Detecting the Spatial Network Structure of the Guanzhong Plain Urban Agglomeration, China: A Multi-Dimensional Element Flow Perspective

Abstract

Element flow has gradually become an important method for studying urban spatial structure. This study examined 11 prefectural cities in the Guanzhong Plain urban agglomeration; constructed a measurement model for information, traffic, migration, and composite networks; and analyzed the spatial structure of the urban network of the urban agglomeration through social network analysis and spatial visualization. The spatial structure of the composite flow network had Xi’an as the center and Xianyang, Baoji, Weinan and Tianshui as important nodes; Yuncheng, Linfen and Qingyang were the secondary nodes, radiating to the surrounding three cities. Element flow connection strength was unbalanced, and only three city pairs were in the first level of the composite flow network. Network density was low-middle, and the network connection was weak. Xi’an was the primary central city of the Guanzhong Plain urban agglomeration with the strongest agglomeration and radiation capabilities; it could communicate with other cities without intermediate cities and was a bridge for other cities. Tongchuan, Pingliang, Shangluo, and Qingyang were at the edge of the urban agglomeration and had weak agglomeration, radiation, and intermediary capabilities. The inner cities of cohesive subgroups were closely related with weak connections between subgroups. The single-polarization of the Guanzhong Plain urban agglomeration was serious, and the single-core spatial structure centered on Xi’an had limited impact on the urban agglomeration. Development of small and medium-sized cities should be strengthened in the future.

1. Introduction

The essence and driving force of urban architecture and dynamic change lie in the connections between cities. The delineation of urban agglomerations, metropolitan areas, and so on is a strategic appeal for the reproduction or expectation of existing relationships between cities with the main purpose to promote better development of the city itself and the radiation area through the exertion of the agglomeration radiation effect. These have long been the focus of academic research [1,2]. In 2018, the Chinese government officially approved “the Guanzhong Plain Urban Agglomeration Development Plan”, another state-level urban agglomeration after the Beijing–Tianjin–Hebei region, the Yangtze River Delta, the Pearl River Delta, the middle reaches of the Yangtze River, and the Chengdu–Chongqing region. The Guanzhong Plain urban agglomeration spans Shaanxi, Shanxi, and Gansu provinces and covers 11 cities with an area of 1.07 × 10⁵ sq. km, a population of 40.4 million by the end of 2021, and a regional gross domestic product of CNY 2.36 trillion. The Guanzhong region has a good geographical location, a rich resource base, and strong industrial strength, and the Guanzhong Plain urban agglomeration plays an important role in supporting the Western Development Strategy in the New Era, the construction of the “One Belt, One Road” economic zone, and the ecological protection and high-quality development of the Yellow River Basin [3]. In October 2021, the Central Committee of the Communist Party of China and the State Council issued the “Planning Outline for Ecological Protection and High-quality Development in the Yellow River Basin”. The plan proposed to “build high-quality and high-standard urban agglomerations along the Yellow River”. The urban agglomeration is the core of the region and the focus of high-quality development of the river basin [4]. However, the Guanzhong Plain urban agglomeration, as the largest urban agglomeration in the middle reaches of the Yellow River Basin, has faced problems such as late development planning, convergence of urban functions, regional administrative barriers, and improper regional competition.

It is difficult for urban agglomeration to achieve high-quality coordinated development [5]. At the same time, the Guanzhong Plain urban agglomeration has shortcomings such as a small number of cities, a low level of development, and a weak radiation and driving effect of central cities. Its radiation effect on the surrounding area and even the northwest region is not obvious, and it has difficulty playing a role in leading the western development in the new era and promoting the rise of the western economy [6].

The development of urban agglomerations is not limited to the development of cities within urban agglomerations. Coordinated development between cities is also crucial [7]. The report of the 19th National Congress of the Communist Party of China presents new requirements for the development direction of urban agglomerations: to rely on the regional coordinated development strategy, build a spatial pattern of coordinated development of cities and towns of various scales, and solve the problem of unbalanced and insufficient regional development [8]. It involves analyzing the structural characteristics of the urban network and identifying the interaction of node cities and the status and role of cities in the network and can provide a reference for further optimizing the resource allocation of urban agglomerations, strengthening the coordinated development of cities, and promoting the integration of urban agglomerations.

The globalization of the economy is profoundly affecting the urban structure and economy. The regional urban system’s trend has changed from polar nuclear to “flattening”, and the status of urban agglomerations as a carrier is increasingly prominent [9]. With the proposal of the flow space theory [10], the analysis of the network structure and system of urban agglomerations based on passenger, cargo, and information flow has become a research hotspot [11]. Although there is no concept in international research that directly corresponds to urban agglomeration, theories and methods such as “network society”, “flow space”, “central flow theory”, and “chain network model” are commonly used in metropolitan area research [12,13,14,15,16,17].

Urban agglomerations play an important role in China’s urbanization pattern [18], and the Beijing–Tianjin–Hebei [19], Yangtze River Delta [20], Pearl River Delta [21], middle reaches of the Yangtze River [22], and Chengdu–Chongqing urban agglomerations [23] are all important research objects. Research methods are mainly based on a gravity model and social network analysis method [1,24,25]. Most research perspectives are based on a single dimension such as economic [26], traffic [27,28], population [29,30], information [31], and consumption flow [32]. Although research regarding Chinese urban agglomeration based on the spatial network structure is growing, there are relatively few articles on the study of urban spatial network structure based on multisource element flow. Moreover, the influence of multisource element flow is either stronger or weaker, and the calculation of the weight that should be included in the final composite flow model does not yet have a definite answer in the academic community [11]. Combining the factors of the region itself, there has been a lack of convincing research to propose countermeasures and suggestions to improve the integrated development level and influence of urban agglomerations. Perhaps influenced and suggested by the development a priori theory and the significance of the research results, most studies in China focus on the early planned urban agglomeration in Beijing–Tianjin–Hebei, the Yangtze River Delta, and Pearl River Delta. Less attention has been paid to the urban agglomeration in Chengdu–Chongqing and Guanzhong, which was only approved in recent years [33]. The polarization effect of the Guanzhong Plain urban agglomeration is more obvious than in other urban agglomerations in China. The division of administrative regions belonging to different provinces makes the differences within the urban agglomeration even greater, and the level of economic development, population size, urban functions, spatial distance, cultural distance, and administrative boundaries have increased the difficulty of the mutually beneficial development of urban agglomerations. Thus, they have more research and practical value.

At present, there are relatively few studies on the spatial network structure of the Guanzhong Plain urban agglomeration. However, some progress has been made. Zhan et al. (2021) combined social networks and a revised gravity model, constructed the tourism economic network model, and analyzed the spatial pattern of the tourism economic network in the Guanzhong Plain urban agglomeration [34]. Li et al. (2021) constructed three urban network models of economic connection, information connection, and connection of bank headquarters and branches and analyzed the urban network structure of the Guanzhong Plain urban agglomeration [35]. Zhou et al. (2019) used National Polar-orbiting Partnership Visible Infrared Imaging Radiometer Suite night light data and calculated the shortest transit time using origin–destination cost analysis to analyze the scale, connection, and scope of influence of 78 county-level administrative units in the Guanzhong Plain urban agglomeration [36]. Fei (2022) built an information flow network model from the perspective of public search and attention and analyzed the spatial structure characteristics of the Guanzhong Plain urban agglomeration [37].

In general, the existing research is based on a single correlation attribute. Comprehensive research based on a multi-dimensional network remains insufficient. Therefore, this study investigates 11 prefecture-level cities in the Guanzhong Plain urban agglomeration using the information, traffic, and migration network measurement model to quantitatively calculate the connection intensity of each element flow. The structural characteristics of the city network are analyzed and compared from different connection perspectives, and the development of each city as well as the connections and differences between cities are evaluated. Meanwhile, the composite network measurement model is used to analyze the structural characteristics of the comprehensive contact network. Analyzing the spatial network structure of the Guanzhong urban agglomeration from the perspective of flow space is of great significance to deeply understanding the characteristics of urban flow space in the Guanzhong area and help the Guanzhong Plain urban circle move towards an era of spatial networking.

2. Materials and Methods

2.1. Study Area

The planning scope of the Guanzhong Plain urban agglomeration includes five cities of Xi’an, Baoji, Xianyang, Tongchuan, and Weinan in Shaanxi Province; the Yangling Agricultural High-tech Industrial Demonstration Zone and Shangzhou District; Luonan, Danfeng, and Zhashui Counties of Shangluo City; Yuncheng City of Shanxi Province (excluding Pinglu and Yuanqu Counties); Yaodu District; Houma City (Xiangfen County); Huozhou City; Quwo County; Yicheng County; Hongdong and Fushan Counties of Linfen City; Kongtong District; Huating County; Jingchuan County; Chongxin and Lingtai Counties of Pingliang City; Qingyang City; and Tianshui City in Gansu Province. The area covers 107,100 square km. The Guanzhong Plain urban agglomeration spans the three provinces of Shaanxi, Shanxi, and Gansu and includes several cities and county-level administrative districts.

Due to the availability of data and the convenience of structural analysis, this study takes the city area as the research scale and ultimately selects 11 prefecture-level cities including Xi’an, Baoji, Xianyang, Tongchuan, Weinan, Shangluo, Yuncheng, Linfen, Tianshui, Qingyang, and Pingliang as the research objects (Figure 1).

2.2. Data Sources

The Baidu search index between cities represents the strength of the information flow connection, which is derived from the Baidu index data analysis platform. The frequency data of ordinary, bullet trains, and high-speed rails in the traffic flow data are from the ticketing system of China Railway Customer Service Center Network (http://www.12306.cn (accessed on 12 June 2022)). The bus frequency data come from Fliggy Travel. The data used in the migration flow come from the Baidu migration data platform provided by Baidu Maps, Baidu Network, based on Baidu Insight technology. The platform excavates and integrates the location information of mobile phone users in China and then realizes the visualization of population spatial displacement, which is finally presented by the in-migration and emigration scale index of the city. This scale characterizes the intensity and direction of population flow in a certain period. The timeframe is from 1 March to 31 May 2022.

2.3. Research Methods

2.3.1. Information Network Measurement Model

Baidu search index uses city names as keywords and can reflect the degree of attention that citizens of one city pay to another city. This study analyzes the information connection strength between the cities by counting the search volume of internet users in each city and analyzing the network pattern of information connection between cities. The calculation formula is as follows:

$$I_{ab}=R_{ab}{R}_{ba}$$

(1)

$$I_a={\displaystyle \sum _{b=1}{I}_{ab}}$$

(2)

where I_ab represents the information connection strength between city a and city b, R_ab is the online search volume of city a to city b, R_ba is the online search volume of city b to city a, and I_a represents the total amount of information flow in city a.

2.3.2. Traffic Network Measurement Model

Based on the practice of Gu et al. in 2015 [38], the traffic connection strength between cities is obtained through the weighted summation of the number of buses, trains, bullet trains, and high-speed rails between cities. The formula is as follows:

$$t_{ab}=\frac{1}{3}{M}_{ab}+\frac{2}{5}{K}_{ab}+\frac{5}{6}{D}_{ab}+G_{ab}$$

(3)

$$T_{ab}=\frac{t_{ab}+t_{ba}}{2}$$

(4)

$$T_a={\displaystyle \sum _{b=1}{T}_{ab}}$$

(5)

where t_ab represents the intensity of traffic connection between city a and city b; M_ab, K_ab, D_ab, and G_ab represent the number of buses, trains, bullet trains, and high-speed rails, respectively, from city a to city b; T_ab represents the mean value of the traffic connection intensity between city a and city b; and T_a is the total amount of traffic flow in city a.

2.3.3. Population Migration Network Measurement Model

The migration scale index of the Baidu migration platform can reflect the scale of the population moving in and out, which can represent the intensity and direction of the population flow in a certain period.

$$R_{ab}=S_{ab}+S_{ba}$$

(6)

$$R_a={\displaystyle \sum _{b=1}{R}_{ab}}$$

(7)

where R_ab is the connection strength of population migration between city a and city b, S_ab is the migration scale index of city a to city b, S_ba is the migration scale index of city b to city a, and R_a is the total number of migration flow in city a.

2.3.4. Composite Network Measurement Model

This paper adopts the game theory combination weighting method [39,40] to empower the information flow, traffic flow, and population migration flow, in which the subjective weighting is realized by the analytic hierarchy process and the objective weighting is realized by applying the CRITIC method.

(1)

Analytic hierarchy process: The analytic hierarchy process is a kind of subjective weighting analysis method to solve the problem that it is difficult to accurately recognize the relative importance degree of multiple objectives. It quantifies the weighting reasonably by measuring the relative importance degree of each objective, and uses the weight value to effectively compare the importance order of each objective. By establishing the hierarchical structure model, constructing the judgment matrix, hierarchical single ranking, and consistency test, the index weight is finally determined [41].

(2)

CRITIC method: The CRITIC method is a type of objective weight method used to solve the problem of multiple targets failing to effectively measure the relative importance of each target due to data differences. The importance of target data is obtained by fully mining and utilizing its own attributes, and a corresponding weight value is derived to effectively compare the order of importance between various targets. The final weight is determined through dimensionless processing of indicators, calculation of index variability, index conflict, and information amount [42].

(3)

Game theory empowerment: The weights of indicators obtained by different weighting methods may differ greatly or even conflict with each other; therefore, the consistency testing of the weights should be carried out before the weighing of game theory combinations. The distance function is as follows: In this study, information, traffic, and population migration flow are regarded as equally important with weights of 1/3 each. The formula is as follows:

$$\mathrm{d}\left[w_{j\_a}{w}_{j\_c}\right]={\left\{\frac{1}{2}{\displaystyle \sum _{j=1}^m{\left[w_{j\_a}-w_{j\_c}\right]}^2}\right\}}^{\frac{1}{2}}$$

(8)

In the formula, $w_{j\_a}$ and $w_{j\_c}$ are the weights of the two groups participating in the game. The smaller $\mathrm{d}\left[w_{j\_a}{w}_{j\_c}\right]$ is, the closer the weights of the two groups are. When $\mathrm{d}\left[w_{j\_a}{w}_{j\_c}\right]$ < 0.2, it is considered to pass the consistency test and can be combined.

A basic weight vector set $w={\left(w_{j\_a},w_{j\_c}\right)}^T$ is established by the analytic hierarchy process and CRITIC method, and any linear combination of the vector set is carried out, $w=\left(a_1{w}_{j\_a}{}^T+a_2{w}_{j\_c}{}^T \right)$, In order to obtain the minimization of the deviation between the combined weight w and two kinds of weights $\left(w_{j\_a},w_{j\_c}\right)$, $a_1$ and $a_2$ are obtained from the differential property of matrix, and then $a_1{}^{*}$ and $a_2{}^{*}$ are obtained by normalization. The formula is as follows:

$$\left(\begin{array}{cc}{w}_{j\_a}{w}_{j\_a}{}^T& w_{j\_a}{w}_{j\_c}{}^T\\ w_{j\_c}{w}_{j\_a}{}^T& w_{j\_c}{w}_{j\_c}{}^T\end{array}\right)\left(\begin{array}{c}{a}_1\\ a_2\end{array}\right)=\left(\begin{array}{c}{w}_{j\_a}{w}_{j\_a}{}^T\\ w_{j\_c}{w}_{j\_c}{}^T\end{array}\right)$$

(9)

$$a_1{}^{\ast }=\frac{a_1}{a_1+a_2}$$

(10)

$$a_2{}^{\ast }=\frac{a_2}{a_1+a_2}$$

(11)

Finally calculate the combination weight $w=\left(a_1{}^{*}{w}_{j\_a}{}^T+a_2{}^{*}{w}_{j\_c}{}^T \right)$.

The formula for calculating the connection strength and total amount of composite flow is as follows:

$$C_{ab}=0.19I_{ab}{}^{\prime }+0.45T_{ab}{}^{\prime }+0.36R_{ab}{}^{\prime }$$

(12)

$$C_a={\displaystyle \sum _{b=1}{C}_{ab}}$$

(13)

where C_ab is the composite connection strength of city a and city b; C_a is the total amount of composite flow of city a; and I_ab′, T_ab′, and R_ab′ represent the result of normalized connection strength of information, traffic, and migration flow between city a and city b.

2.3.5. Social Network Analysis Method

In this study, the network density, centrality, and cohesion subgroup analyses within social network analysis are used to measure the degree of connection between nodes in the overall network, the network structure location of node cities, and the group composition within the overall network structure, respectively [43]. (1) Network density analysis: density is one of the most commonly used indicators in network analysis and describes the closeness of the relationship between nodes in the network. (2) Centrality analysis: degree, closeness, and betweenness centrality are used to quantitatively measure the external attraction, radiation, and intermediary capacity of cities within the urban agglomeration. (3) Cohesive subgroup analysis: a cohesive subgroup is a subset of actors that satisfies the following conditions; that is, there is a relatively strong, direct, close, frequent, or positive relationship between actors in this set.

3. Results

3.1. Spatial Structure Characteristics of Urban Agglomeration from the Perspective of Information Flow

Combining

Table 1. Total information flow and centrality.

City	Total Information Flow	Degree Centrality		Closeness Centrality		Betweenness Centrality
		In-Degree	Out-Degree	In-Degree	Out-Degree
Xi’an	5,315,688,240	10	10	100	100	72.407
Xianyang	2,580,707,456	3	7	58.824	76.923	1.852
Baoji	1,417,753,856	4	5	62.5	66.667	2.593
Weinan	1,216,750,784	4	5	62.5	66.667	2.593
Shangluo	589,644,560	4	1	62.5	52.632	0
Yuncheng	560,723,072	2	3	55.556	58.824	0.556
Tianshui	514,238,784	3	1	58.824	52.632	0
Tongchuan	444,283,824	3	1	58.824	52.632	0
Linfen	434,964,960	2	2	55.556	55.556	0
Qingyang	431,342,368	2	1	55.556	52.632	0
Pingliang	385,086,608	1	2	52.632	55.556	0

and Figure 2 reveals that the total information flow of Xi’an ranks first, accounting for 38.27% of the total information flow of the entire urban agglomeration, which is the first level. The information connection between Xi’an and other cities in the urban agglomeration is relatively close. There is no weak connection between Xi’an and other cities, and Xi’an and other cities in the urban agglomeration have a high degree of mutual concern and are the information center of the urban agglomeration. In addition, the total amount of information flow in Xianyang is strong, accounting for 18.58% and ranking at the second level. Baoji and Weinan are relatively weak, accounting for 10.21% and 8.76%, respectively, which are at the third level. The total amount of information flow in Shangluo, Yuncheng, Tianshui, Tongchuan, Linfen, Qingyang, and Pingliang is relatively low, ranking in the fourth level.

There are three cohesive subgroups in the information flow network. Subgroup 1 includes Linfen and Yuncheng in Shanxi Province, although the total amount of information flow is at the fourth level. The connection strength of Yuncheng–Linfen is second only to Xi’an–Other Cities, Baoji–Xianyang, and Xianyang–Weinan, and the information connection between the two cities in subgroup 1 is very close. Subgroup 2 includes Xianyang and Weinan in Shaanxi Province. The total amount of information flow in the two cities is relatively strong, and they are located at the second and third levels, respectively. The strength of information flow connection between Xianyang and Weinan also ranks at the forefront. Subgroup 3 includes Shangluo and Tongchuan in Shaanxi Province and Tianshui and Qingyang in Gansu Province. Although this subgroup includes four cities, the total information flow of cities and the strength of the information flow connection between cities are relatively weak.

The density of the information flow network is 0.35, which is at a lower-middle level, indicating that the spatial network of information flow in the Guanzhong Plain urban agglomeration is in the development stage, and the information network connection is weak. Centrality can be seen in Table 1. From the point degree centrality, Xi’an has the highest point-in and point-out degrees; as an active city in the city network, it not only receives the attention of other cities but also has a large number of active connections with other cities. Xianyang has a low point-in degree and a high point-out degree, indicating that Xianyang has weak agglomeration ability and strong radiation ability. The in- and out-degree of Baoji and Weinan are at a moderate level. The other cities have low point-in and point-out degrees, their radiation and attractiveness are weak, and the information flow connection with other cities is also weak. Such cities account for the largest proportion, indicating that the interrelation between cities in Guanzhong Plain urban agglomeration is weak and needs to be strengthened.

From the perspective of closeness centrality, Xi’an ranks first, indicating that the communication between Xi’an and other cities does not depend on the intermediate city while the communication between other cities needs to rely on the intermediate city. The polarization of betweenness centrality is serious, and Xi’an ranks first with a huge gap with Xianyang, Baoji, Weinan, and Yuncheng. Xi’an can serve as a bridge for communication between other cities in the Guanzhong Plain urban agglomeration and has a high degree of accessibility with other cities. Cities with betweenness centrality of 0 are mostly those with relatively small populations and low levels in the Guanzhong Plain urban agglomeration. The urban functions are relatively simple, and their status in the urban agglomeration needs to be improved.

From the perspective of information flow, the spatial structure of the Guanzhong Plain urban agglomeration presents the characteristics of “1 + 1 + 2 + 7”—that is, Xi’an as the center, Xianyang as the important node, Baoji and Weinan as the two wings, and radiating to seven surrounding cities. With the approval of the Xi’an metropolitan area, the cooperation between Xi’an and Xianyang has been strengthened, and the integration process of Xi’an and Xianyang has been accelerated. The current them is now “promoting the core area of the metropolitan area to take the lead in realizing the urban integration and driving the integrated development of the whole region”.

3.2. Spatial Structure Characteristics of Urban Agglomeration from the Perspective of Traffic Flow

In

Table 2. Total traffic flow and centrality.

City	Total Traffic Flow	Degree Centrality		Closeness Centrality		Betweenness Centrality
		In-Degree	Out-Degree	In-Degree	Out-Degree
Xi’an	28,510.800	8	9	33.333	50	49.815
Baoji	14,332.067	4	4	29.412	40	1.481
Weinan	12,148.600	3	5	28.571	41.667	2.222
Tianshui	11,395.733	4	3	29.412	38.462	0.37
Xianyang	9158.600	4	3	29.412	38.462	1.111
Yuncheng	5779.133	3	3	28.571	38.462	0.556
Linfen	4652.133	3	2	28.571	37.037	0
Qingyang	4170.667	1	2	27.027	37.037	0
Pingliang	2572.933	0	1	9.091	52.632	0
Shangluo	1646.800	1	0	35.714	9.091	0
Tongchuan	1211.333	1	0	35.714	9.091	0

and Figure 3, the total of traffic flow can be divided into four levels: first (Xi’an), second (Baoji, Weinan, Tianshui, Xianyang), third (Yuncheng, Linfen, Qingyang), and fourth (Pingliang, Shangluo, Tongchuan). Like the Ancient Silk Road and the “Belt and Road”, it shoulders the mission of “connecting the north and the south and connecting the east and the west”. The position of Xi’an in the strategic layout of national transportation planning is self-evident. Xi’an occupies the first place in the total traffic flow of the Guanzhong Plain urban agglomeration with 29.83% of the total; at the same time, Xi’an has established a strong traffic flow connection with other cities in the urban agglomeration. Baoji, Weinan, and Xianyang are adjacent to Xi’an, and the traffic flow with Xi’an is at the first level. Their role as secondary hubs in the transportation network of the Guanzhong Plain urban agglomeration is also increasingly prominent. As the eastern gate of Gansu Province, Tianshui is strategically located and has been a battleground for military strategists since ancient times. Tianshui–Baoji built a “major artery” connecting the traffic of Shaanxi and Gansu provinces. Yuncheng, Linfen, and Qingyang are located on the edge of the Guanzhong Plain urban agglomeration, and the traffic connection with other cities is slightly weak. The traffic between Pingliang, Shangluo, and Tongchuan with other cities is relatively underdeveloped.

There are four cohesive subgroups of traffic flow. Subgroup 1 is Yuncheng and Linfen, which both belong to the southwestern part of Shanxi Province. Although the total traffic flow in the cities is relatively weak, the traffic flow connection between Yuncheng and Linfen is relatively strong. Subgroup 2 includes Qingyang and Pingliang. Both Qingyang and Pingliang belong to Gansu Province. Since Pingliang has not yet opened high-speed rails, it lags behind Qingyang in terms of total traffic flow, and the traffic flow connection between Qingyang and Pingliang is relatively weak. Subgroup 3 includes Shangluo and Tongchuan in Shaanxi Province, and Shangluo and Tongchuan are ranked at the end of the total traffic flow and connection strength. Subgroup 4 is Tianshui, Baoji, and Xianyang. The total traffic flow of the three cities is relatively strong, and the traffic flow connection between cities is at the first and second levels.

The density of the traffic flow network is 0.29, which is at the middle and lower level; that is, the traffic network connection of the Guanzhong Plain urban agglomeration is weak. The results of centrality are shown in Table 2. In terms of point degree centrality, Xi’an has the highest point-in and point-out degree, far greater than other cities, with strong radiation and agglomeration capabilities. Baoji, Weinan, Tianshui, and Xianyang are next, and their radiation and agglomeration capacity is at a moderate level. Xi’an, Baoji, Tianshui, and Xianyang’s point-in degree and point-out degree of closeness centrality are larger than the average, indicating that these cities have short distances from other node cities in the network and have advantages in transmitting information. The betweenness centrality of Xi’an is the largest, indicating that Xi’an is located at the core of the urban agglomeration and is a bridge between cities. This communicates the connections between other cities well. The betweenness centrality of Baoji, Weinan, Tianshui, Xianyang, and Yuncheng is relatively low and at the same level. The betweenness centrality is 0 for Linfen, Qingyang, Pingliang, Shangluo, and Tongchuan, indicating that these cities have a very low intermediary status in the Guanzhong Plain urban agglomeration. Because they are located at the edge of the urban agglomeration, they cannot play a mediating role in the interaction of other cities within the urban agglomeration.

The traffic flow spatial structure of the Guanzhong Plain urban agglomeration presents the characteristics of “1 + 4 + 3 + 3” with Xi’an as the hub, Baoji, Weinan, Tianshui and Xianyang as important hubs, and Yuncheng, Linfen, and Qingyang as secondary hubs, it connects three surrounding cities. The Guanzhong Plain urban agglomeration is located in the junction of China’s central and western regions. It is an important hub connecting the eastern, central, northwestern, and southwestern regions of China. The north-south channel connecting the western region and the New Eurasian Continental Bridge meet here. The Chinese character “米”-shaped high-speed railway network and expressway network with Xi’an as the center being accelerated toward improvement.

The “14th Five-Year Plan for Comprehensive Transportation Development of Shaanxi Province” pointed out that, in 2025, a new pattern of high-quality development of transportation will be built. The Guanzhong Plain urban agglomeration has initially formed the “National 123 Travel Traffic Circle” and “Global 123 Express Cargo Flow Circle” proposed in the “Outline of the Construction of a Strong Transportation State”.

3.3. Spatial Structure Characteristics of Urban Agglomeration from the Perspective of Migration Flow

According to the total amount of migration flow, the four levels are first (Xi’an, Xianyang), second (Weinan), third (Baoji, Shangluo), and fourth (Yuncheng, Linfen, Tongchuan, Qingyang, Pingliang, Tianshui). In

Table 3. Total migration flow and centrality.

City	Total Migration Flow	Degree Centrality		Closeness Centrality		Betweenness Centrality
		In-Degree	Out-Degree	In-Degree	Out-Degree
Xi’an	627.478	5	5	16.667	16.667	16.667
Xianyang	434.380	3	3	16.129	16.129	1.111
Weinan	159.100	2	2	15.873	15.873	0
Baoji	75.246	2	2	15.873	15.873	0
Shangluo	50.956	1	1	15.625	15.625	0
Yuncheng	36.392	1	1	10	10	0
Linfen	32.675	1	1	10	10	0
Tongchuan	30.914	1	1	15.625	15.625	0
Qingyang	19.126	0	0	0	0	0
Pinglaing	18.423	0	0	0	0	0
Tianshui	9.919	0	0	0	0	0

and Figure 4, Xi’an and Xianyang together account for 71.05% of the total migration of the urban agglomeration. The strength of the migration flow connection between Xi’an and Xianyang is at the first level, partly due to the influence of Xi’an–Xianyang International Airport. More importantly, the establishment of the Yangling Demonstration Zone and the proposal of the “Xi-Xian integration” development strategy have made Xi’an and Xianyang increasingly attractive to talent, and economic exchanges between the two cities have become increasingly frequent.

With the gradual emergence of the advantages of “Xi-Xian integration”, “Xi-Wei integration” has also been proposed. The total amount of migration flow in Weinan ranks at the second level while the Xi’an–Weinan migration flow has a strong connection strength, and Xi’an and Weinan will eventually form a development model of transportation interconnection, industrial coordination, and economic integration. This is not only beneficial for the long-term development of Weinan but also the only way for the Xi’an metropolitan area to develop and grow.

Baoji borders Xi’an and Xianyang, and Shangluo borders Xi’an and Weinan. With their unique geographical advantages, the total migration flow of the two cities ranks at the third level. Baoji–Xi’an, Baoji–Xianyang, and Shangluo–Xi’an have established weak migration flow connection strength. The development of Xi’an metropolitan area will also drive the development of Baoji and Shangluo. The cities of Yuncheng, Linfen, Tongchuan, Qingyang, Pingliang, and Tianshui are mostly located on the edge of the urban agglomeration. They lack exchanges and cooperation with other cities in the urban agglomeration, and the connection of population migration is weak. The distribution of migration flow cohesion subgroups is more consistent with the provincial administrative scope.

Subgroup 1 is Yuncheng and Linfen in Shanxi Province, and subgroup 4 is Qingyang, Pingliang, and Tianshui in Gansu Province. The total amount of urban migration flow in these two subgroups is at the fourth level with more migration connections between cities within the subgroups and fewer connections with cities outside the subgroups. Subgroups 2, 3, and 5 are all cities in Shaanxi Province; subgroup 2 is Weinan and Baoji; subgroup 3 is Shangluo and Tongchuan; and subgroup 5 is Xi’an and Xianyang. Xianyang is bigger than Weinan, and Baoji is bigger than Shangluo and Tongchuan, which reflects the migration and flow of population between three types of cities with different development conditions.

The network density of migration flow is 0.15, and the network connection between cities is the weakest. The centrality results are presented in Table 3. In terms of point-degree and closeness centrality, Xi’an ranks first followed by Xianyang, Weinan, and Baoji tied for third. This indicates that these four cities have a large radiation range and great influence on other cities. The point degree and closeness centrality of Qingyang, Pingliang, and Tianshui are all 0, indicating that the influence of these cities is very weak and the radiation range is very small. From the perspective of betweenness centrality, Xi’an has the maximum value, indicating that Xi’an plays an extremely important “bridge” role in the Guanzhong Plain urban agglomeration network and plays an intermediary and communication role to a large extent. The gap between Xianyang and Xi’an is huge, and the intermediary effect is weak. Except for Xi’an and Xianyang, other cities failed to play an intermediary role.

From the perspective of migration flow, the spatial structure of the Guanzhong Plain urban agglomeration presents the characteristics of “2 + 1 + 2 + 6” with With Xi’an and Xianyang as the core, Weinan as the important node, Baoji and Shangluo as the secondary node, radiating to six surrounding cities. The total migration flow of Xi’an, Xianyang, and Weinan exceeds 80%, closely related to the development of the Xi’an metropolitan area, which has become the core area of the Guanzhong Plain urban agglomeration. The total migratory flow in the rest of the region is less than 20%, indicating that the Guanzhong Plain urban agglomeration has a problem of low levels of openness and cooperation.

3.4. Spatial Structure Characteristics of Urban Agglomeration from the Perspective of Composite Flow

Table 4. Total composite flow and centrality.

City	Total Composite Flow	Degree Centrality		Closeness Centrality		Betweenness Centrality
		In-Degree	Out-Degree	In-Degree	Out-Degree
Xi’an	3.027	9	10	50	100	73.889
Xianyang	1.280	2	3	37.037	58.824	0.556
Baoji	1.168	4	3	40	58.824	2.222
Weinan	1.081	3	3	38.462	58.824	1.111
Tianshui	0.819	2	2	37.037	55.556	0
Yuncheng	0.475	3	3	38.462	58.824	1.111
Linfen	0.384	2	2	37.037	55.556	0
Qingyang	0.339	1	1	35.714	52.632	0
Shangluo	0.217	1	1	35.714	52.632	0
Pingliang	0.227	1	1	35.714	52.632	0
Tongchuan	0.154	1	0	52.632	9.091	0

shows the total amount of composite flow and centrality of each city, and Figure 5 shows the spatial structure characteristics and results of cohesive subgroups of Guanzhong Plain urban agglomeration. From the perspective of the total amount of composite flow, Xi’an is the strongest, accounting for 33%, which is the first level. The second level includes Xianyang, Baoji, Weinan and Tianshui; Xianyang is the strongest among them, but the total amount is less than half of Xi’an. The third level contains Yuncheng, Linfen, Qingyang, and the fourth level includes Shangluo, Pingliang, and Tongchuan. From perspective of the composite flow connection strength, Xi’an and Xianyang, Weinan, and Baoji are all strongly connected, and Xi’an–Tianshui, Baoji–Tianshui, Yuncheng–Linfen, Xi’an–Qingyang, and Baoji–Xianyang ranked in the second level. Judging from the results of the agglomerative subgroup of composite flow, subgroup 1 is Weinan, Linfen and Yuncheng; subgroup 2 is Tianshui and Xianyang; subgroup 3 is Shangluo, Qingyang, and Pingliang; and subgroup 4 is Xi’an and Tongchuan.

The composite flow network density is low (0.26), and the connection between cities needs to be strengthened. Xi’an’s point degree centrality ranks first, indicating that Xi’an is more closely connected with other cities and can interact more with surrounding cities. It has strong radiation and agglomeration functions, so it is in the core position of the Guanzhong Plain urban agglomeration. The rest of the cities have low point degree centrality, indicating that their attractiveness and influence are not strong enough to compete with Xi’an. The closeness and betweenness centrality of Xi’an are also at the top, indicating that the communication between Xi’an and other cities does not completely depend on the intermediate cities. This is closely related to its role as the leader of the Guanzhong Plain urban agglomeration; other cities hope to directly communicate with it to obtain more resources to improve their own development.

On the whole, Xi’an has a strong attraction to the surrounding cities, constantly absorbing the advantageous resources of the surrounding cities and at the same time spreading the resources to the surrounding cities, forming a good positive interactive relationship. However, the intermediary degree of the overall network is not high, which means that the degree of mutual exchange of resources between the node cities in the network is low, and the resource utilization efficiency needs to be improved.

The composite flow spatial structure of the Guanzhong Plain urban agglomeration presents the characteristics of “1 + 4 + 3 + 3” with Xi’an as the center and Xianyang, Baoji, Weinan, and Tianshui as important nodes, and Yuncheng, Linfen and Qingyang as secondary nodes, radiating to the surrounding three cities. Xi’an is in the core position in terms of information, traffic, migration, and composite flow. In the “Guanzhong Plain Urban Agglomeration Development Plan”, Xi’an was officially listed for the national central city camp, becoming the ninth national central city. Compared with the other eight cities, a gap remains in the comprehensive development level of Xi’an. However, as the leader of the northwest region, Xi’an will better radiate and drive the surrounding cities through the identity of the national central city. The label of Xi’an as a national central city illustrates the strategic value of Guanzhong Plain urban agglomeration in the northwest region.

The development model of urban agglomerations is not a simple cluster of cities. In the final analysis, the aim is to break down the barriers of institutional mechanisms and optimize the allocation of resources on a larger scale. From this point of view alone, there are still certain problems in the development of the Guanzhong Plain urban agglomeration, which are mainly reflected in the low level of cooperation and unbalanced development. The establishment of the Xi’an metropolitan area will break this predicament and play a positive leading role in the future development of the Guanzhong Plain urban agglomeration.

4. Discussion

Previous studies mostly used statistical data or single factor flow data to study urban network structure, and the research conclusions are both similar and different from this paper. Li et al. (2021) [35] used information flow to explore the spatial connection pattern of Guanzhong Plain urban agglomeration, and concluded that Xi’an had stronger connections with Xianyang, Baoji, and Weinan than other cities, while it had weaker connections with peripheral cities (Yuncheng, Linfen, Tianshui, Pingliang, and Qingyang). Xianyang developed rapidly under the influence of the integration of Xi’an and Xianyang, Baoji is an important hub city connecting Xi’an with the west with a relatively high level of economic development, and Weinan is an important gateway between Xi’an and the east. The rapid development of the three node cities is conducive to the formation of a more complete spatial network structure of the urban agglomeration, which meets the requirements of the planning of the Guanzhong Plain urban agglomeration, cultivating new growth poles in the region. The difference lies in Li’s (2021) [35] conclusion that peripheral cities are weakly connected with Xi’an, while this paper finds that in addition to peripheral cities, Xi’an is also weakly connected with Shangluo and Tongchuan in Shaanxi Province. In the future, it is not only necessary to break administrative boundaries for cross-regional exchanges, but also to strengthen the connections between cities within the province. Ma et al. (2022) [37] has used Baidu search index for many years to study the structure of urban network. In this paper, multidimensional factor flow data is adopted to effectively make up for the unicity of data. This paper and Ma Fei both discussed the hierarchical structure of information flow in Guanzhong Plain urban agglomeration and the cohesive subgroups. Ma Fei concluded that the hierarchical distribution of urban agglomerations is led by Xi’an, with Baoji, Weinan, and Xianyang as the secondary core, and the other seven cities in the peripheral development stage. In this paper, it is found that the hierarchical distribution of urban agglomerations is centered on Xi’an and Xianyang, with Baoji and Weinan as the two wings, radiating to the surrounding 7 cities. The cohesive subgroups are similar to the results of this study, Yuncheng and Linfen form stable subgroup, Xianyang and Weinan belong to the same subgroup, and Tongchuan, Shangluo, Tianshui and Qingyang form a subgroup. The main difference lies in the fact that Xi’an and Baoji, with strong connections, and Pingliang, with weak connections, do not form subgroup relationships with other cities, indicating that the characteristics of the subgroups caused by extreme cases are not obvious. The cohesive subgroups of Guanzhong Plain urban agglomeration mainly develop in groups of cities in the same province and neighboring cities, and the connections among subgroups are weak. In the future, the administrative boundaries should be broken, and the collaborative development mechanism should be established and improved to strengthen the connections among interprovincial cities. On the whole, Guanzhong Plain urban agglomeration spans Shaanxi, Shanxi, and Gansu provinces, but it has not formed strong connections across administrative boundaries. Therefore, it should rely on the development opportunities of “The Belt and Road” and take the existing regional synergy strategy as the development outline, and actively break through administrative barriers to promote the spatial structure transformation of urban agglomeration to a high-quality, multi-center regional balanced spatial layout.

The Development Plan of Guanzhong Plain Urban Agglomeration proposed to strengthen Xi’an’s radiating function, accelerate the cultivation of development axes and growth poles, build the overall pattern of “one circle, one axis and three belts”, and improve the cohesion of spatial development [44]. As the core city of Guanzhong Plain urban agglomeration, a megacity in Northwest China and a national central city, Xi’an has strong radiation-driven development ability. Therefore, Guanzhong Plain urban agglomeration should take Xi’an as the core city; give full play to its radiating, driving role; accelerate the cultivation of Xi’an as the core development pole in the region; strengthen its radiating function; and build it into the distribution center of Guanzhong Plain urban agglomeration. In the Guanzhong Plain urban agglomeration, there are few big cities, and they mainly gather around Xi’an; small and medium-sized cities in the periphery are scattered and far away from the central city; they are limited to being driven by the radiation of the central city, their development level is low, and the connection between cities is weak. Among them, Shangluo, Pingliang, and Tongchuan have the weakest element flow connection. Shangluo is located in the underdeveloped area of southern Shaanxi Province, and the completeness of traffic facilities is insufficient. As a city in Gansu province, Pingliang is far away from the provincial capital and fails to form a strong connection with the cities in Shaanxi province, which hinders the pace of regional development. Tongchuan has a small area and a small population, which results in the flow of all its elements being at the bottom of Guanzhong Plain urban agglomeration. In the future, the Fuyin Development Belt in the “One circle, one axis, three belts” proposed by the National Development and Reform Commission can be relied on to promote the integrated development of Pingliang and Qingyang, guide the development of node cities such as Shangluo, and form a new development belt connecting with the urban agglomeration in the middle reaches of the Yangtze River and radiating Ningxia. The Baomao development belt can promote the integration of Tongchuan into the greater Xi’an metropolitan area and drive the coordinated development of northern Shaanxi and southern Shaanxi [45]. These cities need to strengthen the leading role of Xi’an to change the status quo of weak comprehensive development strength of small and medium-sized cities.

The city is the most basic structural unit of urban agglomerations, the development scale and functional zoning of urban agglomerations determine the development level and direction of urban agglomerations [46]. In order to realize the efficient and coordinated development of Guanzhong Plain urban agglomeration, the core cities and node cities of the urban agglomeration should be cultivated and strengthened first, and the cities with development potential should be cultivated. At the same time, the construction of main functional zones should be accelerated to improve the spatial development efficiency and coordinated development level of urban agglomeration [3]. At present, Guanzhong Plain urban agglomeration has three western node cities: Baoji, Tianshui, and Pingliang; two northern node cities: Tongchuan and Qingyang; and four eastern node cities: Weinan, Shangluo, Yuncheng and Linfen. Generally speaking, the comprehensive development level of node cities in urban agglomeration is generally low, therefore, we should start from promoting interconnection construction and increase the closeness of connection between node cities. The factor endowment and comparative advantages of small and medium-sized cities should be actively considered, the industrial base and service function of small and medium-sized cities should be improved, and a number of distinctive industrial production, cultural tourism, and industrial undertaking cities should be built to become a new carrier of industrial transformation and upgrading and radiation to drive rural development [5]. Finally, the polarization phenomenon of Guanzhong Plain urban agglomeration is serious, so it is necessary to actively build a multi-center urban network pattern of the Guanzhong Plain urban agglomeration, by promoting the integration of Xi’an and Xianyang and deepening the Xi’an metropolitan area. Weinan and Baoji will be made into secondary regional central cities to promote the all-round and coordinated development of the Guanzhong Plain urban agglomeration.

As the second largest urban agglomeration in western China, the operation of flow elements in the flow space of the Guanzhong Plain Urban agglomeration is undoubtedly a very complex process of temporal and spatial changes. The cross-section data obtained in this study within a certain period of time cannot reflect its dynamic changes well. Therefore, the comparison and verification of multi-time period and diversified data (geographical spatiotemporal data, statistical data, etc.) should be added in the next study to improve the accuracy of the study. Taking the cross-section data as an example, it can reflect the spatial structure characteristics of Guanzhong Plain urban agglomeration at a certain time level. In order to obtain a more comprehensive conclusion, it is necessary to conduct exploratory analysis on the dynamic changes and the influencing factors causing the changes. For example, in-depth research is conducted from the aspects of resource input, transportation accessibility, industrial structure, economic development, social services, policy orientation, etc. [47], which can not only increase the richness of research content, but also make the research conclusions more convincing.

5. Conclusions

Based on the perspective of multi-element flow, this study uses ArcGIS visualization, social network analysis, and other methods to analyze the urban network spatial structure of the Guanzhong Plain urban agglomeration from the aspects of connection strength, network density, centrality, and agglomeration subgroups. The main conclusions are as follows:

(1)

From the perspective of the total amount of information, traffic, migration, and composite flow, Xi’an has always been in the core position of the urban agglomeration. Its spatial structure presents the characteristics of “1 + 1 + 2 + 7”, “1 + 4 + 3 + 3”, “2 + 1 + 2 + 6”, and “1 + 4 + 3 + 3”, respectively. From the point of view of connection strength, whether it is information, traffic, migratory, or composite flow, the connection strength is uneven with few strong connections and more weak connections. The relationship between information and migration flow is strong only in one city pair: Xi’an–Xianyang. The city pairs with strong connection between traffic and composite flow are Xi’an–Weinan, Xi’an–Baoji, Xi’an–Tianshui, Baoji–Tianshui, Xi’an–Xianyang, Xi’an–Xianyang, Xi’an–Weinan, and Xi’an–Baoji. Most of the strongly connected city pairs are associated with Xi’an, and the other cities are relatively weak.

(2)

The network density of each element flow is at a low-medium level, and the information, traffic, population migration, and composite network connections are all weak. In terms of point degree centrality, Xi’an has the highest point degree centrality in each element of the flow network and is the primary central city of the Guanzhong Plain urban agglomeration. Xianyang, Baoji, and Weinan are at a moderate level while the rest of the cities have low point degree centrality, and their agglomeration and radiation capabilities are weak. The closeness centrality of Xi’an ranks first in each network, indicating that the communication between Xi’an and other cities does not depend on the intermediate cities. The polarization of betweenness centrality is serious, and Xi’an ranks first, serving as a bridge between other cities. In each element flow network, Linfen, Qingyang, Shangluo, Pingliang, and Tongchuan are located on the edge of the urban agglomeration, and none of them play an intermediary role. Their status in the urban agglomeration needs to be improved. Information, traffic, migration, and composite flow form three, four, five, and four agglomerated subgroups, respectively. The cities within the subgroups are closely connected, and the connections between the subgroups are weak.