of interprovincial freight flow, and its weight is calculated by the interprovincial rail freight interaction.

The mutual volume of transported goods between regions was derived from the statistics of exchanged goods between China's national railway administrative regions in the Yearbook of China Transportation & Communications and the China Statistical Yearbook. The dataset corresponds to 31 provinces between 2005 and 2016. From 2005 to 2014, the volume of interregional rail freight transport was derived from the Yearbook of China Transportation & Communications [43], whereas the data of 2015 and 2016 were derived from the China Statistical Yearbook [44]. China has 34 provinces. Since Hong Kong, Macau, Taiwan, and mainland China do not have direct rail cargo exchanges, the study area is mainland China, excluding Hong Kong, Macao, and Taiwan. According to the above definition, China’s RFTN is shown in Figure 1.

Figure 1: China's RFTN in 2005 and 2016; the legend represents the freight volumes (weights).

2.2. Measuring the Node Importance of the RFTN

Many indexes used for measuring the importance of nodes exist in complex network theory. To consider the interaction strength of the transportation of goods between regions, this study selects two indexes, namely, Hub and PageRank.

(i)Hub: Hub was originally used to explore node sequencing and important node connections in cargo transportation networks and logistics networks. “This measure simultaneously refers to the out-degree connectivity of a province and the in-degree connectivity of the provinces to which the province is linked. It is based on the well-known iterative link analysis algorithm of the HITS algorithm [45]” (the content inside the quotes comes from Tsekeris [9]). According to the HITS algorithm, if a province has a higher Hub value in the Chinese railway freight transport network, it can be considered a key node that promotes the interaction of railway goods in other provinces. The Hub value is thus higher for provinces with outgoing freight flows to more accessible (high in-centrality) provinces.(ii)PageRank: the PageRank algorithm was originally used to calculate web page traffic rankings; it calculates the ranking of web traffic by changes in the traffic between pages [46]. In this paper, the PageRank value can be considered another way to measure the relative importance of each province in the railway freight transport network by considering all direct and indirect links in the transport network and the interaction of goods (weights). It depicts the role of a node (province) as a center in terms of attracting flows from all other nodes in the network, thereby providing a plausible metric of its accessibility [47].

This study uses NetworkX [48] to calculate the Hub and PageRank values in the RFTN. We set the default parameters for the HITS algorithm as follows: max_iter (maximum number of iterations in power method) =100; tol (error tolerance used to check convergence in power method iteration) =1e-08; nstart (starting value of each node for power method iteration) =None; and normalized (normalize results by the sum of all of the values) =True. Similarly, the PageRank algorithm was initialized with the following parameters: alpha (damping parameter for PageRank) =0.85; personalization (the “personalization vector” consisting of a dictionary with a key for some subset of graph nodes and the personalization value of each of them) =None; max_iter=100; tol=1e-06; nstart=None; weight (edge data key to use as weight)= “weight”; and dangling (the outedges to be assigned to any “dangling” nodes) =None.

2.3. Methodology and Data for Detecting the Influencing Factors on the Node Importance

By analyzing the influencing factors on the importance of each provincial node of the RFTN, we can more scientifically explore effective ways to improve both the cargo distribution capacity of a railway freight hub and the overall efficiency of the railway freight network. As a key node of the high-intensity economic connection between provinces and regions, the importance of a railway freight transport hub is affected by many factors, such as the socioeconomic development, geographical conditions, and resource distribution.

Tsekeris [9] chose the economic development, population density, geographical location, and transport channels, among other factors, for an investigation into the influencing factors of the Greek trade network hubs and found that the hub role of a prefecture is strongly influenced by high population densities and manufacturing specialization in addition to its location along highway corridors. Wittman and Swelbar [49] showed that the macroeconomic environment has a great impact on transport hubs. In the period of 2007-2012, the US air transportation system experienced a series of changes as a result of the global financial crisis in addition to high fuel prices and airlines’ profit-focused capacity discipline strategies. The connectivity at medium hub airports declined the most (15.6%), while large hub airports lost only 3.9% of their connectivity. In addition, according to the new economic geography theory, the existence of a transportation hub often represents a favorable geographical position, which can further enhance the economic vitality of a region and promote regional economic development [50, 51]; a transportation hub also promotes the efficiency of railway freight transportation turnover and improves the cargo transportation accessibility, which represents the performance of the agglomeration economy.

Following the above discussion, based on theoretical considerations and in accordance with the relevant economic theory, we considered the macroeconomic environment and the impacts of resource endowments in various regions on the importance of the railway transport network nodes. The factors influencing the importance of the RFTN nodes and the regression model are specified as follows:

where

(i) is the importance of a node (Hub and PageRank) for province in year .(ii) is the population density of province in year . The population density is calculated by the following equation: , where and denote the population and area of province in year .(iii) is the GDP of province in year .(iv) is the highway density of province in year .(v) is the value of the transportation fixed asset investment of province in year . Constrained by the acquired data, the transportation infrastructure investment in this study includes railway, highway, storage, postal, and other transportation infrastructure investments.(vi) is the railway freight concentration (RFC) in year . It indicates the concentration of China’s railway freight volume at the provincial level, reflecting the degree of monopoly of the Chinese railway freight market at the provincial level. To measure this more accurately, this paper uses the calculation method of the HHI (Herfindahl-Hirschman index) from industrial economics to measure the index. The RFC is calculated by the equation , where is the railway freight traffic of province in year and is the total railway freight transport volume of all provinces in year .(vii) denotes the longitude of the capital city in each province.(viii) denotes the latitude of the capital city in each province.(ix) is a dummy variable to indicate whether province is in a coastal region. If province is in a coastal region, then the variable is equal to 1; otherwise, it is equal to 0.(x) is a dummy variable and an abbreviation for the Yangtze River Economic Zone, which is an important inland shipping center in China. If province belongs to the YEZ, it is counted as 1; otherwise, it is 0.(xi) is a dummy variable and an abbreviation for the Silk Road Economic Belt. If province belongs to the area of ​​the SREB, it is counted as 1; otherwise, it is 0.(xii) signifies a resource-based province and is a dummy variable. If province is a resource-based province, it is counted as 1; otherwise, it is 0. The resource-based provinces here refer to those containing abundant natural resources such as coal and ore, and the economic growth mainly depends on the output of natural resources.(xiii) is a variable controlling for the global financial crisis between 2008 and 2009.(xiv) is a variable controlling for the macroeconomic conditions ranging from 2014 to 2016. In 2014, substantial changes took place in the macroeconomic conditions of the Chinese government, and the “new normal” development model was proposed. The “new normal” economic model states that the industrial structure of China's economy has been readjusted from extensive development to sustainable development, the speed of economic development has changed from high-speed growth to moderate-high growth, and the industrial structure has been continuously optimized.

In this study, all continuous explanatory variables are taken to be logarithmic in the estimation, as this approach removes nonlinearities and limits changes in the variance [9]. We use one-year lagged values of all time-variant variables for the estimation to avoid the potential endogeneity caused by the simultaneity between these variables and the explanatory variables.

In (1), is an error term, and we assume the error term to consist of a time-invariant province-specific unobservable . In the model, we use panel-specific first-order autocorrelated AR (1) residuals; that is, . Because the Breusch-Pagan [52]/Cook-Weisberg [53] test rejects the null hypothesis of homoscedasticity (or constant error variance), the sample data have heteroscedastic properties. “Psarian’s test of cross-sectional correlation also rejects the null hypothesis that the residuals are uncorrelated, and therefore, the model is specific to the panel-specific AR (1) residuals” (the content inside the quotes comes from Tsekeris [9]); at the same time, because the number of cross sections in the given dataset is greater than the time series, we have a large N and small T panel. Therefore, “we chose the panel-corrected standard error (PCSE) estimator for linear cross-sectional time-series models [54]. To facilitate a comparison and test for the robustness, the spatial correlation consistent standard error (SCCSE) estimator for linear panel models [55] was applied in this study. The SCCSE estimator constitutes a modification of the PCSE estimator to provide robust parameter estimates of general forms of the cross-sectional (spatial) as well as temporal (autocorrelation) dependence; in contrast to the empirical assumption, the spatial correlations are the same for every pair of prefectures, as the SCCSE estimator uses a nonparametric time-series covariance matrix estimator to adjust the standard error estimates in a consistent way that is independent of the cross-sectional dimensions [9]” (the content inside the quotes comes from Tsekeris [9]).

The provincial population, provincial GDP, transportation fixed asset investment data of each province, and railway freight traffic of each province are available in the China Statistical Yearbook [56]. The longitude and latitude data are obtained through Python and Baidu MAP API platforms. The provinces included in the coastal region, the YEZ, and the SERB in addition to the resource provinces are listed in Table 1. Table 2 provides the summary statistics of our variables, and the correlations among the explanatory variables are shown in Table 3.

Table 1: Provinces included in the coastal region, the YEZ, and the SREB and the resource provinces.

Coastal region
Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi, Hainan

YEZ
Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Guizhou, Yunnan

SREB
Guangxi, Chongqing, Sichuan, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang

Resource provinces
Shanxi, Inner Mongolia, Liaoning, Heilongjiang, Anhui, Shandong, and Henan

Table 2: Descriptive statistics of the variables.

Variable
No. of Obs
Mean
Std. Dev
Min
Max
Unit

Hub
372
0.03
0.12
0
0.7467788
Unit

PageRank
372
0.03
0.02
0
0.0865906
Unit

Provincial PopDen
372
0.04
0.06
0.0002329
0.3825895
Ten thousand people per square kilometer

Provincial GDP
372
15502.66
14390.62
248.8
80854.91
Billion RMB

Highway density
372
0.79
0.48
0.0363449
2.097461
Kilometers per square kilometer

Provincial fixed asset investments
372
829.51
665.11
32.48
3737.95
Billion RMB

RFC
372
0.09
0.01
0.0835294
0.1228885
Unit

Longitude
372
111.94
8.78
87.56499
126.6577
Unit

Latitude
372
33.37
6.61
20.02207
45.77322
Unit

Coastal region
372
0.35
0.48
0
1
Dummy

YEZ
372
0.35
0.48
0
1
Dummy

SREB
372
0.29
0.45
0
1
Dummy

Resource-based province
372
0.23
0.42
0
1
Dummy

Crisis
372
0.17
0.37
0
1
Dummy

The “new normal” economic model
372
0.25
0.43
0
1
Dummy

Table 3: Correlations among the independent variables.

PopDen
GDP
HighwayDen
Fixedasset
RFC
Longitude
Latitude
Coastalregion
YEZ
SREB
Resource
Crisis
Newnormal

PopDen
1

GDP
0.24
1

HighwayDen
0.68
0.59
1

Fixedasset
0.05
0.81
0.40
1

RFC
-0.03
-0.27
-0.32
-0.26
1

Longitude
0.37
0.37
0.49
0.20
-0.39
1

Latitude
-0.05
-0.11
-0.19
-0.15
0.04
0.17
1

Coastalregion
0.40
0.45
0.36
0.26
-0.20
0.40
-0.26
1

YEZ
0.24
0.13
0.40
0.18
-0.27
0.07
-0.43
-0.13
1

SREB
-0.29
-0.32
-0.40
-0.13
-0.02
-0.63
-0.03
-0.33
-0.03
1

Resource
-0.09
0.13
0.05
0.06
-0.10
0.34
0.42
-0.08
-0.24
-0.35
1

Crisis
-0.01
-0.13
-0.02
-0.19
0
0
0
0
0
0
0
1

Newnormal
0.02
0.32
0.15
0.53
0
0
0
0
0
0
0
-0.26
1

3. Results and Discussion

3.1. Analysis of the Node Importance Calculation Results

The Hub and PageRank values of all research provinces are listed in Appendices A and B, and the changes in Hub and PageRank in 2005-2016 in all provinces are shown in Figures 2 and 3. From the Hub calculation results, the provinces with higher Hub values are relatively stable, and the Hub values tend to cluster around the average, indicating that the importance of the nodes in the provinces is similar and that the economic structure of the provinces based mainly on the output has improved. This is basically consistent with the reality insomuch as China's economic structure has been continuously optimized and that the protection measures for the environment and resources are continuously being strengthened. The PageRank values of many provinces in the central and western regions have increased significantly, indicating that goods are exchanged between the central and western provinces and other provinces more frequently. This is basically consistent with China’s economic development status and the Silk Road Economic Belt initiative.

Figure 2: The evolution of Hub from 2005 to 2016.

Figure 3: The evolution of PageRank from 2005 to 2016.

Comparisons of the top six provinces in 2005 and 2016 with regard to the Hub and PageRank values are shown in Tables 4 and 5. These comparisons show that the six provinces with the highest calculated Hub and PageRank values are very different; this finding is related to the calculation methods for these two indicators. Hub is calculated by the out-degree of each node, whereas PageRank is calculated by the sum of the out-degree and in-degree. Therefore, the six provinces with the highest Hub values are those that export resources such as coal, timber, and minerals; the exception is Tianjin, which is one of the largest railway marshaling stations in China and an important railway hub connecting Northeast China to the North China Plain. The top-ranked PageRank provinces are Guangdong, Jiangsu, and other provinces characterized by a developed economy, high inputs of resources, and high product outputs, in addition to western provinces such as Sichuan and Chongqing that possess traffic location advantages. This is basically consistent with reality and represents the embodiment of China’s resource distribution pattern consisting of the Northern Coal South Transportation and Western Oil East Transportation systems within the railway freight network. At the same time, according to changes in the calculation results of the Hub index, the top six provinces from 2005 to 2016 are basically unchanged; most of them are resource-exporting provinces. This finding also shows that the mass freight transportation in China’s RFTN still accounts for a large proportion. Meanwhile, from the changes in the calculation results of PageRank, during the period from 2005 to 2016, the importance of southwestern provinces with a relatively low economic development level increased. Sichuan rose from the 5th to the 1st, while Guangdong with a higher economic development level fell from 1st to 5th. This finding shows that both the volume of railway input and the volume of railway output are increasing in the provinces of Southwest China and that the level of economic development therein is rising rapidly.

Table 4: Top-ranked provinces in 2005 and 2016 based on Hub.

2005
2016

Rank
Province
Hub
Rank
Province
Hub

1
Shanxi
0.627
1
Shanxi
0.735

2
Inner Mongolia
0.082
2
Inner Mongolia
0.117

3
Shandong
0.038
3
Tianjin
0.035

4
Heilongjiang
0.031
4
Shandong
0.024

5
Tianjin
0.03
5
Shaanxi
0.017

6
Hebei
0.027
6
Hebei
0.008

Table 5: Top-ranked provinces in 2005 and 2016 based on PageRank.

2005
2016

Rank
Province
PageRank
Rank
Province
PageRank

1
Guangdong
0.063
1
Sichuan
0.087

2
Hebei
0.062
2
Yunnan
0.081

3
Hunan
0.054
3
Guangxi
0.067

4
Guangxi
0.051
4
Guizhou
0.06

5
Sichuan
0.049
5
Guangdong
0.055

6
Jiangsu
0.049
6
Chongqing
0.046

The changes in the top six provinces according to the calculated Hub and PageRank values in 2005-2016 are shown in Figures 4 and 5. The changes in the Hub values shown in Figure 4 are all fluctuating, but the variation trends are quite different. Shanxi and Tianjin are generally on the rise, which is related to the large scale of coal transportation in Shanxi and the location advantages of the Tianjin transportation hub. Shandong and Hebei show an overall downward trend related to the rapid development of highways and shipping ports in Shandong Province and the continuous decline in the scale of steel production in Hebei Province. As seen from the changes in PageRank in Figure 5, Guangdong shows a downward trend, while all the others show upward trends, which is consistent with the comparative analysis results of the calculated PageRank values in Table 5.

Figure 4: Top-ranked provinces in 2005-2016 based on Hub.

Figure 5: Top-ranked provinces in 2005-2016 based on PageRank.

3.2. Presentation and Discussion of the Regression Results

Before reporting the regression results, we first discuss the correlations among the explanatory variables. As shown in Table 3, the Fixedasset variable (transportation fixed asset investment) has a high positive correlation with the GDP and HighwayDen variable, and HighwayDen also exhibits a high positive correlation with PopDen. Therefore, when referring to the estimates of the Fixedasset and HighwayDen variables, we need to consider the mediation of the effects of Fixedasset and HighwayDen on GDP and PopDen, respectively. In addition, we observe a relatively high positive correlation between HighwayDen and GDP, indicating a multicollinearity problem between these variables. However, the multicollinearity caused by the high correlation among the variables affects only the estimation efficiency but not the consistency, indicating that we can still obtain unbiased estimators [57]. Therefore, we still include these variables in the estimation model to avoid potential endogeneity problems caused by the omission of variables.

The results of the determinants of Hub and PageRank using the PCSE and SCCSE estimators are collated in Table 6; the results are very similar. Accordingly, this article will discuss the effects of the explanatory variables on Hub and PageRank by explaining the regression coefficients of the variables and the significance of the statistics. If the sign of the regression coefficient is positive, it has a positive effect on Hub and PageRank, and vice versa. The value of reflects the degree of influence of the explanatory variable on Hub and PageRank; the larger the regression coefficient is, the greater the influence is, and vice versa.

Table 6: Results of the determinants of Hub and PageRank using the PCSE and SCCSE estimators.

Dependent variable
Hub
PageRank

Explanatory variable
PCSE
SCCSE
PCSE
SCCSE

PopDen
0.0201∗∗∗
0.0201∗∗
0.0027∗∗
0.0027∗

(0.0074)
(0.0088)
(0.0015)
(0.0021)

GDP
-0.0631∗∗∗
-0.0631∗∗
-0.0011
-0.0011

(0.0188)
(0.0201)
(0.0024)
(0.0046)

HighwayDen
-0.0127
-0.0127
-0.0066∗∗∗
-0.0066∗∗

(0.0094)
(0.0096)
(0.0024)
(0.0028)

Fixedasset
0.0551∗∗
0.0551∗
0.0120∗∗∗
0.0120∗

(0.0221)
(0.0249)
(0.003)
(0.0055)

RFC
-0.2917∗∗∗
-0.2917∗∗∗
-0.0713∗∗∗
-0.0713∗∗∗

(0.0288)
(0.0244)
(0.0039)
(0.0041)

Longitude
-0.0040∗∗∗
-0.0040∗∗∗
-0.0002∗∗∗
-0.0002∗∗∗

(0.0001)
(0.0002)
(0.0000)
(0.0000)

Latitude
-0.0009∗∗∗
-0.0009∗∗∗
-0.0006∗∗∗
-0.0006∗∗∗

(0.0003)
(0.0003)
(0.0001)
(0.0001)

Coastalregion
-0.0410∗∗∗
-0.0410∗∗∗
-0.0038∗∗∗
-0.0038∗∗

(0.003)
(0.0023)
(0.001)
(0.0013)

YEZ
-0.0510∗∗∗
-0.0510∗∗∗
-0.0007
-0.0007

(0.003)
(0.0022)
(0.0011)
(0.0012)

SREB
-0.0579∗∗∗
-0.0579∗∗∗
0.0015
0.0015

(0.0021)
(0.0021)
(0.0018)
(0.0028)

Resource
0.1129
0.1129∗∗∗
-0.0028∗∗∗
-0.0028∗∗

(0.0019)
(0.0032)
(0.0011)
(0.0012)

Crisis
0.0042
0.0042
0.0039∗∗
0.0039∗

(0.0056)
(0.0058)
(0.0028)
(0.0031)

Newnormal
-0.006
-0.006
-0.0088∗∗∗
-0.0088∗∗∗

(0.0063)
(0.0042)
(0.0028)
(0.0022)

Constant
0.0788
0.0788
-0.1776∗∗∗
-0.1776∗∗∗

(0.0554)
(0.0957)
(0.0089)
(0.0114)

Wald test
44430.65
44330.61
50333.31
74668.83

(0.0000)
(0.0000)
(0.0000)
(0.0000)

N
341
341
341
341

Note: (1) The standard errors in parentheses (except Wald test) are statistically significant at the 1% (∗∗∗), 5% (∗∗), and 10% (∗) levels. (2) In all cases, the Wald test (the value in parentheses is the p value) rejects the null hypothesis that the explanatory variables as well as the dummy variables are jointly equal to zero.

First, for the transportation infrastructure fixed asset investment, the PCSE and SCCSE regression results with Hub (the regression coefficients are both 0.0551) highlight its impact on the Hub values of the RFTN nodes, indicating that the transportation infrastructure fixed asset investment constitutes the most important factor influencing the importance of an RFTN node. This finding shows that increasing the amount of investment in transportation infrastructure can effectively increase the importance of RFTN nodes. China boasts a large land area and an uneven distribution of natural resources; thus, the impact of transportation infrastructure investments on the importance of RFTN nodes is even more obvious. The PCSE and SCCSE regression results with PageRank (the regression coefficients are both 0.0120) also support this conclusion. However, despite these PCSE and SCCSE results, the regression coefficient of the transportation infrastructure fixed asset investment with PageRank is not as large as that with Hub.

Second, the agglomeration economy represented by the population density is also an important positive factor influencing both Hub and PageRank, with regression coefficients of 0.02 and 0.0027, respectively. A higher population density signifies a greater market demand and more specialized and diversified services compared with less densely populated areas, thereby promoting the region as one with a higher node importance, namely, a freight hub. This result is supported by both theoretical and empirical evidence: the effect of the regional/local market size on the importance (hub) of a rail freight network node, that is, the importance of a rail freight network node, is highly consistent with the size of the regional market.

Third, the RFC regression coefficients with Hub and PageRank are both negative, indicating that the RFC coefficient has a negative role on the importance of RFTN nodes. In other words, the higher the RFC coefficient is, the higher the concentration of freight in the province is and the lower the importance of the RFTN node is, and vice versa. The railway freight transportation industry is a typical network-type industry with strong natural monopoly characteristics. China’s railway freight transportation industry is currently a monopoly composed of state-owned railways; this state constitutes the main reason for the negative RFC regression coefficient. These results show that any regulatory policy that relaxes competition in the Chinese railway freight transport market (including access mechanisms and price mechanisms) can enhance the node importance of the RFTN.

In terms of other explanatory variables, from the regression results of Hub (Table 6), the location of a province in a coastal region has a negative influence on the importance of an RFTN node. Relatively speaking, provinces in coastal areas have excellent natural harbors, and sea transport is more advantageous than railway transport. This result shows that China’s rail-sea transport system is not developed. The location of the YEZ also plays a negative role in the regression of Hub (regression coefficient is 0.051, significantly negative). The YEZ represents China’s inland river shipping center, and thus the development of inland river shipping in the provinces within the YEZ presents more favorable conditions than the development of railway transportation; this has affected the enhancement of the importance of the RFTN nodes in these provinces. However, the regression coefficient of the YEZ is not statistically significant in the regression results of PageRank, so the YZE factor is thus not very important for PageRank.

The regression results also demonstrate that the geographical location has an impact on the Hub and PageRank regression results of the RFTN node. In terms of the longitude, the sign of the regression coefficient is negative, indicating that the larger the longitude is, the smaller the node importance is; that is, the relative importance of China’s RFTN gradually strengthens from east to west. Relative to the eastern provinces, the central and western provinces are rich in natural resources such as coal (Shanxi, Shaanxi, and Inner Mongolia), iron ore (Sichuan), and oil and gas. The regression coefficient for the latitude is also negative, indicating that the higher the latitude is, the smaller the importance of the RFTN node is; that is, the relative importance of China’s railway cargo transport gradually increases from north to south. This may be because the south has a more dynamic economy than the north with more frequent exchanges of goods and a greater transport demand.

Finally, the regression results also show that although the highway density, financial crisis, and “new normal” economic model are not statistically significant in the Hub regression results, they are statistically significant in the PageRank regression results. In general, the impacts of the abovementioned explanatory variables on Hub are similar to those on PageRank (Table 6). In other words, the factors affecting a province as a cargo hub are basically the same as those of the entire railway freight transportation network center. In addition, the similarity of the PCSE and SCCSE estimation results shows that the estimated coefficients of the factors affecting the importance of RFTN nodes are robust.

4. Conclusions

The main purposes of this study were to explore the influencing factors on the importance of China’s RFTN nodes, to reveal the causal relationships between the changes in the node importance and the influencing factors, and to provide scientific decision-making support for the reasonable establishment of RFTN hubs.

From the calculation results of Hub and PageRank, the uneven distribution of natural resources will cause spatial changes in the importance of RFTN nodes. From 2005 to 2016, the Hub values of resource-exporting provinces were ranked at the top; the Hub values tended to cluster around the average, and the economic structure of the output-oriented provinces improved as a whole. At the same time, the PageRank values of many provinces in the central and western regions significantly increased, and the central and western provinces exhibited more frequent exchanges of goods with other provinces and closer economic ties with other regions. According to the Hub and PageRank regression results, the transportation infrastructure fixed asset investment and population density variables have positive effects on the importance of RFTN nodes. In contrast, the influences of the RFC coefficient, geographical location (longitude and latitude), and special location (proximity to a coastal region) on the importance of RFTN nodes are negative.

Based on an analysis of the results of multiple indicators, the transportation infrastructure fixed asset investment has the greatest impact on the importance of RFTN nodes, and increasing the transportation infrastructure fixed asset investment still constitutes the key means for improving the importance of RFTN nodes. Specifically, strengthening the fixed asset investment of the railway infrastructure in the province, improving the railway freight transportation network, and enhancing the accessibility of the railway freight transportation network are beneficial to improving the importance of the RFTN. The local government should focus on improving the railway freight transportation network in the central and western regions, making the central and western regions closer to the eastern region. At the same time, the investment policy in transportation infrastructure fixed asset should be tilted towards important hub areas, as these areas are critical to maintaining the entire rail freight transportation network.

Second, the agglomeration economic effect represented by the population density has an important influence on the status of a railway freight transportation hub, which is mainly reflected in the increase in population density. This will bring more cargo transportation needs and greater cargo transportation scale. In addition, the larger the market size is, the more frequent economic activities are, and the higher the hub status will be. Therefore, we should improve the professional service level of railway freight transport and improve the railway branch line network, thereby promoting the improvement of the urbanization level. Furthermore, we should also give play to the guiding role of the agglomeration economy, effectively improve the status of the railway freight transport network nodes, and finally promote the development of the regional economy.

Third, the high degree of monopoly in the rail transport market will reduce the importance of rail freight network nodes. Hence, we should introduce market competition, relax the conditions for railway cargo transportation market access, and implement market pricing mechanisms to enhance the market vitality. This will help reduce the operating cost of railway freight transportation and improve the scale economic efficiency of railway freight transportation to improve the utilization rate of railway transportation resources.

Finally, port development in coastal areas has a certain negative effect on the importance of railway freight network nodes. However, this does not mean that sea and water transport have not been developed. In contrast, considering the comprehensive transportation level, the natural and geographical conditions of each province should be fully tested when formulating comprehensive transportation planning, and the technical and economic advantages of the various modes of transportation should be fully utilized according to local conditions. Coastal areas should give full play to the advantages of seaports, focusing on the development of sea-rail combined transport. The western inland areas should expand their railway transport capacity, focus on the development of public-rail rail transport, and improve the connectivity between inland areas and coastal areas, thereby improving the operational efficiency of the entire integrated transportation network.

However, our study still has some limitations. Due to data availability constraints, the analysis in this study can take only provincial regions as nodes to investigate the differences in the node importance and influencing factors on RFTN nodes between the provinces, which cannot be described in more detail. In future research, we will search for more comprehensive data to refine our model and pay more attention to the influence of the RFTN status on the importance of provincial nodes.

Appendix

A.

See Table 7.

Table 7: Provincial Railway Freight Transport Hub value in China 2005-2016.

Province
Y2005
Y2006
Y2007
Y2008
Y2009
Y2010
Y2011
Y2012
Y2013
Y2014
Y2015
Y2016

Beijing
0.0140915
0.0139128
0.0120751
0.0118958
0.0118177
0.00913
0.0081819
0.0079569
0.0067434
0.0073467
0.0074523
0.004648

Tianjin
0.029765
0.0264251
0.0232248
0.028791
0.0334385
0.0310173
0.0328231
0.0372697
0.0354688
0.0358196
0.0394732
0.0351692

Hebei
0.0267062
0.0220316
0.0161264
0.0140053
0.0126411
0.0135427
0.0144122
0.0124377
0.0109019
0.0096697
0.0077443
0.0077404

Shanxi
0.6268702
0.6485834
0.6835235
0.6531463
0.5702008
0.5572563
0.5782964
0.624994
0.6361534
0.6711601
0.7467788
0.7346002

Inner Mongolia
0.0820665
0.0898378
0.0875637
0.1265891
0.1784428
0.2054984
0.2025359
0.1671743
0.1808367
0.1682984
0.104697
0.1173417

Liaoning
0.0172819
0.0168378
0.0146154
0.0131196
0.0144548
0.014356
0.0117541
0.0101986
0.0089378
0.0080439
0.0061888
0.0061695

Jilin
0.013584
0.0118057
0.0095747
0.0093626
0.0089292
0.00877
0.0083091
0.0067226
0.0060084
0.0054724
0.0027188
0.0032046

Heilongjiang
0.0305351
0.0261735
0.0237674
0.0209181
0.0205825
0.0167195
0.0163264
0.0135268
0.0115135
0.0092316
0.0040395
0.0055336

Shanghai
0.0020276
0.0015082
0.001194
0.0010411
0.0008914
0.0008259
0.0006156
0.0004816
0.0003863
0.0002819
0.0002581
0.0003709

Jiangsu
0.0060954
0.0055492
0.0044252
0.0045894
0.0090195
0.0106393
0.0089849
0.0078168
0.0061795
0.0034269
0.0024011
0.0058184

Zhejiang
0.0018307
0.0015011
0.0012575
0.001044
0.0009246
0.0008093
0.000858
0.0007788
0.0006413
0.0004494
0.0005367
0.0006198

Anhui
0.0118495
0.010441
0.009047
0.0075888
0.0072946
0.0073594
0.0068666
0.0057793
0.0043711
0.0036179
0.0034096
0.0037101

Fujian
0.0023103
0.0017491
0.001522
0.0013676
0.0011593
0.000967
0.0007274
0.0005658
0.0004201
0.0003741
0.0003272
0.0005511

Jiangxi
0.0026023
0.0024431
0.0021919
0.0019567
0.0017428
0.0013437
0.0010783
0.0009701
0.0007892
0.0006312
0.0006337
0.0007985

Shandong
0.0375563
0.0390412
0.0328026
0.0340678
0.0410324
0.0398271
0.0397275
0.0394382
0.0356137
0.02987
0.0267917
0.0244956

Henan
0.0214186
0.0184971
0.0163154
0.013699
0.0118466
0.0106545
0.0088086
0.0070259
0.0073531
0.0059532
0.0051913
0.00596

Hubei
0.0078472
0.0060592
0.0055415
0.0054546
0.0052082
0.0044735
0.0036867
0.0029742
0.0024206
0.0017259
0.0013202
0.0013526

Hunan
0.0034232
0.0029088
0.0025727
0.002347
0.0021532
0.001751
0.001342
0.0010906
0.0008838
0.0006358
0.0005623
0.0005233

Guangdong
0.0033969
0.0027788
0.00245
0.0022581
0.0020757
0.0019514
0.0014359
0.0012369
0.0011477
0.0012137
0.0012976
0.0014973

Guangxi
0.0033529
0.0028739
0.002794
0.0026786
0.0024514
0.0019965
0.0017276
0.0014553
0.0011057
0.000795
0.0006367
0.0007264

Hainan
0
0
0
1.355E-05
1.36E-05
1.154E-05
2.542E-05
9.751E-06
1.014E-05
1.383E-05
1.366E-05
1.267E-05

Chongqing
0.0013135
0.0012464
0.0011145
0.00091
0.001092
0.000906
0.000642
0.0005192
0.0005527
0.0003167
0.000384
0.000462

Sichuan
0.0074034
0.0060752
0.0055882
0.0039161
0.0033783
0.0031908
0.0030828
0.0025699
0.0019416
0.0016862
0.001419
0.0013435

Guizhou
0.004453
0.0037329
0.0033066
0.0025143
0.0029074
0.0028426
0.0024324
0.0018101
0.0016444
0.0014706
0.0012708
0.0016028

Yunnan
0.0048993
0.0041062
0.003596
0.0030229
0.0035264
0.0027214
0.0025318
0.0024391
0.0023363
0.0018452
0.0018989
0.0021888

Sitsang
0
4.182E-06
1.113E-05
6.117E-06
4.948E-06
9.271E-06
1.436E-05
1.987E-05
1.143E-05
8.373E-06
1.13E-05
5.264E-05

Shaanxi
0.0161385
0.0136525
0.0136972
0.0123465
0.012981
0.01276
0.0133588
0.0139009
0.0147321
0.0143815
0.0184619
0.0168522

Gansu
0.0042898
0.0047856
0.0048947
0.0054504
0.0047948
0.0052491
0.0036289
0.0031656
0.0024874
0.0019563
0.0019684
0.0023702

Qinghai
0.0033564
0.0030863
0.003514
0.0031171
0.0035236
0.0034378
0.0042355
0.004055
0.0028824
0.0026806
0.0024874
0.0036607

Ningxia
0.0075217
0.0069508
0.0063219
0.0064864
0.0255053
0.0252519
0.0171685
0.0169686
0.0107371
0.0065878
0.005543
0.0068258

Xinjiang
0.0060131
0.0054015
0.0053709
0.0062962
0.0059657
0.004731
0.0043814
0.0046482
0.0047887
0.0050354
0.0040828
0.0037973

B.

See Table 8.

Table 8: Provincial Railway Freight Transport PageRank value in China 2005-2016.

Province
Y2005
Y2006
Y2007
Y2008
Y2009
Y2010
Y2011
Y2012
Y2013
Y2014
Y2015
Y2016

Beijing
0.0323042
0.0309066
0.0279627
0.0227377
0.0226562
0.0209103
0.0153913
0.0161169
0.0153163
0.0143129
0.0127383
0.0127668

Tianjin
0.0431424
0.0413598
0.0409668
0.0407406
0.0333998
0.0354163
0.0341886
0.0285134
0.0260028
0.0275132
0.0230904
0.0220384

Hebei
0.062328
0.0601864
0.0569595
0.0632581
0.0695173
0.0700008
0.0692456
0.0669669
0.0616151
0.0577607
0.0478008
0.0453338

Shanxi
0.030739
0.029205
0.0299905
0.0304925
0.0332561
0.0297992
0.0300966
0.0306897
0.0277936
0.0235896
0.016611
0.0205147

Inner Mongolia
0.0205175
0.0204698
0.0219403
0.0239372
0.0211289
0.0197259
0.0206151
0.020347
0.0181674
0.0185478
0.02135
0.0207592

Liaoning
0.0443199
0.0439171
0.0419278
0.0415792
0.0398492
0.0395156
0.0422657
0.0405511
0.037965
0.0361509
0.0375571
0.0371486

Jilin
0.025799
0.0254945
0.0249711
0.0266014
0.0271057
0.0249884
0.0271206
0.0266431
0.0260323
0.0262368
0.0280289
0.0266696

Heilongjiang
0.02439
0.0243002
0.0239701
0.0239696
0.0265037
0.0248671
0.0262359
0.0256523
0.0230666
0.0224503
0.0237785
0.0233902

Shanghai
0.022659
0.0223463
0.0204827
0.0184087
0.0159221
0.0158863
0.0144893
0.0135143
0.0127633
0.0122684
0.0120068
0.0119964

Jiangsu
0.0485834
0.0460219
0.0440363
0.038461
0.0323201
0.0317987
0.0309719
0.0301979
0.0290717
0.0279086
0.0282289
0.0279438

Zhejiang
0.0463867
0.0452488
0.042779
0.0374558
0.0326686
0.0330852
0.0307949
0.0282191
0.0243196
0.0228879
0.0217283
0.0203866

Anhui
0.0230104
0.0233689
0.0234213
0.021229
0.0196706
0.019709
0.0197688
0.0194541
0.0196077
0.0199023
0.0187296
0.0182603

Fujian
0.0291278
0.029742
0.0307374
0.0270515
0.0235223
0.0235033
0.0227986
0.0221022
0.0231858
0.02186
0.0217209
0.0204349

Jiangxi
0.0436145
0.0454226
0.0462649
0.0434057
0.0453008
0.0502441
0.0520551
0.051719
0.0504454
0.0439445
0.0429781
0.0414647

Shandong
0.0376278
0.0388727
0.0406977
0.0397078
0.0430618
0.0408648
0.040244
0.0392667
0.0383911
0.0371373
0.032242
0.0303607

Henan
0.0377801
0.0417223
0.0415822
0.040975
0.0421246
0.0395529
0.038866
0.0407407
0.0425519
0.040109
0.0394184
0.0389577

Hubei
0.0382895
0.0386566
0.0390377
0.0407307
0.0400414
0.0408908
0.0382543
0.035758
0.0339177
0.0328759
0.0332157
0.0320149

Hunan
0.0538336
0.0539961
0.053787
0.0530203
0.0557266
0.059305
0.0583583
0.0539151
0.050463
0.045574
0.0435163
0.0438058

Guangdong
0.0629027
0.0629095
0.0616519
0.0599834
0.0529067
0.0547839
0.0543415
0.0512052
0.0496472
0.0509791
0.0556201
0.0548821

Guangxi
0.0510166
0.0509154
0.0544739
0.0571354
0.0574881
0.0602087
0.0605601
0.0618762
0.0594894
0.0636851
0.0653011
0.0665754

Hainan
0.0057819
0.0058047
0.0059547
0.0061458
0.0058613
0.0059241
0.0059404
0.005786
0.0057645
0.0060562
0.0064283
0.0063508

Chongqing
0.0203838
0.0209887
0.0223541
0.0245824
0.027434
0.0302214
0.0315912
0.0309238
0.0371216
0.0461757
0.0477394
0.0459715

Sichuan
0.0493621
0.0471254
0.0493878
0.0554776
0.062844
0.0652898
0.0661372
0.0696521
0.078524
0.0823503
0.0844245
0.0865906

Guizhou
0.0293893
0.0309977
0.0322461
0.0324823
0.0369155
0.0361366
0.0385228
0.0449611
0.0523152
0.0554666
0.054647
0.0599661

Yunnan
0.0342135
0.0322921
0.0339357
0.0349569
0.0394927
0.0387452
0.0421733
0.048168
0.0525582
0.0643748
0.0769535
0.081023

Sitsang
0
0.0052702
0.005592
0.0057619
0.0062083
0.006276
0.0061336
0.0066441
0.0073719
0.0077696
0.0082677
0.0091039

Shaanxi
0.0236421
0.0233826
0.0223499
0.0224806
0.0241655
0.0226317
0.022524
0.024471
0.0253769
0.0228604
0.0218938
0.0242163

Gansu
0.0238747
0.0230044
0.0237398
0.0259352
0.0238069
0.0234542
0.0230362
0.0253248
0.0273368
0.0262748
0.0264554
0.0251035

Qinghai
0.0103965
0.0103799
0.0099563
0.0112113
0.0125874
0.0106957
0.0099345
0.0111183
0.0125692
0.0133757
0.0152336
0.013457

Ningxia
0.0086054
0.0086645
0.0089388
0.0096248
0.0092824
0.0090174
0.0093315
0.0088477
0.0082364
0.0077584
0.0085496
0.0088594

Xinjiang
0.0159786
0.0170274
0.0179042
0.0204608
0.0172312
0.0165516
0.0180132
0.0206542
0.0230123
0.0218431
0.023746
0.0236534

Data Availability

The data studied in this paper are all from the “Yearbook of China Transportation & Communications (2006-2016)” and the “China Statistical Yearbook (2006-2017).” The Statistical Yearbook is published as a publicly available document in China, which is open access to researchers. We have listed it in the paper as a reference, so there are no copyright conflicts. In addition, the data are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research has been funded by the Special Funds of the Basic Scientific Research Operating Expenses of the Central University of China (300102238655, 300102238605, and 300102238401) and the National Social Science Fund of China (17BJY139).

References

M. Huihui, W. Jiaoé, and J. Fengjun, “Complexity Perspectives on Transportation Network,” Progress in Geography, pp. 112–120, 2008.

W. Chengjin, “Railway cargo flow in china since:spatial configur ation and its evolution,” Progress in Geography, pp. 46–55, 2008.

W. Wei, L. Jun, J. Xi, and W. Ying, “Topology properties on chinese railway network,” Journal of Beijing Jiaotong University, vol. 34, no. 3, pp. 148–152, 2010.

MTPRC, Statistical Bulletin on The Development of Transportation Industry for 2017, Ministry of Transport of the People's Republic of China (MTPRC), Beijing, China, 2018.

D. A. Macheret, N. A. Valeev, and A. V. Kudryavtseva, “Formation of the railway network: Diffusion of epochal innovation and economic growth,” Economic Policy 1, vol. 13, no. 1, pp. 252–279, 2018.

T. Ago, I. Isono, and T. Tabuchi, “Locational disadvantage of the hub,” Annals of Regional Science, vol. 40, no. 4, pp. 819–848, 2006.

M. Fujita, P. R. Krugman, and A. J. Venables, The Spatial Economy: Cities, Regions, and International Trade, MIT press, 2001.

M. Fujita and T. Mori, “The role of ports in the making of major cities: Self-agglomeration and hub-effect,” Journal of Development Economics, vol. 49, no. 1, pp. 93–120, 1996.

T. Tsekeris, “Interregional trade network analysis for road freight transport in Greece,” Transportation Research Part E: Logistics and Transportation Review, vol. 85, pp. 132–148, 2016.

D. L. Bryan and M. E. O'kelly, “Hub-and-spoke networks in air transportation: an analytical review,” Journal of Regional Science, vol. 39, pp. 275–295, 1999.

P. Arnold, D. Peeters, and I. Thomas, “Modelling a rail/road intermodal transportation system,” Transportation Research Part E: Logistics and Transportation Review, vol. 40, no. 3, pp. 255–270, 2004.

T. S. Hanssen, T. A. Mathisen, and F. Jørgensen, “Generalized transport costs in intermodal freight transport,” Procedia - Social and Behavioral Sciences, vol. 54, pp. 189–200, 2012.

M. Janic, “Modelling the full costs of an intermodal and road freight transport network,” Transportation Research Part D: Transport and Environment, vol. 12, no. 1, pp. 33–44, 2007.

A. Fügenschuh, H. Homfeld, M. Johann, H. Schülldorf, and A. Stieber, “Use of Optimization Tools for Routing in Rail Freight Transport,” in Handbook of Optimization in the Railway Industry, R. Borndörfer, T. Klug, L. Lamorgese, C. Mannino, M. Reuther, and T. Schlechte, Eds., pp. 161–179, Springer International Publishing, Cham, Swizerland, 2018.

W. Yin, S. He, Y. Zhang, and J. Hou, “A product-focused, cloud-based approach to door-to-door railway freight design,” IEEE Access, vol. 6, pp. 20822–20836, 2018.

M. Barthélemy, “Spatial networks,” Physics Reports, vol. 499, no. 1–3, pp. 1–101, 2011.

Z. Li, M. Xu, and Y. Shi, “Centrality in global shipping network basing on worldwide shipping areas,” GeoJournal, vol. 80, no. 1, pp. 47–60, 2015.

J. Lin and Y. Ban, “Complex network topology of transportation systems,” Transport Reviews, vol. 33, no. 6, pp. 658–685, 2013.

G. Bagler, “Analysis of the airport network of India as a complex weighted network,” Physica A: Statistical Mechanics and its Applications, vol. 387, no. 12, pp. 2972–2980, 2008.

Y.-R. Dang and L.-N. Peng, “Hierarchy of air freight transportation network based on centrality measure of complex networks,” Journal of Transportation Systems Engineering and Information Technology, vol. 12, no. 3, pp. 109–114, 2012.

R. Guimerà, S. Mossa, A. Turtschi, and L. N. Amaral, “The worldwide air transportation network: anomalous centrality, community structure, and cities' global roles,” Proceedings of the National Acadamy of Sciences of the United States of America, vol. 102, no. 22, pp. 7794–7799, 2005.

T. Kotegawa, D. Fry, D. DeLaurentis, and E. Puchaty, “Impact of service network topology on air transportation efficiency,” Transportation Research Part C: Emerging Technologies, vol. 40, pp. 231–250, 2014.

J. Lin, “Network analysis of China's aviation system, statistical and spatial structure,” Journal of Transport Geography, vol. 22, pp. 109–117, 2012.

G. Malighetti, G. Martini, S. Paleari, and R. Redondi, “The impacts of airport centrality in the EU network and inter-airport competition on airport efficiency,” 2009.

S. Wandelt and X. Sun, “Evolution of the international air transportation country network from 2002 to 2013,” Transportation Research Part E: Logistics and Transportation Review, vol. 82, pp. 55–78, 2015.

J. Wang, H. Mo, and F. Wang, “Evolution of air transport network of China 1930–2012,” Journal of Transport Geography, vol. 40, pp. 145–158, 2014.

R. Ding, N. Ujang, H. B. Hamid, and J. Wu, “Complex network theory applied to the growth of Kuala Lumpur's public urban rail transit network,” PLoS ONE, vol. 10, Article ID e0139961, 2015.

J. Feng, X. Li, B. Mao, Q. Xu, and Y. Bai, “Weighted complex network analysis of the Beijing subway system: Train and passenger flows,” Physica A: Statistical Mechanics and its Applications, vol. 474, pp. 213–223, 2017.

V. Latora and M. Marchiori, “Is the Boston subway a small-world network?” Physica A: Statistical Mechanics and its Applications, vol. 314, no. 1, pp. 109–113, 2002.

M. Barthélemy and A. Flammini, “Modeling Urban street patterns,” Physical Review Letters, vol. 100, no. 13, Article ID 138702, 2008.

J. Buhl, J. Gautrais, N. Reeves et al., “Topological patterns in street networks of self-organized urban settlements,” The European Physical Journal B, vol. 49, no. 4, pp. 513–522, 2006.

S. Lämmer, B. Gehlsen, and D. Helbing, “Scaling laws in the spatial structure of urban road networks,” Physica A: Statistical Mechanics and its Applications, vol. 363, no. 1, pp. 89–95, 2006.

F. G. Laxe, M. J. F. Seoane, and C. P. Montes, “Maritime degree, centrality and vulnerability: port hierarchies and emerging areas in containerized transport (2008-2010),” Journal of Transport Geography, vol. 24, pp. 33–44, 2012.

Y. Hu and D. Zhu, “Empirical analysis of the worldwide maritime transportation network,” Physica A: Statistical Mechanics and its Applications, vol. 388, no. 10, pp. 2061–2071, 2009.

P. Kaluza, A. Kölzsch, M. T. Gastner, and B. Blasius, “The complex network of global cargo ship movements,” Journal of the Royal Society Interface, vol. 7, no. 48, pp. 1093–1103, 2010.

S. Ghosh, A. Banerjee, N. Sharma et al., “Statistical analysis of the Indian Railway Network: A complex network approach,” Acta Physica Polonica B, vol. 4, no. 2, pp. 123–137, 2011.

P. Sen, S. Dasgupta, A. Chatterjee, P. A. Sreeram, G. Mukherjee, and S. S. Manna, “Small-world properties of the Indian railway network,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 67, no. 3, Article ID 036106, 2003.

W. Li and X. Cai, “Empirical analysis of a scale-free railway network in China,” Physica A: Statistical Mechanics and its Applications, vol. 382, no. 2, pp. 693–703, 2007.

X. Meng, L. Jia, J. Xie, Y. Qin, and J. Xu, “Complex characteristic analysis of passenger train flow network,” in Proceedings of the 2010 Chinese Control and Decision Conference, CCDC 2010, pp. 2533–2536, IEEE, China, May 2010.

T. H. Oum, A. Zhang, and W. Swan, “Air cargo logistics and hub developments,” Transportation Research Part E: Logistics and Transportation Review, vol. 40, no. 2, pp. 81-82, 2004.

C. Ducruet, S.-W. Lee, and A. K. Y. Ng, “Centrality and vulnerability in liner shipping networks: Revisiting the northeast asian port hierarchy,” Maritime Policy & Management, vol. 37, no. 1, pp. 17–36, 2010.

Y. Wang and K. Cullinane, “Determinants of port centrality in maritime container transportation,” Transportation Research Part E: Logistics and Transportation Review, vol. 95, pp. 326–340, 2016.

Y. B. O. C. Transportation &Comunications, Year Book of China Transportation & Comunications, China Statistics Press, National Statistics Bureau of the People's Republic of China, 2015.

C. S. Yearbook, China Statistical Yearbook, China Statistics Press, National Statistics Bureau of The People's Republic of China, 2016-2017.

J. M. Kleinberg, “Authoritative sources in a hyperlinked environment,” Journal of the ACM, vol. 46, no. 5, pp. 604–632, 1999.

L. Page and S. Brin, “The anatomy of a large-scale hypertextual Web search engine,” Computer Networks and ISDN Systems, vol. 30, no. 1-7, pp. 107–117, 1998.

C. Zhong, S. M. Arisona, X. Huang, M. Batty, and G. Schmitt, “Detecting the dynamics of urban structure through spatial network analysis,” International Journal of Geographical Information Science, vol. 28, no. 11, pp. 2178–2199, 2014.

A. Hagberg, P. Swart, and D. S. Chult, Exploring Network Structure, Dynamics, And Function Using NetworkX, Los Alamos National Lab. (LANL), Los Alamos, NM, USA, 2008.

M. D. Wittman and W. S. Swelbar, “Modeling changes in connectivity at US airports: a small community perspective,” 2013.

M. Fujita and T. Mori, “Frontiers of the New Economic Geography∗,” Studys in Regional Science, vol. 84, no. 3, pp. 377–405, 2005.

P. Krugman, “The hub effect: or, threeness in interregional trade,” in Theory, Policy and Dynamics in International Trade, E. Helpman, J. P. Neary, and W. J. Ethier, Eds., pp. 29–37, Cambridge University Press, Cambridge, UK, 1993.

T. S. Breusch and A. R. Pagan, “A simple test for heteroscedasticity and random coefficient variation,” Econometrica, vol. 47, no. 5, pp. 1287–1294, 1979.

R. D. Cook and S. Weisberg, “Diagnostics for heteroscedasticity in regression,” Biometrika, vol. 70, no. 1, pp. 1–10, 1983.

N. Beck and J. N. Katz, “What to do (and not to do) with time-series cross-section data,” American Political Science Review, vol. 89, no. 03, pp. 634–647, 1995.

J. C. Driscoll and A. C. Kraay, “Consistent covariance matrix estimation with spatially dependent panel data,” Review of Economics and Statistics, vol. 80, no. 4, pp. 549–560, 1998.

C. S. Yearbook, China Statistical Yearbook, China Statistics Press, National Statistics Bureau of The People's Republic of China, 2006–2017.

Y. Zhang, A. Zhang, Z. Zhu, and K. Wang, “Connectivity at Chinese airports: The evolution and drivers,” Transportation Research Part A: Policy and Practice, vol. 103, pp. 490–508, 2017.