Exploration of Urban Network Spatial Structure Based on Traffic Flow, Migration Flow and Information Flow: A Case Study of Shanxi Province, China

Abstract

Urban coordinated development is an important aspect of regional development. The high-quality development of the Yellow River Basin cannot be separated from the coordinated and sustainable development of its inner cities. However, the network connection and spatial structure of cities in the Yellow River Basin have not received sufficient attention. Therefore, this study considered 11 prefecture-level cities in Shanxi Province, an underdeveloped region in the Yellow River Basin, as case areas and selected data on traffic, migration, and information flow that can better represent the urban spatial network structure and depict the spatial connection between cities. Based on the flow intensity calculation, flow direction judgment, spatial structure index, and social network analysis, the spatial structural characteristics of Shanxi Province were comprehensively analyzed from the perspective of flow space. The results showed the following: (1) Cities in Shanxi Province present a development trend of “one core and multiple centers.” The strong connection concerns mostly Taiyuan and radiates outward and presents a Chinese character “大”—shaped spatial connection pattern. (2) Taiyuan is the first connecting city of most cities in Shanxi Province, and the element flows particularly towards the central city and geographical proximity. (3) The urban spatial pattern of Shanxi Province presents an obvious unipolar development trend, where the network structure is an “absence-type pyramid.” The imbalance of the urban network connection strength is prominent in Shanxi Province, which is strong and numerous in the south but opposite in the north. (4) The overall network element flow density is low, the network connection is weak, Taiyuan agglomeration and radiation are the strongest, and Changzhi centrality ranks second, but the gap between Changzhi and Taiyuan is wide, and the polarization phenomenon is serious. Future research should focus on the rapidly developing provincial capital city of Taiyuan, coordinating the steady development of the central Shanxi city cluster, and driving the common development of neighboring cities.

1. Introduction

According to the first law of geography, physical proximity is the key to the spatial aggregation of geographical phenomena and an important prerequisite for the formation of geographical spatial connections [1]. With the rapid development of globalization and informatization, regional research has changed from “place space” to flow space, a concept put forward in 1969 by Castells, an urban sociologist. It refers to material organization that can “realize the social practice of sharing time without geographical proximity” [2]. It realizes time sharing by eliminating geographical adjacency through the flow of elements—population, commodities, capital and information—and has become the dominant form of spatial organization [3].

Flow space is composed of interactive networks, and its theory provides an important starting point for the study of urban networks [4]. The interaction between cities is reflected in element relationship data, which promote the study of regional spatial structures from a city’s internal characteristics to its external relationships [5], thus, forming an “urban network”. The research perspective of cities and regions has also begun to turn to the urban network, which is the extension and improvement of traditional urban and regional spatial structure research [6]. The connection between cities is mainly achieved through the flow of elements, which promotes the interconnection and functional complementarity of social and economic activities, thus forming a multi-scale and multi-level system [7]. To ensure normal operation, the elements are constantly exchanged among cities.

In recent years, the study of urban networks has risen to focus on global, national, regional or urban agglomerations using different types of city correlation data. International scholars measure the connection between cities through network analysis based on information flow such as internet traffic [8,9], parcel delivery [10], and traffic, flow such as airline flights [11,12] and freight volume [13,14]. The Globalization and World Cities Study Group and Network (GaWC) represented by Taylor builds a global city network through the distribution of enterprise headquarters, regional centers, and local offices [15].

Chinese scholars also conducted research on the spatial structure of regions or urban agglomerations based on flow space. In the early stage, traffic flow data (such as highways, railways, air flights and passengers) [16,17,18] were mainly used to study urban network structure and organization modes, urban centrality, and evolution of urban network levels. Today, big data has become an important source for multi-element flows, such as information [19,20], population [21], logistics [22], and capital [23], as well as a new research direction. In general, the shortcoming of the current research on flow space lies in the single selection of flow elements, and little exploration of the spatial structure characteristics in which multiple flow elements work together.

Against the background of implementing the “ecological protection and high-quality development of the Yellow River Basin” strategy, Shanxi Province seized a great opportunity to develop the river basin economy. It improved the transportation infrastructure and steadily promoted the integration of the social economy into the overall economic development of the Yellow River basin [24]. However, the unbalanced development of its cities is very conspicuous, so the transformation and development of resource-based cities face huge challenges; at the same time, the radiating effect of the Jinzhong urban agglomeration on the development of the province is limited, and the scattered development of the three major town agglomerations (northern, southern, and southeastern) affects its coordinated and sustainable development [25]. Because of globalization, cities are no longer isolated: the city center and surrounding areas are inextricably linked, and the network structure of the city is more intricate [26]. Therefore, clarifying the status of Shanxi’s urban network is of great practical significance for optimizing the development, enhancing the strength of the province, and promoting Shanxi’s deep integration into the overall development of the Yellow River Basin.

Taking Shanxi as the study area, this paper selected the three most representative flows among the cities, traffic flow, migration flow and information flow, and made quantitative analyses and expressions of the relationship and spatial structures. This paper is divided into four parts. Section 1 introduces the research background of the paper. Section 2 presents the materials and methods and a detailed introduction of the study area overview and data. Section 3 analyzes the results and discusses the main content of Shanxi city level division, factor flow direction analysis, urban spatial pattern, and urban network structure. Section 4 presents the conclusion and discussion. The research in this paper is expected to provide some suggestions for Shanxi Province to speed up urban integration, strengthen urban interconnection, allocate social resources, and close the urban development gap.

2. Materials and Methods

Figure 1 presents this paper’s flow chart, which mainly includes the following key steps: (1) Traffic frequency data (buses, trains, bullet trains, and high-speed rail), the Baidu migration scale index, and Baidu search index, three 11 × 11 matrices of traffic, information, and migration are constructed. The weighted sum of the flow matrix data of the three elements was used to obtain the comprehensive flow data. (2) Traffic, migration, and information matrices were used to calculate the flow intensity of each factor, and natural breakpoint classification, membership model, and spatial analysis methods were used to obtain the urban hierarchy, factor flow direction, and urban spatial patterns of Shanxi Province, respectively. (3) Social network analysis was conducted on the flow data of each element to obtain its urban network structure and explore the spatial structure of the urban network in Shanxi Province.

2.1. Study Area

Shanxi Province is located in the central inland region of China. As a major national strategy for ecological protection and high-quality development of the Yellow River Basin, Shanxi Province is in an “intermediate location” and plays an important role in connecting the north to south and east to west. It is located in the middle reaches of the Yellow River and east of the Loess Plateau. The terrain is high in the northeast and low in the southwest, and relatively complex. Most of the areas are between 1000 and 2000 m above sea level, for a total area of 156,700 sq. km. At the end of 2021, the number of permanent residents in Shanxi Province was just over 34.8 million, with a regional GDP of CNY 2259 billion and a per capita GDP of CNY 64,905. The research object for this paper comprised 11 cities: Taiyuan, Datong, Shuozhou, Xinzhou, Yangquan, Lvliang, Jinzhong, Changzhi, Jincheng, Linfen and Yuncheng (Figure 2).

2.2. Data Sources

Based on traffic, information, and migration flow data, this study investigated the spatial structure of urban networks in Shanxi Province. A time cross section was selected from March to May 2022, and the characteristics of the urban network in Shanxi Province were analyzed using the data of three element flows in this period and the comprehensive flow data obtained by weighted sum.

(1)

Traffic flow. In the provincial area, there is mainly short—and medium—distance commuting, and railway and road transportation reflect the interactions between cities [27]. Therefore, this study uses frequency data between the two cities as the traffic data source. The frequency of trains, bullet trains, and high-speed rails is obtained from the ticketing system of the China Railway Customer Service Center website (http://www.12306.cn (accessed on 28 June 2022)), and the bus data are obtained from Fliggy Travel. Both road and rail trip frequencies are relatively fixed, and both are selected as representatives of the 28 June 2022 data to calculate inter-city transportation connections.

(2)

Migration flow. The migration scale index between the two cities is used. It is derived from the Baidu migration data platform provided by Baidu Map (http://index.baidu.com (accessed on 24 June 2022)), which displays the trajectory of population flow in the selected period in real time, dynamically and intuitively, and shapes the path and intensity of the population flow process. The Baidu migration platform shows the in-migration/out-migration scale index of the provinces and cities in mainland China and provides about 100 of the most popular migration destinations at the prefecture and provincial levels, as well as the highest percentage people moving from/into neighboring regions [28]. The migration size index is used to reflect the size of the in-migration or out-migration population; the popular in-migration/out-migration location ratio is the ratio of the in-migration/out-migration to a city to the total in-migration/out-migration population of the country. In this study, the product of the scale index of in-migration/out-migration and the proportion of the in-migration/out-migration population is used to characterize the scale index of in-migration/out-migration between the two cities.

(3)

Information flow. Based on the search volume between the two cities, data are derived from the Baidu Index platform (https://index.baidu.com (accessed on 20 June 2022)), which consist of trend research, demand mapping, and crowd profiling. By using the Baidu index trend research function and taking the input keywords as the statistical object, it can scientifically and effectively analyze and calculate the sum of the search frequency of the searched keywords on the Baidu website, which can be expressed by a visual curve and specific index (the search index includes PC daily mean, moving daily mean, and overall daily mean) [20]. This study adopts the overall daily average between the two cities and obtains the search volume of Baidu users between cities using the place names of cities in Shanxi Province as keywords in the “Classification by region” of the Baidu Index interface. For example, if “Taiyuan” is imputed in the Baidu Index and “Jinzhong” is selected in “classification by region,” Jinzhong can focus its attention on Taiyuan.

2.3. Research Methods

2.3.1. Calculation of Element Flow Intensity

(1)

Traffic flow:

The intensity of traffic flow in each city was simulated by estimating the traffic connection quantity of the 11 cities in Shanxi Province, acquiring the frequency information of buses, trains, bullet trains and high-speed rail between cities. Weights are set for different traffic modes, and the weighted sum reflected the traffic flow intensity between cities [27]:

$$T_{mn}=\frac{1}{3}{A}_{\mathrm{mn}}+\frac{2}{5}{B}_{mn}+\frac{5}{6}{C}_{mn}+D_{mn}$$

(1)

$$C_{mn}=(T_{mn}+T_{nm})/2$$

(2)

$$C_m={\displaystyle \sum _{n=1}{C}_{mn}}$$

(3)

where T_mn represents the total traffic connection between city m and city n; C_mn represents the average traffic connection between the two cities; C_m represents the traffic flow intensity of city m; and A, B, C, and D represent number of shifts of buses, trains, bullet trains, and high-speed rails, respectively.

(2)

Migration flow:

Baidu’s migration data can reflect the characteristics of the population network. In this study, an index scale of the movement of people between cities was used to represent the strength of the population connection. The migration scale index was calculated according to the population migration activities between cities. After the population migration volume of each city was obtained, s feature scaling was carried out to convert it into a dimensionless migration scale index so that it could be compared in horizontal cities and vertical history [28].

(3)

Information flow:

The rapid development of the Internet has strengthened the connection between cities, and Internet searches have become the main way for cities to understand each other. On the Internet, search attention between cities can be regarded as an important part of the information flow between cities [20]. By searching for the attention of network users between cities, the strength of information connections made it possible to analyze the network pattern of information connections. The formulae are

$$I_{\mathrm{mn}}=R_{mn}{R}_{nm}$$

(4)

$$I_m={\displaystyle \sum _{n=1}{I}_{mn}}$$

(5)

where I_mn is the information connection strength between city m and city n; R_mn is the network attention degree of city m to city n; R_nm is the network attention degree of city n to city m; and I_m is the total amount of information flow connection of city m.

(4)

Comprehensiveness flow:

This paper regarded the traffic, migration and information networks as equally important, and gave each a weight of 1/3. The intensity of traffic, migration, information connection, and weighted sum were normalized to obtain the comprehensive flow connection intensity, and the total amount of comprehensive flow connection was calculated.

2.3.2. Determination of Element Flow Direction

This paper applied the economic relationship membership formula to the analysis of the direction of the traffic, information, migration and comprehensiveness flows. Its membership formula [29] is

$$F_{mn}=R_{mn}/R_m$$

(6)

where R_mn is the element flow intensity between city m and city n; R_m is the total element flow of city m; and F_mn is the membership degree of city m to city n. The larger the F_mn value, the greater the importance to the external connection of city m, as it determines the main direction of the city’s element flow in a quantitative form.

2.3.3. Spatial Structure Index

The spatial structure index is an improved algorithm based on the study of a regional center structure and was proposed by Hanssens in 2013. The results are in the range of 0 to 1, where 0 indicates that the regional spatial structure exhibits a significant unipolar development trend, and 1 indicates obvious multi-polar characteristics so that the discrete degree of regional spatial structure can be determined [30]. The formula is

$$SSI=\left\{\begin{array}{l}(2-SD/S{D}_{rc})/2,SD<S{D}_{rc}\\ S{D}_{rc}/2SD,SD>S{D}_{rc}\end{array}\right.$$

(7)

where SD is the standard deviation of the connection flow intensity R_m of city nodes; SD_rc is the standard deviation of the serial numbers of all city nodes after sorting; and SSI is the spatial structure index of the region.

2.3.4. Social Network Analysis

Social network analysis methods are widely used in the study of spatial network structures. This paper used network density, centrality, structural holes to analyze the structural characteristics of the urban networks.

3. Results

3.1. City Node Hierarchy

The connection flow matrix data of each city were normalized and analyzed (Figure 3). In terms of connection strength, Taiyuan had the strongest among information, traffic, and migration flows, and the rest of the cities had widely different rankings. Judging from the results of the comprehensiveness flow, there was a large gap in intensity: the difference in connection between Taiyuan (the strongest) and Shuozhou (the weakest) was 7.77 times. To express the characteristics of the city ranking further, Natural Breaks was used to divide the connection strength of each city into five levels. For Taiyuan, traffic, migration, information, and comprehensiveness flow were all at the first level. Among the three flow elements, the ranking of cities at the other levels changed greatly. Each city had different advantages. For example, Yuncheng and Jincheng had strong external connections for traffic and information flow, while the migration flow was weak. Conversely, the migration flow in Lvliang had a strong external connection, but for traffic and information flow, it was weak. It can be seen that multiple flow elements avoided the uncertainty of a single flow element and reflect a city’s external connection network pattern better. Concerning the connection strength of the comprehensiveness flow, the cities showed a development trend of a “one core and multiple centers” competition and balance. One core city is Taiyuan, and the multiple centers include Jinzhong, Linfen, Changzhi, and Yuncheng, all of which have higher total element flows and are at the second level. Among them, Linfen, Changzhi, and Yuncheng are located in the southwest of Shanxi, Changzhi, and Yuncheng belong to the Zhongyuan urban agglomeration, while Linfen and Yuncheng are cities in the Guanzhong Plain urban agglomeration. Jinzhong is located in the middle and is part of the Central Shanxi urban agglomeration. These three urban agglomerations are national; they have high development potential. In addition, Linfen and Changzhi are sub-centers of Shanxi Province, which can improve their status in the city groups, help them actively integrate national strategies, and accelerate the pace of their high-quality development. There was a significant difference in the intensity of cities at different levels, and when combined with the geographical location of each city, the hierarchical structure of the connection flow closely related to their spatial location. For example, Shuozhou is in a fringe area far from the core, so it is located at the fifth level. Although flow space does not focus on the effect of geographic location on urban communication, traditional spatial distance still affects the strength of the inter-city connection.

At present, Shanxi is committed to building the central Shanxi urban agglomeration, comprising Taiyuan, Jinzhong, Xinzhou, Yangquan and Lvliang. Except for Lvliang, which is at a high altitude and has many mountains and hills, the other four are located with a relatively flat and open terrain. This urban agglomeration is the gathering place of transportation, population and information, and its total comprehensiveness flow accounts for 56.9% of the total connection flow of all cities in Shanxi with the potential to drive the coordinated development of cities in the region.

3.2. Element Flow Direction Analysis

The membership degree of each city to other cities can be calculated using Equation (6), and the one with the largest membership degree is its first connection city. Based on the element flow intensity between each city and the first connected city, this paper considered the difference in intensity and the reasonableness of the different classification results. The 11 cities were divided into 3 grades according to element flow intensity. ArcGIS software was used to draw the main action directions of each element in each city. The results are shown in Figure 4.

For traffic flow, the first connection city of Taiyuan was Yuncheng, and for Jincheng it was Changzhi. The first connection city of the other cities was Taiyuan. It can be seen that Taiyuan is an important transportation hub, for which Lvliang has the largest membership degree because it is close. The main direction of traffic flow was dominated by the directionality of the central city. For migration flow, Jinzhong is the first connected city for both Taiyuan and Yangquan with membership degrees of 39.5% and 51.1% respectively; Datong and Shuozhou, Linfen and Yuncheng are each other’s first connected cities; and Jincheng’s first connected city is Changzhi. The first connected cities in Taiyuan include Xinzhou, Lvliang, Jinzhong and Changzhi, with the highest membership degree in Jinzhong at 61.3%. The main action direction of migration is determined by geographical proximity. For information flow, Changzhi, the first connected city to Taiyuan, and the first connected cities in the remaining 10 cities, are concentrated in Taiyuan, with membership degrees of 25–45%, and the main direction of action has the directionality of the central city. Taiyuan has a strong centrality in network information, and it radiates well to most cities.

As shown in

Table 1. The first connection city of each element flow network.

City	Traffic Flow		Migration Flow		Information Flow		Comprehensiveness Flow
	First Connection City	Membership Degree	First Connection City	Membership Degree	First Connection City	Membership Degree	First Connection City	Membership Degree
Taiyuan	Yuncheng	17.1%	Jinzhong	39.5%	Changzhi	14.4%	Jinzhong	16.0%
Datong	Taiyuan	37.2%	Shuozhou	65.1%	Taiyuan	38.6%	Taiyuan	35.6%
Shuozhou	Taiyuan	51.9%	Datong	63.6%	Taiyuan	38.3%	Taiyuan	35.5%
Xinzhou	Taiyuan	43.1%	Taiyuan	55.8%	Taiyuan	40.5%	Taiyuan	44.8%
Yangquan	Taiyuan	53.2%	Jinzhong	51.1%	Taiyuan	35.8%	Taiyuan	44.5%
Lvliang	Taiyuan	77.1%	Taiyuan	55.6%	Taiyuan	44.3%	Taiyuan	53.7%
Jinzhong	Taiyuan	35.7%	Taiyuan	61.3%	Taiyuan	36.4%	Taiyuan	44.0%
Changzhi	Taiyuan	37.5%	Taiyuan	29.0%	Taiyuan	38.3%	Taiyuan	37.7%
Jincheng	Changzhi	45.1%	Changzhi	48.9%	Taiyuan	28.4%	Changzhi	33.0%
Linfen	Taiyuan	37.2%	Yuncheng	40.6%	Taiyuan	33.5%	Taiyuan	48.9%
Yuncheng	Taiyuan	41.7%	Linfen	70.0%	Taiyuan	34.9%	Taiyuan	48.4%

, in the comprehensiveness flow network connection, the first connection city of Taiyuan is Jinzhong; the first connection city of Jincheng is Changzhi; and the first connection city of the other nine cities is Taiyuan, which is inseparable from its status as a provincial capital. Among them, the membership degree of Lvliang is the highest at 53.7%, followed by Linfen, Yuncheng, Xinzhou, and Yangquan, indicating that Taiyuan has a strong driving effect on these five cities, while the driving effect on the other five needs to be strengthened. The main direction of the comprehensiveness flow also has the directionality of the central city.

3.3. Urban Spatial Pattern

The spatial structure index of the urban comprehensiveness network is 0.112 (

Table 2. Comprehensiveness network space structure index.

Rank	City	Rm	rc
1	Taiyuan	5.085	1
2	Jinzhong	1.849	0.5
3	Linfen	1.732	0.333
4	Changzhi	1.637	0.25
5	Yuncheng	1.563	0.2
6	Jincheng	1.196	0.167
7	Xinzhou	1.159	0.143
8	Yangquan	1.078	0.125
9	Lvliang	1.011	0.111
10	Datong	0.946	0.1
11	Shuozhou	0.654	0.091
Standard deviation		1.149	0.257
Space structure index		0.112

), as calculated from Equation (7). Based on multi-dimensional element flow, the urban spatial pattern of Shanxi presents an obvious unipolar development trend, and the aggregation degree of regional space is relatively high. Taiyuan is Shanxi’s connection hub with a comprehensiveness connection strength of 5.085, accounting for 28.4% of the entire region. Jinzhong, in second place, accounts for only 10%. Thus, the urban network shows an “absence-type pyramid structure”.

To further identify the urban spatial pattern of Shanxi, the ArcGIS visualization of the element flow connection strength of each city was carried out (Figure 5). Regarding traffic flow, the first-level connections consist of six connecting axes between Taiyuan and Yuncheng, Linfen, Yangquan, Changzhi, Jinzhong and Jincheng, and two axes of Linfen-Yuncheng and Changzhi-Jincheng, accounting for 14.5% of all city pairs. Traffic connection volume accounts for 60.9% of the total of which Taiyuan and Yuncheng have the strongest connection, forming the most obvious transportation axis. The central and southern regions with Taiyuan as the center have well-developed traffic and strong traffic connection strength, whereas in the north, intensity of traffic connection intensity is weak in Datong, Shuozhou, and Xinzhou, and traffic is relatively backward. Concerning the strength of migration flow, the first-level connection includes only Taiyuan-Jinzhong, which accounts for 1.8% of all city pairs and 22.4% of the total of migration connection strength. Secondary connections include Taiyuan-Lvliang, Taiyuan-Xinzhou, Datong-Suozhou, and Linfen-Yuncheng. It can be seen that migration follows the law of distance decay since cities with stronger connection strength in the first-level and second-level connections are all close to each other. Under normal circumstances, the population flow between cities would show an adjacency pattern; that is, short-distance migration is the main one. For information connection intensity, the first level includes 6 axes between Taiyuan and Changzhi, Xinzhou, Jinzhong, Lvliang, Linfen, Yuncheng, which accounts for 36.8% of the total information connection intensity. Taiyuan and Changzhi have the strongest information connection, and Changzhi, as the second largest city, has a high degree of interconnectedness with the provincial capital.

Judging from the comprehensiveness flow of the three elements, first-level connection accounts for 40.8% of the comprehensiveness flow, the six city pairs with Taiyuan (Jinzhong, Changzhi, Linfen, Yuncheng, Lvliang, Xinzhou). Among these, the Taiyuan-Jinzhong connection is the strongest, and Jinzhong developed itself by taking advantage of its geographical proximity to Taiyuan, which gave Jinzhong a seat in the urban network of Shanxi.

3.4. Social Network Analysis

The density of the traffic and information network is 0.3; the density of migration and comprehensiveness network is 0.29; and the overall network density is at the lower level. The overall network shows a low degree of connection between cities, and there are few ways to obtain information or share resources. Since the strength of the connection between each city is different, the density analysis can only reflect the characteristics of the city network to a certain extent. In this paper, (Figure 5), the natural breakpoint point method is used to classify the strength of each element flow connection into five levels, with the strongest connection at level one and the weakest connection at level five. There was a great difference in the urban and comprehensiveness flow connection strength. The fourth- and fifth-level urban pairs accounted for 61.8%; city pairs with first- and second-level linkages accounted for 20%, so the weak connection was dominant, which is similar to the previous densitometric analysis. Geographical distance is an important factor in determining the strength of city connections, and most of the cities with strong connections occur between two bordering cities.

With the help of Ucinet software, the point-degree, closeness and betweenness centrality of each city was calculated, and it revealed the influence and control of different cities in the urban network. From the results of point-degree centrality, Taiyuan had the highest in-degree and out-degree in each element of the flow network, and the strongest agglomeration and radiating ability. As an active city, Taiyuan has not only attracted the attention of other cities, but also has a large number of active connections. Figure 6 shows that most of the cities had low in-degree and out-degree centrality, and weak radiation attractiveness and connection with other cities. These cities account for the largest proportion, indicating that the connection between cities needs to be strengthened. Regarding comprehensiveness flow, the in-degree and out-degree of Changzhi are both high, indicating that its agglomeration and radiation capabilities are also strong. Jinzhong has a low in-degree and a high out-degree, indicating that its outward radiating force is greater than its inward cohesive force and that it mainly radiates resources and has a greater influence in the urban network. The number of cities with low in-degree and out-degree account for 64%. These cities—Xinzhou, Yangquan, Lvliang, Jincheng, Yuncheng, Datong, Shuozhou—are less attractive and less influential to other cities. The in-degree of Linfen is greater than the out-degree, and the intensity of the radiation received by the provincial capital is greater than its effect on the surrounding cities.

It can be seen from

Table 3. Closeness centrality of the urban network.

City	Traffic Flow		Migration Flow		Information Flow		Comprehensiveness Flow
	In-Degree	Out-Degree	In-Degree	Out-Degree	In-Degree	Out-Degree	In-Degree	Out-Degree
Taiyuan	50	50	76.92	76.92	100	100	100	100
Linfen	41.67	38.46	55.56	55.56	66.67	55.56	62.5	55.56
Changzhi	38.46	40	52.63	52.63	55.56	71.43	58.82	62.5
Datong	37.04	37.04	50	50	55.56	52.63	55.56	55.56
Jincheng	37.04	38.46	35.71	35.71	58.82	58.82	55.56	55.56
Lvliang	35.71	35.71	52.63	52.63	55.56	52.63	55.56	52.63
Jinzhong	41.67	40	62.5	62.5	52.63	71.43	55.56	66.67
Shuozhou	9.09	9.09	37.04	37.04	52.63	52.63	55.56	55.56
Yuncheng	38.46	40	37.04	37.04	58.82	55.56	55.56	55.56
Yangquan	37.04	37.04	47.62	47.62	55.56	52.63	55.56	52.63
Xinzhou	37.04	37.04	50	50	58.82	52.63	52.63	52.63

that Taiyuan, as the capital city of Shanxi province, has the highest closeness centrality, indicating that the distance between Taiyuan and other cities is relatively short, which means that communication with other cities is not completely dependent on an intermediate city, so it can achieve higher efficiency. This is closely related to Taiyuan, and other cities hope to communicate directly with it to obtain more resources to develop better. The centrality of Xinzhou, Yangquan and Lvliang is obviously smaller, and their dependence on the central city Taiyuan is stronger.

Table 4. Betweenness centrality of urban network.

City	Traffic Flow	Migration Flow	Information Flow	Comprehensiveness Flow
Taiyuan	56.30	60	81.48	82.78
Jinzhong	2.41	12.22	0	1.11
Changzhi	0.93	20	1.48	1.67
Jincheng	0	0	0.56	0
Linfen	1.48	20	0.93	1.11
Yuncheng	1.11	0	0	0
Datong	0	8.89	0	0
Shuozhou	0	1.11	0	0
Xinzhou	0	8.89	0	0
Yangquan	0	0	0	0
Lvliang	0	0	0	0

shows the betweenness centrality results. In each flow network, Taiyuan’s betweenness centrality always ranks first, indicating that it is an important bridge between cities. It also has a significant intermediary role and strong control over other cities from its core position. Taiyuan radiates to the south and the north, so it can communicate well with other cities. In the comprehensiveness flow network, Changzhi ranks second in betweenness centrality, and Jinzhong and Linfen are tied for third far behind Taiyuan. The phenomenon of polarization is serious, but these three are still important nodes. It is worth noting that the betweenness centrality of the comprehensiveness flow network of Jincheng, Yuncheng, Datong, Shuozhou, Xinzhou, Yangquan, and Lvliang is zero. These cities have relatively simple functions, and their status in the network needs to be improved.

In the social network analysis, structural holes, as a kind of favorable capital, are usually regarded as the ability of node cities to grasp key elements and control favorable information; among them, the limit degree plays the most critical role in the structural hole index. In

Table 5. Urban network structure holes.

City	Traffic Flow		Migration Flow		Information Flow		Comprehensiveness Flow
	Efficiency Size	Constraint	Efficiency Size	Constraint	Efficiency Size	Constraint	Efficiency Size	Constraint
Taiyuan	7.22	0.28	5.57	0.34	8.6	0.24	8.8	0.23
Jinzhong	2.33	0.63	3	0.59	3.71	0.72	2.93	0.73
Changzhi	1.71	0.76	2.33	0.61	3.56	0.64	2.21	0.73
Linfen	2.19	0.68	2.5	0.58	2.5	0.68	2	0.78
Xinzhou	1	1.13	2	0.5	1.5	1.04	1	1
Datong	1	1.13	2	0.5	1	1.24	1	1.13
Shuozhou	1	1.13	2	0.5	1	1	1	1.13
Jincheng	1	0.97	1	1	1.92	0.79	1	1.13
Yuncheng	1.64	0.78	1	1	1.3	0.95	1	1.13
Yangquan	1	1.02	1	1.13	1	1.24	1	1.24
Lvliang	1	1	1	0.93	1	1.24	1	1.24

, Taiyuan, the provincial capital of Shanxi, has the fewest restrictions: on the one hand, its transportation and Internet infrastructure are relatively complete, and transportation and Internet are easily attainable; on the other hand, it radiates strongly and is less dependent on other cities. Therefore, Taiyuan can effectively drive the development of other cities in the overall network. From the perspective of the effective scale, Taiyuan ranks first. It is at the core of transportation, migration, information, and comprehensive networks.

4. Conclusions and Discussion

4.1. Conclusions

This paper selected the traffic, migration and information flow data between 11 cities in Shanxi Province and analyzed their spatial connection from the perspectives of the intensity and direction of element flow using the spatial structure index and social network analysis The research concluded the following:

(1)

Shanxi Province presents a development trend of “one core and multiple centers”. Level I traffic, migration, information, and comprehensive networks are all Taiyuan, and levels II, III, IV, and V are significantly different. The main direction of migration flow depends on the directionality of geographical proximity; the main direction of traffic, information and comprehensiveness flow relies on the directionality of the central city. The provincial Taiyuan is the first connecting city of most cities.

(2)

Regarding flow space, the urban spatial structure of Shanxi presents an obvious unipolar development trend, and Taiyuan is a comprehensiveness connection hub at the top of the pyramid. The urban network structure presents an “absence-type pyramid structure”, and network maturity is still in the developmental stage. The unbalanced phenomenon of urban network connection strength is prominent; the south is strong and the north is weak, but the strength is lesser and the weakness is greater. Centered on, and radiating from, Taiyuan, the urban network presents a Chinese character “大”—shaped spatial connection pattern.

(3)

The network density of each element flow is at a lower level, and network connection is weak. Taiyuan has the largest centrality and the strongest agglomeration and radiating ability, and it is a communication bridge for other cities. Most cities in Shanxi have a low centrality, weak radiation and attractiveness, and their connection strength with other cities is also weak. From the perspective of structural holes, Taiyuan is the least restrictive and is weakly dependent on other cities; Taiyuan’s effective scale has always ranked first and is at the core. The remaining cities have large restrictions and small effective scales, so the phenomenon of urban network polarization in Shanxi is serious.

4.2. Discussion

Sorting urban network connections and spatial structures can provide a reference for high-quality urban development. In view of the above findings, this paper proposes three considerations related to the urban development of Shanxi Province in the context of high-quality development of the Yellow River Basin, as follows:

(1)

Based on the above study, it was found that Shuozhou, Yangquan, Datong, and Luliang have weak information flow connections, especially Yangquan and Lvliang; as important cities in the central Shanxi city cluster, they are not closely connected with other cities in Shanxi province. Information technology is a current trend, and communication and cooperation between cities will be the focus of future social development [20]. Therefore, while increasing attention on the central Shanxi city cluster, we must vigorously promote communication and cooperation between neighboring cities in Shanxi Province and the cities in the core region and effectively promote the interaction of information and resource sharing between cities. Yangquan and Jincheng have the weakest migration connections, and their small population bases lead to limited development. In the future, they should attract outsiders and reduce population loss by developing advantageous industries and enhancing the positive impact of population density on urban development. Lvliang, Shuozhou, Xinzhou, and Datong are weakly connected to other cities in terms of traffic flow due to the blockage of the Taihang and Lvliang Mountains, resulting in low accessibility [25]. In the future, the transportation connectivity between cities in the region should be improved by strengthening the construction of transportation infrastructure, improving urban connectivity, and improving transportation modes, such as railroads, highways, and civil aviation [31]. In general, for cities that are currently ranked low in terms of the intensity of all elements of the flow, strengthening the close connections between them and cities in the core area, improving the level of transportation connectivity, and gradually narrowing the gap with cities in the core area. Taiyuan and other cities in the core area still have more room for development, and should keep developing city agglomerations by establishing a reasonable urban spatial pattern, relying on the central cities, and realizing inter-city linkage development so that they can radiate the surrounding cities more widely and strongly.

(2)

This study explores the spatial patterns of information, population, traffic, and comprehensiveness connection networks among provincial cities using multi-dimensional element flow data with 11 prefecture-level cities in Shanxi Province as research objects. Previous studies have mostly explored the spatial structure of 19 urban agglomerations in China, including the central Shanxi urban agglomeration [32,33] and the Yellow River Basin urban agglomeration [34,35], without focusing on the urban spatial structure of Shanxi Province from the perspective of multi-dimensional element flow. This closely relates to that of Cao [25] on the coordinated development of urban agglomerations in central Shanxi. Both conclude that Taiyuan is developing rapidly and differs greatly from the development of other cities in Shanxi Province. There are three main differences: one is the overlapping study area between the two. Cao concluded that Taiyuan has the strongest economic connection with Jinzhong, followed by Xinzhou and Lvliang in the central Shanxi urban agglomeration; Jinzhong and Yangquan are also stronger. In addition to its similar conclusion, this study finds that the traffic flow connection yields a stronger connection between Taiyuan and Yangquan, indicating that although the economic connection between Taiyuan and Yangquan is weak, its traffic connection can lead to gradual economic improvement. The migration and information flow connections conclude that Jinzhong is strongly connected to Lvliang, indicating that future economic development between the two cities can be promoted through population flow and information exchange. The comprehensive flow also shows that Taiyuan and Yangquan, Jinzhong, and Lvliang are strongly connected, which confirms that the multi-dimensional element flow can be used for a comprehensive study and perspective of the urban network structure. Second, this study uses the dynamic spatial data of information, population, and traffic flow between two cities in Shanxi Province to explore the spatial pattern of urban networks and uses the “flow” data as the basis to reflect the interconnection between cities; therefore, the study of regional spatial structure changes from the morphology and hierarchy of cities to the structure, function, and connection of urban networks [5]. In contrast, Cao’s article uses the population, industry, and economic statistics of five cities in the Central Urban Agglomeration to calculate the strength of inter-city connections through a gravity model, which only characterizes the connections between the two, but is objectively different from the actual “flow” data. Third, the study area includes the central Shanxi urban agglomeration and explores the spatial network connections among cities in Shanxi Province as a whole. The research results are richer, and the spatial structure among provincial cities was explored from four aspects: hierarchical distribution, factor flow direction, spatial pattern, and network structure. Overall, it seems that this study has a rich variety of data, the study area is typical, and the region contains the central Shanxi urban agglomeration and the surrounding cities, which have important theoretical and practical value for the development of Shanxi provincial cities to fully realize the strategy of taking the lead in central China.

(3)

In October 2021, the “Outline of the Plan for Ecological Protection and High-Quality Development of the Yellow River Basin” by the State Council of the CPC Central Committee elevated the ecological protection and high-quality development of the Yellow River Basin as a major national strategy, highlighting the strategic position of the Yellow River Basin in the overall development of the country and overall socialist modernization. The Fourteenth Five-Year Plan of National Economic and Social Development and the Outline of Vision 2035 have clarified that the seven major urban agglomerations in the Yellow River Basin cover the majority of the basin and can play a radiating role in ecological protection and economic development. The 20th National Congress of the Communist Party of China emphasized the construction of a coordinated development pattern of large, medium, and small cities based on urban agglomerations and metropolitan areas, promoting the accelerated rise of the central region and advancing the high-quality development of the Yellow River Basin. Shanxi Province is a central province in the interior of China, located on the Loess Plateau on the east bank of the middle reaches of the Yellow River and west of the North China Plain [36], and this case study area enriches the current research on the urban network structure and urbanization in the Yellow River Basin, which is a major national strategy for ecological protection and high-quality development of the Yellow River Basin. According to China’s new urbanization strategy, the rapidly developing provincial capital city of Taiyuan should take the lead in coordinating the steady development of the central Shanxi urban agglomeration and driving neighboring cities to develop together. This study found that Taiyuan is ranked first in all element flows and is moving toward high-quality development. However, the central Shanxi urban agglomeration, as one of the six new regional urban agglomerations that China is guiding to cultivate [37], fails to form a strong network connection through Taiyuan’s central leading role, indicating that Taiyuan’s level of synergy with the central Shanxi urban agglomeration and driving the development of neighboring cities is not high. Therefore, to solve the problem of unipolarity, it is necessary not only to strengthen the core function of Taiyuan, but also to promote the construction of provincial sub-center cities (Datong, Changzhi, Linfen) and urban agglomeration in central Shanxi, strengthen urban networks, gather development momentum, and accelerate the formation of an intensive and efficient, open, and synergistic urbanization development pattern. In the future, Taiyuan should focus on synergistically driving the development of neighboring regions and strengthening cross-regional connections. Simultaneously, it should promote the common construction and sharing of key industries and open platforms, accelerate the construction of national regional center cities, continuously enhance the agglomeration and diffusion effect of Taiyuan, and promote the balanced, connected, and overall development of cities in Shanxi Province.

This study examined the spatial patterns of urban networks in Shanxi Province based on multi-dimensional element flow data. The urban network shows an “absence-type pyramid” for the future not only to continue to play the role of Taiyuan’s radiation drive, but also need to strengthen the development of small- and medium-sized cities themselves. However, the exploration of the spatial mechanism behind the formation of this structure is still inadequate. Future research can be enriched by the continuous collection of relevant data and increasing the analysis of mechanisms, such as in-depth research on resource endowment, policy orientation, transportation accessibility, industrial structure, economic development, and social services. In addition, this study uses a social network analysis method to analyze the characteristics of urban networks, and the data processing adopts binarization processing, which loses some information. Future research can consider the space-time graph attention network (STGAT) [38], cab track data [39], and other multi-source data for in-depth and comprehensive analysis and portrayal.