Validation of the Basic Supporting Role of Traffic Networks in Regional Factor Flow: A Case Study of Zhejiang Province

Abstract

Castells proposed that “space of flow” has multiple layers, and considered that transportation infrastructure is the carrier of its formation. However, few studies have focused on whether the infrastructure behind factor flows can provide sufficient support. In this paper, the basic supporting role of traffic networks in regional factor flows is examined. Firstly, we use traffic-connection data, enterprise-investment data and human-flow data to build a traffic network, enterprise-association network and inter-city-trip network, respectively. Then, we construct fitting models of the traffic network and the other two networks from two aspects: centrality and connection degree. Finally, this paper analyzes the standard residuals of the fitting results and looks for outliers that are greater than 1.65 or less than −1.65. Through outliers, we can find out where the traffic network cannot support the inter-city factor flows, and where the traffic network is too developed. The conclusions are as follows: First, the immaterial capital flows are still affected by the connectivity of transport facilities. With an improvement in traffic conditions, the capital links between cities can be enhanced correspondingly. Therefore, cities can gather more capital. Second, the attraction and radiation power of high-grade cities in terms of both human and capital flows are far beyond the traffic condition. They also motivate the neighboring cities to form a scale of capital- and human-flow connection that exceeds the average traffic conditions of the whole province. By analyzing the relationship between factor flows and infrastructure, and identifying mismatched networks, this paper will be helpful in many regards. It can provide guidance for Zhejiang Province in formulating transportation strategies. In addition, the conclusions can also provide decision-making support for optimizing regional infrastructure construction.

1. Introduction

Since the 1990s, globalization has profoundly affected the regional development and evolution of all countries. With the deepening of globalization, the time–space compression effect brought about by the transportation revolution continues to intensify. More and more factors flow around the world with the help of high-speed infrastructure and Internet between cities. Cities are no longer isolated material individuals, and the connections between cities can no longer rely entirely on “space of place”. This creates a network relationship of space–time sharing between cities at multiple spatial scales and levels.

“Enhancing infrastructure connectivity to promote the free flow of factors” is the foundation of globalization. According to the theory of “space of flow” [1], in the context of globalization, elements such as information, capital, technology, and human resources can overcome the “proximity” of space of place in the form of “flow” and shorten the distance between cities [1,2,3,4,5,6,7]. The Globalization and World Cities Study Group study (also known as the GaWC study) initiated by Taylor [8] established a paradigm for studying urban networks based on the theory of “space of flow”. With improved access to data, the types of “flow” data have become more diverse, which promotes the diversification of research. Examples include research findings on passenger-flow networks using data on high-speed railway schedules [9,10,11], freight networks using data on logistics routes [12], inter-city-trip networks using data on human flow [13,14,15], and enterprise-association networks using data from corporate-headquarters branches [16,17,18]. Discussions of the interrelationships among different types of networks have also appeared in related studies in recent years [18,19,20,21]. According to Castells’ theory, there is a hierarchical relationship in the space of flow supported by infrastructure, and global cities are formed based on the global reach of infrastructure [22]. However, existing studies rarely pay attention to whether the infrastructure behind factor flows can provide sufficient support. Therefore, we believe that it is of great significance to analyze the relationship between various types of networks and infrastructure interconnection and identify the mismatched networks for optimizing regional infrastructure construction.

This paper will focus on transportation infrastructure and verify the supporting effect of traffic networks constructed by transportation interconnection on enterprise-association networks (formed by capital flow) and inter -city-trip networks (formed by human flow) commonly seen in urban networks. The study can provide decision support for the improvement in transportation routes, the optimization of infrastructure layout, the enhancement of traffic carrying capacity, and the formulation of transportation strategic guidance. The following sections are organized as follows. In Section 2, the methods of obtaining “flow” data and the concepts of an “urban network” will be categorized and summarized. In Section 3, the data and methods used in the paper will be discussed. In Section 4, the paper will take Zhejiang Province as an example to analysis the basic supporting effect of transportation network on regional capital and human flow. In Section 5, the research results will be discussed based on the theory of “flow space”. Finally, the conclusion will be presented.

2. Literature Review

2.1. Development of Urban Network Research

Urban networks are network systems formed by the relationship between cities and the flow of factors [23]. Its foothold lies in the relationship between cities, which can be traced back to Friedman’s hypothesis of world cities. He put the world cities and their relationship on the agenda of urban research and put forward a new global perspective on the relationship between cities [24]. Later, based on Friedman, Sassen argued that world cities were global service centers [25]. Her emphasis on advanced producer services would also become the core of the definition of world city network in GaWC research in the future. Although Friedman and Sassen focused on the connections between world cities, they paid more attention to the city level, and thought that the level is based on the network [23]. In 1996, Castells put forward the theory of “space of flow”, which made a great difference to regional and urban studies [1]. Based on it, GaWC, led by Taylor, carried out study on the world urban network and sparked a wave of research around the world. With the emergence of new data, new technologies and new methods, the breadth and depth of urban-network research have been further expanded in recent years.

In terms of breadth, there are three main points. First, the research data has expanded from the enterprise association to the flow of humans, traffic, and information, which greatly enriched the research perspective, and the focuses of relevant research are different. For example, the studies based on human flow not only focus on the flow direction of people [26,27], but also focus on the travel situation and differences between holidays and daily days [28]. Traffic-flow data is generally divided into three types: highway, high-speed railway, and flight. The first two are more suitable for short- and medium-distance research, focusing on the characterization of the internal network of urban agglomeration [29,30]. Flight data is more suitable for long-distance research and is often used for national or world urban-network research [30,31]. This is because cities with airports are usually important nodes in the region. The information-network research (formed by information flow) pays more attention to the influence on cities of the Internet [26,32,33]. Second, the study area has been expanded from regional urban agglomeration to entire countries, enriching the research level. Taylor et al., pioneered the empirical study of the world urban network, but many studies still focused on regional urban agglomeration, or states, or provinces [26,34]. With the rise of big data, researchers can obtain various data. Therefore, the area of research has been expanding. It extends not only to the whole country, but also to some international regions, and even the whole world [11,34,35]. The third point is that its content also extends from urban systems and network structures to network evolution, network resilience, network performance, polycentricity, and so on [36,37,38,39,40].

When it comes to depth, first of all, many scholars continuously optimized the network correlation calculation method and deepened the understanding of the law. The relevant calculation methods have experienced changes from the interlocking network model (used by GaWC) to the gravity model, and then to the real scale of connections between cities [41,42,43]. Some scholars also improved the calculation method of network relevance based on the gravity model, social network analysis and other methods, to reveal the deeper spatial organization of urban networks [44,45]. The emergence of new methods does not represent the obsolescence of old methods, but the application is different. Second, the existing studies continue to deepen consideration of the internal logic of space of flow and geographical space. Many studies have proved that the relationship between cities has exceeded the administrative jurisdiction, administrative level, and geographical distance, but there is still a certain distance attenuation [13,26]. This shows that geographical space still has restrictions on space of flow. In recent years, some scholars have introduced quantitative methods to analyze the differences in urban networks from the perspective of mobile space and geographical space, and proposed that the constraints of space–time distance should not be ignored while paying attention to network connections [44].

Although the urban-network research has attracted more and more attention and related research results have also increased, we find that there are still some problems in the study perspective that have not yet been addressed. First, the flow data currently used are real, simulative, and alternative. Therefore, what kind of data should be used for urban network research? The second is that different networks can be built based on different flow data, which results in different conclusions. Therefore, what is the relationship between different networks?

2.2. Discussion of “Flow” Data

“Flow” data is the basic data for urban-network research, but it is difficult to obtain real data in research. In many cases, simulations or alternative methods are used to obtain them [46,47]. The simulation method is generally based on a law (i.e., gravity model), wherein the number of connections is proportional to the scale and inversely proportional to the distance; the population data corresponds to the simulated human flow [48], and the GDP (gross domestic product) data corresponds to the simulated economic flow [29]. Combined, they can be transformed into “flow” data using the simulation method as long as the corresponding static scale data are available. Alternative methods are used to replace unobservable or unavailable data with other approximate data, such as replacing passenger flow with high-speed railway or airplane trips instead of actual passengers [46,49] and replacing capital flows with the association of corporate headquarters and its branches [50,51,52,53].

Although both the simulation and alternative methods can be used to obtain “flow” data, they fundamentally differ. The alternative method does not represent the actual measured value of the data being substituted, but the data itself is reliable. The data obtained by the simulation method is only that of “maximum likelihood”; although studies assume that the simulation results are representative of the actual situation, there is no way to verify the actual situation. However, this does not mean that the value of the simulated data is not as good as the real data. Sometimes, the researcher must simulate this “maximum likelihood,” such as by calculating the bearing capacity of a facility to obtain the ideal theoretical limit value.

2.3. Correlation Studies of Urban Networks

In global city networks, the connections between cities still depend on infrastructure interconnections, especially transportation facilities [22]. Even though the impact of transportation on immaterial economic and information connections is relatively weak, it still has a strong impact on connections such as human and information flows [19], especially since the transportation revolution has brought about a time–space compression effect and the global movement of factors has become possible [54,55].

Taylor et al., used the least squares method and verified that a strong correlation exists between the centrality of cities in air-passenger networks and enterprise-association networks [21], and identified cities where passenger flows did not match the city hierarchy (enterprise-association representation) based on standard residuals. Lao et al., used the same method to verify that the centrality of Chinese cities in air-passenger networks and economic networks also had a strong correlation [19]. A study by Zhang et al., further demonstrated that the network centrality of cities is still influenced by geographical proximity based on road traffic [43]. However, the above studies have the following shortcomings.

First, the purpose of these studies was not to verify the hierarchical relationship of the space of flow. They intended to verify the correlation between the different networks. For example, although Taylor’s study relies on the theoretical hypothesis that there are two levels—the existence of infrastructure in space of flow and the use of infrastructure—the data and conclusions of the study do not respond to this hypothesis. Instead, Taylor argues that the differences between air-passenger networks and enterprise-association networks are due to the existence of multiple examples of globalization and the fact that cities assume different functions in different global urban networks [22]. The purpose of Lao’s study is more explicit. He just wanted to compare urban networks from two different perspectives—air-passenger and economic networks [19].

Second, the quantification of traffic connections is open to question. Passenger flow and traffic connection are two different concepts, as both real passenger flow and passenger frequency as a substitute for flow are manifestations of traffic connection; however, they are not the traffic connection itself. The traffic network is the carrier of various urban networks, providing support for the flow of factors; furthermore, real passenger-flow data is influenced by the occupancy rate but cannot represent the bearing capacity. In reality, the closeness of traffic connections between cities is not only influenced by the frequency of transportation but also the travel time (distance), which is an important influencing factor. In other words, the higher the capacity of transportation and the shorter the travel time (distance), the higher the possibility of closer connection. Therefore, the quantification of traffic connection should take into account both parameters; the gravity model can simulate exactly this carrying capacity.

The last is the correlation test. The urban network includes not only the cities as nodes but also the connections between cities. The correlation test of two networks should consider the consistency of the connection degree in addition to testing the correlation of centrality, which has not been covered in previous studies.

In summary, there is a correlation between different urban networks, and the study of the difference is meaningful. The traffic network should be a network representing the carrying capacity obtained by the simulation method, a concept different from the passenger-flow network based on transportation. To verify the basic supporting role of traffic networks in urban networks, further research can provide deeper exploration into quantifying traffic connections and constructing traffic networks, and verifying the theory with real and simulated data.

3. Materials and Methods

3.1. Research Hypothesis

According to Castells’ theory of space of flow, infrastructure is the carrier, and transportation infrastructure is critical to the flow of factors. It is the time–space compression effect brought about by the transportation revolution that has brought cities closer together and made the global flow of factors possible. Although the theory of space of flow challenges the distance-decaying nature of traditional space, it has been demonstrated that distance decay continues to exist for both material inter-city trips and immaterial mobile communications [55,56,57].

Accordingly, in this paper, we select the enterprise-association network and the inter-city-trip network, which are common in urban networks, to examine their relationships with traffic networks, respectively. The former is typical for characterizing immaterial capital flows between cities [11], and the latter is typical for characterizing material human flows between cities [58], which can reflect the supporting role of traffic networks for both material and immaterial factor flows in a more comprehensive manner. The study hypothesizes that both immaterial and material factor flows, still constrained by space of place, are dependent on traffic networks to move between cities, although the former is relatively less dependent on traffic networks. There is spatial heterogeneity in the constraints of space of place: low-ranking cities rely more on traffic networks, and high-ranking cities can break through their dependence on traffic networks, to some extent.

3.2. Study Case

Zhejiang Province, located on the eastern coast of China and the southern wing of the Yangtze River Delta city cluster (Figure 1), is one of the most economically developed provinces in China and a province strong in transportation construction. There are 11 prefecture-level cities in Zhejiang Province. Hangzhou, the capital city, is the most economically developed, with a GDP of CNY 161.08 billion and a resident population of 11.94 million in 2020, accounting for 24.9% of the province’s total GDP and 18.5% of the total resident population, respectively, with a GDP 1.3 times that of the second city, Ningbo, and a resident population 1.2 times that of the second city, Wenzhou, both of which are far ahead.

Zhejiang Province was selected as the study case in this paper for two reasons. First, the level of economic development in Zhejiang Province is relatively high, and the differences in flows of immaterial and material factors between cities are comparable. Second, the traffic network in Zhejiang Province is relatively complete, but the difference between the north and the south is significant, and the characteristics of the various networks themselves lend themselves to comparisons of differences.

3.3. Research Data

3.3.1. Traffic Network

According to the discussion on the quantification of transportation connections above, the traffic network should be a network formed by the carrying capacity of traffic connections between cities under existing transportation conditions. The greater the carrying capacity of transportation means and the shorter the passage time (distance), the closer the connection. Based on this definition, and to avoid the impact of COVID-19 on the traffic carrying capacity, the study selects two modes of transportation—road and high-speed railway—to measure the inter-city traffic links in 2019 (according to Zhejiang Statistical Yearbook 2020, these two modes of transportation accounted for 92% of the trips in 2019, and for the sake of simplifying the study, ordinary railroad, air, and waterway trips were not considered for the time being).

To calculate the road traffic connection, we need the civil car ownership data for each city and the data of travel time between two cities. The civilian vehicle ownership data was obtained from the statistical yearbook of each city in Zhejiang Province. The travel time data was obtained using the API interface on the website of AutoNavi mapping (AMap) (https://lbs.amap.com/ (accessed on 30 April 2021)) to calculate the travel time between two cities at the location of each city’s government. The total number of high-speed railway schedules and the average travel times of each city were needed to calculate the traffic connection of the high-speed railway. High-speed railway refers to 3 types: G-series high-speed railway, D-series high-speed train, and C-series inter-city trains, and the data were collected from the website of 12306 (https://www.12306.cn/index/ (accessed on 30 April 2021)). The average travel time was calculated by adding a total of 60 min, considering the travel time between the origin and destination, respectively, and the high-speed railway station is about 30 min. The above data are of different magnitudes; thus, to make them comparable, the MaxAbs method was used for standardization. The MaxAbs standardization method is suitable for data without outliers and must maintain the distribution structure, which fits the requirements of this study for data standardization.

Urban networks include two types of elements, nodes, and edges. Usually, the connectivity between nodes is represented by connection degree, and the attraction and radiation power of nodes are represented by centrality. The connection degree and centrality of traffic networks are calculated as follows.

$$V_{JTij}==k_R\frac{R_i{R}_j}{t_{Rij}^2}+k_G\frac{G_i{G}_j}{t_{Gij}^2}$$

(1)

$$N_{JTi}={\displaystyle \sum }_{i=1}^{n-1}{V}_{JTij}$$

(2)

where $V_{JTij}$ is the traffic connection degree between city i and city j, and $N_{JTi}$ is the traffic centrality of city i. $k_R$ and $k_G$are the weights of road connection and high-speed railway connection, respectively. According to the passenger volume ratio of these two transportation modes in Zhejiang Province in the Zhejiang Statistical Yearbook 2020, $k_R$= 0.75 and $k_G$= 0.25. $R_i$ is the civil car ownership of city i, $R_j$ is the civil car ownership of city j, and $t_{Rij}$ is the minimum time of road travel between city i and city j. $G_i$ is the total number of high-speed railway trips outbound to city i, $G_j$ is the total number of high-speed railways out to city j, and $t_{Gij}$ is the average time of high-speed railway trips between city i and city j. n is the number of cities.

3.3.2. Enterprise-Association Network

Enterprise-association networks initially refer to the association networks between cities constructed based on the association of corporate headquarters and branches. Taylor proposed that economic connections between cities are the essence of urban networks; cities as the fulcrums of capital are the agglomeration of firms, firms within cities are the actors of urban networks [8], and urban networks can be identified and analyzed by aggregating the enterprise associations between cities [59]. World city network studies tend to calculate network connections using the association data of the headquarters and the branches of major multinational companies in high-end productive services [17,60]. Since then, applications at the national and regional levels have expanded the associations to include industry-wide firm associations as well as investments in listed firms [60,61]. Some researchers have also suggested that the all-firm association data still lack the weight of connection, and the connection is only established in the headquarters and branch relationship, which is not consistent with reality. The study is conducted based on the investment data of listed companies and lacks the investment of non-listed companies [62]. In this paper, we use the investment data of all firms to construct an enterprise-association network, which can solve the above data-bias problem. The data was obtained from the Tianyancha website (https://www.tianyancha.com/advance/search (accessed on 30 April 2021)), covering all enterprises registered with the China Industry and Commerce Bureau. They includes shareholder enterprises and invested enterprises, as well as their location, operating status, investment amount and other fields. We screened the data and only retained the investments that both enterprises made. We summarized the investment amount according to the city where the enterprise is located, so as to obtain the data required for the study. Next, the connection degree and centrality of the enterprise-association network were calculated using the following formulas.

$$V_{QYij}=I_{ij}+I_{ji}$$

(3)

$$N_{QYi}={\displaystyle \sum }_{i=1}^{n-1}V{F}_{QYij}$$

(4)

where $V_{QYij}$ is the connection degree of enterprise association between city i and city j, and $N_{QYi}$ is the centrality of enterprise association of city i. $I_{ij}$ and $I_{ji}$are the investment amounts of city i to city j and city j to city i, respectively. N is the number of cities.

3.3.3. Inter-City-Trip Network

An inter-city-trip network is a network constructed by trips that cross cities. High-speed-railway-passenger flow and air-passenger flow commonly used in the study belong to inter-city trips, but the sampling is biased. In this paper, we use a large sample and all trips to construct an inter-city-trip network based on the travel connections identified by positioning data retrieved from the “Maps” mobile application for Baidu. The data are the average daily inter-city trip volume between two cities on ordinary weekdays and weekends in October 2020 (although the website only provides the relative values of travel volume, it is still possible to make cross-sectional comparisons), obtained from the Baidu migration website (https://qianxi.baidu.com/#/ (accessed on 30 April 2021)). The connection degree and centrality of the inter-city trip network are calculated as follows:

$$V_{CXij}=T_{ij}+T_{ji}$$

(5)

$$N_{CXi}={\displaystyle \sum }_{i=1}^{n-1}{V}_{CXij}$$

(6)

where $V_{CXij}$ is the connection degree of inter-city trip between city i and city j, and $N_{CXi}$is the centrality of inter-city trip of city i. $T_{ij}$ and $T_{ji}$are the travel volume from city i to city j and from city j to city i, respectively. N is the number of cities.

3.3.4. Data Standardization

The data were standardized using MaxAbs method: the maximum connection degree and centrality are converted to 1, and other values are standardized by the percentage of the maximum value to facilitate comparative analysis and not change the data distribution structure.

$$V_{Sij}=\frac{V_{ij}}{V_{max}}$$

(7)

$$N_{Si}=\frac{N_i}{N_{max}}$$

(8)

where $V_{Sij}$ is the standardized connection degree of city i and city j, $V_{ij}$ is the connection degree of city i and city j, and $V_{max}$ is the maximum connection degree in the network. $N_{Sij}$ is the standardized centrality of city i and city j, $N_{ij}$ is the centrality of city i and city j, and $N_{max}$ is the maximum centrality in the network. After processing,

Table 1. Connection degree.

City 1	City 2	Traffic Network	Enterprise-Association Network	Inter-City-Trip Network
Hangzhou	Jiaxing	0.57	0.57	1.00
Hangzhou	Shaoxing	1.00	0.56	0.88
Hangzhou	Huzhou	0.34	0.49	0.63
……	……	……	……	……

Note: Ellipses mean there are a lot of rows which are not all listed in the table.

and

Table 2. Centrality.

City	Traffic Network	Enterprise-Association Network	Inter-City-Trip Network
Hangzhou	1.00	1.00	1.00
Huzhou	0.15	0.24	0.26
Jiaxing	0.23	0.36	0.50
……	……	……	……

Note: Ellipses mean there are a lot of rows which are not all listed in the table.

are obtained as the base data of the study.

3.4. Research Method

The research framework of this paper is as follows (Figure 2). This study is divided into four parts, including network construction, model building, indicator analysis, and advice. Among them, the second and third parts are the most significant. We chose curve fitting to build models, and identified mismatched networks using standardized residuals.

The curve-fitting method is generally used to test the correlation between two data sets. In contrast to the least squares method, curve fitting does not presuppose a fitting function. Fitting functions are generally linear, exponential, logarithmic, and power functions, and fitted one by one until the correlation coefficient is maximized.

With traffic connection degree as the independent variable, we fit the connection degree curves with enterprise-association connection degree and inter-city-trip connection degree as the dependent variables, respectively. When traffic centrality was the independent variable, we fit the centrality curves with enterprise-association centrality and inter-city-trip centrality as the dependent variables, respectively. This process can be implemented with Microsoft Excel, and the formulas and correlation coefficients of the fitted curves can be generated automatically.

The study also pays particular attention to outliers that deviate from the fitted curve (standard residuals greater than 1.65 or less than −1.65), implying that enterprise associations or inter-city trips are much higher or lower than they should be between cities under existing traffic-network conditions at the 10% significance level. The standard residuals were calculated according to the following formula.

$${\delta }^{*}{}_i=\frac{{\delta }_i}{{\sigma }_{\delta }}$$

(9)

where ${\delta }^{*}{}_i$ is the standard residual of the i-nth connection degree in city i or network, ${\delta }_i$ is the residual of the i-nth connection degree in city i or network (the result obtained by substituting the independent variable into the fitted curve minus the independent variable), and ${\sigma }_{\delta }$ is the standard deviation of the residual. The above calculation can be implemented in Microsoft Excel.

4. Results

4.1. Network Characteristics

The data in Table 1 and Table 2 were used to generate the traffic network, enterprise-association network, and inter-city-trip network on the ArcGIS10.7 platform (Figure 3). The three networks show the following common features: First, the connection degree differs significantly from north to south, the connection degree in northern Zhejiang is large, and that in southern Zhejiang is small. All of them are attracted and radiate outward, with Hangzhou as the core. Second, there is a significant difference in centrality between north and south, with high centrality in northern Zhejiang and low centrality in southern Zhejiang, and the centrality decreases outward, with Hangzhou as the core. Overall, the three networks are relatively similar.

However, there are also differences among the three networks: the areas with high traffic-network connections are concentrated only along Hangzhou Bay. Hangzhou is the core linking Jiaxing, Shaoxing, and Ningbo, while the areas with more connections of enterprise-association networks and inter-city-trip networks can extend further out to Jinhua, Wenzhou, and Huzhou.

4.2. Correlation Test of Traffic Network and Enterprise-Association Network

The connection degree and centrality of the traffic network and the enterprise-association network were separately curve fitted (Figure 4). The fitted curves of connection degree are power functions, and the connection degree of traffic and enterprise association between cities are significantly positively correlated (correlation coefficient 0.69) at a 1% significance level, and the increase in enterprise-connection degree tends to slow down as the traffic-connection degree increases. This indicates that, at this stage, in Zhejiang Province, with an improvement in transportation conditions, the capital flows between cities can be enhanced accordingly, but with diminishing marginal effects. At the 10% significance level, the standard residuals of enterprise-association connection degree between Hangzhou and Ningbo (5.24); Hangzhou and Zhoushan (2.80); Hangzhou and Wenzhou (2.45); Hangzhou and Jiaxing (2.41); Hangzhou and Huzhou (2.31); and Hangzhou and Shaoxing (1.82) are high, especially between Hangzhou and Ningbo and Hangzhou and Zhoushan; where the standard residual significance level of connection degree is as high as 1% (Figure 4a). This shows that the capital flows between Hangzhou and these cities along the South Taihu Lake–Hangzhou Bay, as well as between Hangzhou and the core cities of the two metropolitan areas of Ningbo and Wenzhou, have far exceeded the size of the enterprise association corresponding to the current average transportation conditions (Figure 5).

The fitted curve of centrality is an exponential function, and the centrality of the traffic network and enterprise-association network of each city are significantly positively correlated (correlation coefficient 0.84) at a 1% significance level, and with the increase in traffic-network centrality, the magnitude of the increase in the enterprise-association network centrality becomes larger. This indicates that the influence of cities on capital flows will increase significantly with the improvement in transportation conditions in Zhejiang Province at this stage, and the marginal effect is still in the incremental stage. At the 1% significance level, the standard residual (2.71) of Hangzhou’s enterprise-association centrality is high (Figure 4b). Which indicates that Hangzhou’s influence on the provincial capital flows far exceeds the support of the current average transportation conditions for its economic status, which is consistent with the characteristic that Hangzhou’s economic development level far exceeds that of other cities in the province.

In summary, traffic networks have a supportive effect on enterprise-association networks. Although the impact of transportation-facility interconnection on immaterial capital flows is usually considered weak, the overall impact is still present. However, along the South Taihu Lake–Hangzhou Bay, which has the highest level of economic development, economic connections have broken through both the spatial limits of space of place and Hangzhou’s influence on the provincial economy.

4.3. Correlation Test of The Traffic Network and Inter-City-Trip Network

The connection degree and centrality between the traffic network and the inter-city-trip network were curve fitted separately (Figure 6). The fitted curves of connection degree are power functions, and the connection degree of traffic and inter-city trips between cities are significantly positively correlated (correlation coefficient 0.92) at a 1% significance level, and the increase in inter-city-trip connection degree tends to slow down as the traffic-connection degree increases. This indicates that, at this stage in Zhejiang Province, with an improvement in transportation conditions, the human flow between cities can be enhanced accordingly, but with diminishing marginal effects. At the 10% significance level, the standard residuals of inter-city-trip connection degree between Hangzhou and Jiaxing (5.28); Hangzhou and Huzhou (3.43); Hangzhou and Jinhua (2.06); and Hangzhou and Shaoxing (1.78) are high, especially between Hangzhou and Jiaxing and Hangzhou and Huzhou, where the standard residuals of significant-level connection degrees are as high as 1% (Figure 6a). This shows that the human flows between Hangzhou and its metropolitan areas of Jiaxing, Huzhou, Shaoxing, and Jinhua on the G60 corridor have far exceeded what volume of inter-city trips corresponding to the current average transportation conditions (Figure 7).

The fitted curves of centrality are power functions, and the centrality of the traffic network and inter-city-trip network of each city are significantly positively correlated (correlation coefficient 0.96) at a 1% significance level, and with an increase in traffic network centrality, the magnitude of the increase in the inter-city-trip network centrality slows down. This indicates that the influence of cities on the human flows will not increase indefinitely with an improvement in transportation conditions in Zhejiang Province at this stage, and the marginal effect has entered a downward stage. At the 1% significance level, the standard residual (3.13) of Hangzhou’s inter-city-trip centrality is high (Figure 6b), which indicates that Hangzhou’s influence on the provincial human flow far exceeds the support of the current average transportation conditions for its ability to gather people.

In comparison, traffic networks are more relevant to inter-city-trip networks in terms of both connection degree and centrality, which is consistent with the reality that the human flow is more dependent on the interconnection of transportation facilities than capital flow. However, the human-flow connection in the Hangzhou metropolitan area and G60 corridor has broken through the limits of space of place; Hangzhou’s own ability to attract and radiate human flow in Zhejiang Province has also broken through the limit.

5. Discussion

5.1. Roles of Traffic Facilities

The flow of factors is freer than before under the background of time–space compression caused by the traffic revolution. However, the premise is still the interconnection of transportation facilities, which was verified in the case study of Zhejiang Province, China. The immaterial capital flows actually depend on the financial barrier between cities, which determines whether it will restrict business cooperation. This kind of barrier should not exist in China’s market-economy environment. The reason why capital flows are related to the interconnection of transportation facilities is that business exchanges between enterprises still require face-to-face communication. If the distance between the two cities is long and the trips are inconvenient, business exchanges between the two cities and capital flows will be restricted. Therefore, it is very important to strengthen capital and build a more closely connected transportation network in the region.

As the capital city of Zhejiang Province, Hangzhou has the highest level of economic development in the province. Its attraction and radiation of capital and human flows have far exceeded the scale supported by the average traffic conditions of the province. The flow of factors between Hangzhou and Huzhou, Jiaxing and other cities have also exceeded the average support level of the traffic network. The traffic network in this paper only included the high-speed rail and cars, but human flows which must rely on transportation facilities to realize going to another city may use other ways, such as train, coach and so on. It is also possible that the full load of high-speed rail and cars enables an excess of people to travel from one city to another. All these can lead to the flow of factors exceeding the average support level of the transportation network. In brief, the capital and human flows of high-grade cities can indeed go beyond the dependence on the “proximity” of the space of place, to a certain extent.

5.2. Application Values and Relevant Suggestions

The study has the following application values. Firstly, through this paper, cities in Zhejiang Province can better understand their roles in the regional urban network, and gain some guidance for the formulation of regional and urban development strategies. Secondly, the results provide a reference for optimizing the layout of transportation infrastructure in Zhejiang Province. In particular, it can provide decision-making support for the construction priorities of major transportation projects.

In order to enhance the carrying capacity of traffic connections, the development of cities should be promoted in various ways, and the layout of transportation infrastructure in the province optimized, we put forward the following feasible suggestions. For transportation infrastructure, the government should prioritize construction projects to improve the transportation network. Especially for the cities whose transportation facilities are still not perfect, or two cities whose capital flow and human flow far exceed the support of the existing traffic network, priority should be given to the implementation of their construction projects. For example, Zhoushan is the only city in Zhejiang Province that does not have high-speed rail, and it relies only on roads and waterways to connect with the outside world. If the high-speed rail line with other cities, especially Hangzhou, can be opened, it will be of great benefit to the development of Zhoushan and the improvement in the average traffic level of the whole province. When it comes to traffic connections, we believe that increasing the number of high-speed trains and passenger trains between cities can enhance the traffic carrying capacity. Of course, increasing the speed of high-speed rail is a practical proposal. At present, the speed of high-speed trains in Zhejiang Province is generally 300 km/h, while the fastest high-speed trains in operation in China can reach 400 km/h, and some cities have even begun to use maglev trains with speeds up to 600 km/h. In addition to optimizing the transportation facilities between cities, cities themselves can also play a role. For example, they can increase the number of civilian cars by issuing subsidies, or implement policies to promote economic development and population inflow.

6. Conclusions

Urban networks currently constitute a dominant topic in regional research. The prototype of urban networks is the enterprise-association network based on corporate headquarters and their branches. Academic research has interpreted and empirically examined city networks from different perspectives, such as passenger-flow, freight, and information networks, based on the prototype of city networks. Nevertheless, abundant relevant research has overshadowed the research on infrastructure support, which is the condition for the formation of urban networks.

The “flow” data is the basic data for urban-network research, and urban-network researchers hope to use real data to reveal the characteristics of the connection between cities. As real data is difficult to obtain, researchers often use simulation and alternative methods to obtain “flow” data. Nevertheless, the current research focuses on the characteristics of urban networks reflected by different types of “flow” data, ignoring the basic role of infrastructure in supporting the space of flow and confusing the conditions for the application of simulation and alternative methods. In this paper, through a literature review, we clearly distinguish the concepts of passenger connection and traffic connection and point out that the former is the manifestation of traffic connections. At the same time, the latter is the carrier of the urban network, which provides support for the flow of factors, including passenger connections.

In the context of the time–space compression effect caused by the transportation revolution, factor flows are freer than ever. However, the interconnection of transportation facilities remains an important prerequisite for the flow of factors, whether it is immaterial or material. In this paper, we constructed fitting models of a traffic network and enterprise-association network and of a traffic network and inter-city-trip network to test the basic supporting role of the traffic network as a carrier of urban networks. The research results confirmed the research hypothesis proposed at the beginning of this paper, and the following conclusions are obtained.

(1)

Both immaterial capital flows and material human flows are strongly dependent on transportation interconnections, with the latter being more dependent on transportation interconnections than the former.

(2)

Not all factor flows between cities follow the rule that the closer the traffic connections are, the closer the city network links. In the case of Zhejiang Province, it is found that the high-grade city of Hangzhou attracts and radiates both people and capital far beyond what the current traffic conditions can support and drives the formation of economic and human-flow connections with cities such as Jiaxing, Huzhou, and Shaoxing that exceed the average traffic conditions.

The research conclusions provide another way for urban development, that is, to promote economic development by improving traffic conditions. The results can help cities in Zhejiang Province understand their respective roles in the regional urban network better. They also provide decision support for optimizing the layout of transportation infrastructure in Zhejiang Province. New highways and high-speed railway lines should be selected, with priority given to lines with capital flows and human flows far beyond those supported by existing traffic networks, which can yield a higher return on investment. However, it is also necessary to consider the coordination and proper tilting to the lagging development areas to avoid the Matthew effect, wherein the strong are even stronger and the weak are even weaker due to all the resources being invested only in those areas that already have a good foundation.

This paper demonstrates that traffic networks are strongly correlated with inter-city-trip networks and enterprise-association networks, respectively. However, it is hard to explain clearly whether the traffic network promotes the flow of factors within the region or the flow of factors promotes the traffic interconnection. This is because convenient transportation connections do facilitate inter-city trips for residents, thus promoting the more extensive inter-city movement of people, facilitating face-to-face exchanges, and enhancing investment between cities. Conversely, transportation infrastructure development is a costly project, and the layout of routes and stations will inevitably consider the basis and potential for inter-city connections.

This paper differs from previous studies in that it not only analyzes the correlation of urban networks from different perspectives but also validates the relationship between carriers and performance in Castells’ theory of space of flow. However, the study also has some limitations. Due to the inability to obtain an exact comparison of inter-city-trip-network and enterprise-association-network data before and after the interconnection of transportation infrastructure between cities, it cannot be proven that transportation-infrastructure connectivity has a causal relationship with economic and human-flow connections between cities. In the future, we can continue to pay more attention to the changes in inter-city-trip-network and enterprise-association-network data before and after the opening of transportation infrastructure, provide insights into the spatiotemporal evolution of urban networks, and investigate the relationship between urban-network connections and their material carriers from the perspective of causal evolution.