Study on the Spatial Association Network Structure of Urban Digital Economy and Its Driving Factors in Chinese Cities

Abstract

The digital economy has become an important engine for global economic development by promoting optimal resource allocation and advancing industrial restructuring. Based on the panel data from 279 prefecture-level cities in China from 2012 to 2021, this paper constructs the spatial association networks of urban digital economy using a modified gravity model and analyzes the complex network characteristics and driving factors of urban digital economy growth by the social network analysis methods and the Quadratic Assignment Procedure (QAP). This study finds that (1) the level of urban digital economy in China shows a rising trend year by year and displays an uneven spatial distribution. (2) Spatial association networks of urban digital economy are relatively well-connected, with increasing density and stability of spatial associations, yet some hierarchical structure remains, and overall connectivity still needs to be improved. (3) Most cities in the east region occupy the core positions within the complex network, significantly influencing the overall complex network through a “siphon effect”, while cities in the central region play more of a “bridge” role in the spatial association network. In contrast, cities in the northwest, northeast, and southwest regions are situated on the periphery of this spatial association network. (4) The economic development level, informatization level, technological innovation, urbanization level, industrial structure, and human capital contribute to the formation of the spatial association network of the digital economy. Based on these conclusions, specific policy implications for the future development of the spatial association network of the urban digital economy are proposed.

1. Introduction

The report from the Communist Party of China’s 20th National Congress has advocated for the establishment of digital industry clusters that are globally competitive, the rapid acceleration of the digital economy, and the close connection between digital and real economies [1]. A new economic paradigm is being created based on the economy driven by digital technologies. As the world’s economies are changing, a new trend in global development is the merging of the digital and physical sectors. The rise of the digital economy has injected new momentum into China’s economic and social progress, opening new fields and providing new driving forces [2]. It has rapidly become a key driver of economic growth and social development [3]. The digital economy, by leveraging modern information networks, has transcended geographical limitations, facilitated the networked sharing of knowledge, technology, and data, and strengthened economic linkages between cities. This connection not only optimizes the economic cycle [4] but also promotes the coordinated development of urban economies [5].

However, there are significant differences in resource allocation, economic foundation, scientific and technological level, and policy environment among different regions in China that have implemented region-specific policies and investments, which cause apparent disparities in the growth of the digital economy across various areas. This discrepancy has a significant influence in several areas, including regional economic coordination and the balanced development of the digital economy itself.

Existing studies have preliminarily discussed the regional differences of the digital economy, mainly focusing on the construction of measurement indicators [6], the analysis of influencing factors [7,8], and the analysis of economic effects [9]. However, most of the existing literature treats regions as independent individuals and uses traditional geographical or statistical methods to analyze static differences, which fail to fully reveal the dynamic network properties of the digital economy’s spatial correlation. Especially in the context of digital technology breaking through the limitations of space and time, the complex network correlation between regions through the flow of data elements, the collaboration of the digital industry chain, and the diffusion of technology is becoming a key mechanism to reshape the regional economic pattern. This network development mode makes the digital economy level of a single region not only depend on the local resource endowment but also be deeply affected by its place and function within the overall structure of the network. The complex network structure is an important feature indicating the connection of the digital economy, which is trans-regional and multithreaded. Therefore, a deep understanding of the complex network structural features of the spatial association in the digital economy, exploring its influencing factors and complex network effects, is of great significance for narrowing the digital divide between cities, constructing the development model of a new economy, and fostering high-level growth in China’s economy.

The rest of this paper is arranged as follows: Section 2 includes a literature review and research hypothesis. Section 3 discusses the research methodologies, model setting, and variable selection. Section 4 examines the spatial association network of the urban digital economy in China. Section 5 presents a study of the driving elements of the digital economy spatial association network. Finally, Section 6 closes this article by discussing the policy implications.

2. Literature Review and Research Hypothesis

2.1. Research on the Development of Digital Economy

Don Tapscott [10] pioneered the idea of the digital economy and summarized its characteristics, including complete digitization, high knowledge intensity, pervasive virtualization, and interconnectivity. Some academics conducted in-depth research on how the digital economy developed. In China’s quest for economic progress, the digital economy plays a crucial role as an integral part of the current economic system. According to Dan [11], by adjusting industrial structures and introducing new green technologies, the digital economy may propel top-notch green development. Wang and Chen [12] highlighted that the digital economy creates new opportunities for shaping the pattern of economic development. Wang et al. [13] emphasized that the important avenue digital economy has become a new engine for promoting top-notch economic development. Therefore, we make the following hypothesis:

H1: 

The growth of the digital economy’s spatial association network is positively impacted by the economic development level.

With the quick advancement and widespread use of spatial econometric techniques in recent years [14], as well as complexity theory and social network analysis methods, an increasing number of academics have focused on the spatial correlation properties [15]. When it comes to quantifying the spatial correlation feature of the digital economy, scholars have widely used spatial weight matrices to construct Moran’s index, a classic indicator that measures the similarity and spatial dependence of economic activities between regions. Additionally, the application of inverse distance spatial weight matrices [16] provides a geographically distance-based alternative for assessing spatial correlation. However, the digital economy network exhibits spatial heterogeneity and complexity, which can significantly influence how spatial relationships are formed [17]. It is challenging to create and sustain a direct spatial linkage of the digital economy between geographically disparate places despite the fact that digital technology has partially overcome the constraints of time and space. Therefore, we make the following hypothesis:

H2: 

Geographical distance has a negative effect on the formation of spatial association network of digital economy.

2.2. Research on the Driving Factors of Digital Economy

Dewan [18] carried out a comprehensive investigation on the advantages of Information and Communications Technology (ICT) investment in 36 countries, finding that a high degree of digital foundation in developed countries significantly impacts economic development. The development of information technology not only enables enterprises to share data, enhances the productivity of industrial sectors, and promotes industrial development, but also reduces regional disparities between cities. Therefore, the widespread application of digital technology offers economic and social advantages to countries worldwide [19]. Innovation in technology is the main engine propelling the growth of the digital economy. Recently, researchers have looked into the mechanism of technological innovation in the digital economy from multiple dimensions. Rammer et al. [20], based on the data of German enterprises, verified that AI technology can enhance the innovation ability of enterprises and improve the speed of product iteration, thus expanding the scale effect of the digital economy. Zhong et al. [21] noted that the development of spatial relational network structure benefits from technological progress. Therefore, we make the following hypothesis:

H3: 

The degree of technical innovation and information technology has a favorable impact on the development of the digital economy’s spatial association network.

Urbanization level and industrial structure are important structural variables affecting the evolution of the digital economic landscape. Acemoglu and Restrepo [22] point out that urbanization accelerates the integration of digital technology across sectors through the agglomeration effect. According to the modular innovation theory of Yoo et al. [23], the increase in the proportion of service industries promotes trans-regional digital economy network connectivity by enhancing inter-industry technical compatibility. Li et al. [24] point out that urbanization and industrial structure are the primary drivers of the spatial association network and show significant variations over time and across different regions. Therefore, we make the following hypothesis:

H4: 

Urbanization and industrial structure play a positive role in shaping the spatial association network of the digital economy.

As the carrier of knowledge and skills, one key factor in the growth of the digital economy is human capital. The author of [25] emphasizes that human capital with advanced digital skills is the source of innovation in the digital economy. Zhang et al. [26] found that human capital narrows the urban–rural gap through fostering digital economic development. Wang et al. [27] point out that the difference in human capital level plays a key role in shaping the spatial correlation network. Therefore, we make the following hypothesis:

H5: 

Human capital has a positive influence on the formation of the spatial correlation network of the digital economy.

Although traditional theories hold that marketization can help improve the efficiency of resource allocation, some studies have shown that excessive marketization levels may inhibit the development of the digital economy due to problems such as market structure imbalance and lagging regulation. Song et al. [28] found that the degree of marketization has no significant influence on the role of the digital economy. Garcia-Murillo and MacInnes [29] pointed out that, in highly market-oriented economies, capital and talent are more likely to converge in developed regions with well-developed digital infrastructure, resulting in less developed regions falling into the “digital poverty trap”. Therefore, we make the following hypothesis:

H6: 

The level of marketization negatively affects the formation of the spatial correlation network of the digital economy.

2.3. Research on the Digital Economy Spatial Association Network

Lately, the study of spatial association networks has garnered a lot of interest from international scholars. Fingleton [30] constructs a spatial association network of inter-regional economic ties and finds that the location of a region in the development of the economic network is closely tied to its inherent structure and interactions. By studying the spatial network, Dilworth et al. [31] found that the “digital divide” between British regions has intensified over time. There has not been much study performed on the structural characteristics and driving factors of China’s digital economy spatial association network [32]. Some scholars have studied the spatial association and spatial spillover mechanism of the digital economy, but mainly at the provincial level. Zhu and Chen [33] have made an attempt to probe into the core role of the spatial distribution of the digital economy in the development of Hangzhou city. At the provincial level, the complex network structure is the primary focus of most of these studies, but few scholars have examined it at the prefecture-level city scale. Zhang et al. [34] discovered that the development shows significant spatial distribution differences, with noticeable disparities in the levels and capabilities of the digital economy across different regions, forming a differentiation between core and peripheral regions. Li et al. [35] hold the view that the progress in the realm of the digital economy promotes regional green innovation efficiency enhancement through spatial spillover effects. Technological innovation flow strengthens the digital economy links between different cities, forming a complex spatial association network structure. Spatial heterogeneity leads to significant differences in digital economic activities across different regions and the establishment of a complex network supporting the digital economy [36]. The driving factors contribute to shaping the spatial association network of the digital economy.

On the whole, the existing research focused on the economic advantages that the digital economy creates, and further study is needed on its characteristics in spatial association networks and the driving factors of spatial association network within China’s urban digital economy. Therefore, the contributions of this paper are threefold. First, this paper makes up the related research on digital economy from an overall complex network perspective. In order to investigate the spatial association characteristic across 279 Chinese cities at the prefecture level, we build the intricate topological network of the urban digital economy. We next examine the spatial association network distribution in each city at the network level. Second, the centrality of the spatial association network, along with the spatial clustering mode of the digital economy through block modeling and structural hole analysis, are examined in this paper. Finally, the driving factors influencing the formation of spatial association networks of urban digital economy are deeply explored using QAP (Quadratic Assignment Procedure) analysis in social network analysis. This study not only enriches the research content on the characteristics of the spatial association networks of the digital economy but also provides new perspectives and methods for future research.

3. Research Design

3.1. Research Methods

3.1.1. Modified Gravity Model

The gravity model theory, based on Newton’s universal gravitation theory, has evolved through understanding and application into an economic gravity theory with broad application prospects [37]. In practical applications, we need to modify the gravity model according to the research question. Existing literature often uses the gravity model to establish spatial connections [38]. Considering the digital economy’s cross-regional characteristics to calculate spatial associations in the digital economy, the gravity model used in this paper has been adjusted as follows:

$${\mathrm{R}}_{\mathrm{i}\mathrm{j}}={\mathrm{K}}_{\mathrm{i}\mathrm{j}}{\displaystyle \frac{\sqrt[3]{{\mathrm{G}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}{\mathrm{E}}_{\mathrm{i}}}\sqrt[3]{{\mathrm{G}}_{\mathrm{j}}{\mathrm{P}}_{\mathrm{j}}{\mathrm{E}}_{\mathrm{j}}}}{{\mathrm{D}}_{\mathrm{i}\mathrm{j}}^2}}, {\mathrm{K}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{E}}_{\mathrm{i}}}{{\mathrm{E}}_{\mathrm{i}}+{\mathrm{E}}_{\mathrm{j}}}}, {\mathrm{D}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{d}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{g}}_{\mathrm{i}}-{\mathrm{g}}_{\mathrm{j}}}}$$

(1)

where i and j denote cities; R_ij implies the spatial relevance distance of the digital economy between cities; P_i represents total population; G represents total GDP; E refers the digital economy development index; K_ij represents the contribution rate in the growth of digital economy link between cities; d_ij implies the geographical distance between cities; g represents the economic growing performance level, calculated by GDP per capital. According to Formula (1), we calculate the gravitational matrix of digital economy associations between cities, constructing a 279 × 279 directed binary asymmetric matrix.

3.1.2. Social Network Analysis

Through Social Network Analysis (SNA), researchers can investigate the complex web of connections that define relationships in societal networks [39]. It primarily includes three main components: whole network analysis, individual network analysis, and blockmodeling analysis. In China, the complex network attributes of the digital economy in general are usually described using four dimensions: network efficiency, network density, network hierarchy, and network association degree. Particular network characteristics are typically captured using three indicators: the centrality of degree, betweenness, and closeness. Main indicators and explanations are referenced in [40], as can be seen in

Table 1. Key indicators and descriptions of the urban digital economy spatial network structure.

Indicator	Calculation Formula	Formula Description	Indicator Meaning
Network Density	$\mathrm{D}=\mathrm{L}/[\mathrm{N}\times (\mathrm{N}-1)$	Actual number of relationships/Maximum possible total number of relationships	The higher the density, the closer the spatial association relationships between cities.
Network Connectivity	$\mathrm{C}=1-\mathrm{V}/[\mathrm{N}\times (\mathrm{N}-1)/2$	Degree to which any two members in the network are directly or indirectly reachable	Higher connectivity indicates stronger stability of the overall network structure.
Network Hierarchy	$\mathrm{H}=1-\mathrm{K}/\mathrm{m}\mathrm{a}\mathrm{x}\left(\mathrm{K}\right)$	Degree of asymmetric reachability among members in the network	Higher hierarchy indicates a more stringent network structure, with some cities having stronger dominant positions.
Network Efficiency	$\mathrm{E}=1-\mathrm{M}/\mathrm{m}\mathrm{z}\mathrm{x}\left(\mathrm{M}\right)$	Degree of redundancy in network connections	Lower efficiency indicates more spillover paths and a more stable network structure.
Degree Centrality	$\mathrm{D}\mathrm{C}=\mathrm{n}/(\mathrm{N}-1)$	Number of members directly connected to a member/Maximum possible number of direct connections	Higher degree centrality indicates stronger control of one city over others.
Closeness Centrality	$\mathrm{C}\mathrm{C}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{N}}}{\mathrm{d}}_{\mathrm{i}\mathrm{j}}$	Sum of shortest distances from a member to all other members in the network	Higher closeness centrality means shorter distances between members, leading to closer association and collaboration.
Betweenness Centrality	$\mathrm{B}\mathrm{C}={\displaystyle \frac{2\sum _{\mathrm{j}}^{\mathrm{N}}\sum _{\mathrm{k}}^{\mathrm{N}}{\mathrm{b}}_{\mathrm{j}\mathrm{k}}(\mathrm{i})}{{\mathrm{N}}^2-3\mathrm{N}+2}}$ ${\mathrm{b}}_{\mathrm{j}\mathrm{k}}(\mathrm{i})={\displaystyle \frac{{\mathrm{g}}_{\mathrm{j}\mathrm{k}}(\mathrm{i})}{{\mathrm{g}}_{\mathrm{j}\mathrm{k}}}}$	Extent to which a member acts as an intermediary for other members	Higher betweenness centrality indicates a more prominent intermediary role of a city in the network.

Note: N is the network’s total number of members. The actual number of relationships is L. V represents the number of member pairs in the network that cannot reach each other. K denotes the count of symmetrically accessible member pairs in the network. In the other case, M is the network’s number of redundant connections. The number of members that are directly related to a particular member is denoted by n. b_jk(i) is the likelihood that member i is on the shortest path between j and k, with j ≠ k ≠ i and j < k. g_jk is the number of shortest paths between members j and k, while g_jk(i) is the number of those paths that pass through member i.

.

The block model must be used as the main technique for spatial clustering analysis in social network analysis. It examines the functions of various locations (blocks) in the intricate network [41]. Moreover, this model divides the overall complex network into sectors with different responsibilities, revealing the information transmission paths between sectors. Based on an iteratively converging correlation matrix, nodes are classified and clustered to form a single module. This analysis method helps delve into the association relationships between nodes within and between clusters after clustering.

Ronald Burt initially presented the structural hole theory in his book “Structural Holes: The Social Structure of Competition”. It emphasizes that structural holes within a social complex network can provide organizations or individuals located in these positions with advantages in information and other resources. This concept is significant for analyzing social complex network structures under the internet economy. In the digital economy’s spatial complex network structure, if two cities lack direct contact and must connect through a third city, then the third city occupies a structural hole. This type of city has information and control advantages and can attract more resources and benefits. Structural holes are typically characterized by four indicators: effective size, efficiency, constraint, and hierarchy, and the calculation methods for these indicators are as follows:

Effective size: The effective size is used to calculate and measure the overall influence and importance of a node. The formula to calculate the effective size of a node is as follows:

$$\mathrm{E}{\mathrm{S}}_{\mathrm{i}}={\sum }_{\mathrm{j}}(1-{\sum }_{\mathrm{q}}{\mathrm{P}}_{\mathrm{i}\mathrm{q}}{\mathrm{P}}_{\mathrm{j}\mathrm{q}})=\mathrm{n}-{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{j}}{\sum }_{\mathrm{q}}{\mathrm{P}}_{\mathrm{j}\mathrm{q}}$$

(2)

where n is the magnitude of node i, j represents the adjacent nodes of node i, and the nodes that are adjacent between node i and node j are represented by q. P_iq and P_jq are the proportions of node q in the adjacency of nodes i and j, respectively.

Efficiency: To calculate the efficiency of a node, it is necessary to divide its effective size by its actual size within the network. The calculating formula is as follows:

$$\mathrm{E}{\mathrm{F}}_{\mathrm{i}}={\displaystyle \frac{\mathrm{E}{\mathrm{S}}_{\mathrm{i}}}{\mathrm{n}}}$$

(3)

The calculation of i is determined by the number of nodes, and n represents the number.

Constraint: This indicates the extent to where a node is restricted by its peers in the network. A higher constraint implies stronger dependency and fewer structural holes. The calculation formula is as follows:

$${\mathrm{C}}_{\mathrm{i}}={\sum }_{\mathrm{j}}{\mathrm{C}}_{\mathrm{i}\mathrm{j}}\hspace{1em}{\mathrm{C}}_{\mathrm{i}\mathrm{j}}=({\mathrm{P}}_{\mathrm{i}\mathrm{j}}+{\sum }_{\mathrm{q}}{\mathrm{P}}_{\mathrm{i}\mathrm{q}}{\mathrm{P}}_{\mathrm{q}\mathrm{j}}{)}^2$$

(4)

where nodes i and j share an adjacent location with node q, and the percentage of node j among all nodes that are adjacent to node i, P_ij, is indicated.

Hierarchy: This indicates how much constraint is concentrated on a particular node. The formula for calculating the hierarchical level of a node is as follows:

$$\mathrm{H}{\mathrm{I}}_{\mathrm{i}}={\displaystyle \frac{\sum _{\mathrm{j}}({\mathrm{C}}_{\mathrm{i}\mathrm{j}}/\frac{\mathrm{C}}{\mathrm{N}}){\mathrm{I}}_{\mathrm{n}}({\mathrm{C}}_{\mathrm{i}\mathrm{j}}/\frac{\mathrm{C}}{\mathrm{N}})}{\mathrm{N}{\mathrm{I}}_{\mathrm{n}}\left(\mathrm{N}\right)}}$$

(5)

These indicators help understand the strategic positioning of cities within the digital economy network and the potential advantages or disadvantages they hold due to their specific structural roles.

3.1.3. QAP Analysis

To verify the existence of correlations between matrices, matrix data are permuted in a regression analysis using the Quadratic Assignment Procedure (QAP), which is commonly used for analyzing the factors affecting complex network structures [42]. In the study of the correlation between associated variables, traditional empirical tests often overlook problems such as autocorrelation among independent variables or multicollinearity [43]. QAP regression analysis, a non-parametric method, is used to permute matrix data in a regression analysis in order to confirm the presence of correlations between matrices. Accordingly, this study employs the nonlinear QAP analysis method from social network analysis to conduct an analysis of influencing and driving factors.

3.2. Model Setting and Variable Selection

The factors that have an effect on the improvement of the digital economy involve economic, social, and demographic characteristics. Therefore, this study selects eight factors: geographical distance, differentiated levels of economic development, industrial structure, urbanization level, information development level, human capital, marketization level, and technological innovation. Together, these elements have an impact on how China’s digital economy spatial association network is formed and help to explain the network’s more intricate structural changes. This serves as the foundation for this study’s development of the subsequent model below:

Q = f (D, E, S, C, I, H, M, T)

(6)

In the above model, a spatial association matrix, which is represented by the dependent variable Q, is present in the digital economy of China. D is the matrix of geographical proximity; the matrix of variations in economic development levels is represented by the letter E, measured by the ratio of institutional deposits and loans to gross regional product (ECO); S represents the matrix of industrial structure disparities, calculated using the ratio of tertiary industry output to total production (ISL). C denotes the matrix of urbanization level disparities, based on the proportion of the urban population to the total population (UDL). I is the matrix of differences in the performance of information development, and I is computed by the ratio of broadband internet users to total population (IDL); H is the matrix of human capital differences, determined by the proportion of the numbers of middle school students to the total population (EDU); M is the matrix of marketization level differences, derived from the proportions of government spending to GDP (MAL). T is the matrix of technological innovation differences, measured by the percentage of government spending on technology and science compared to total fiscal expenditure (TEL).

3.3. Data Sources and Explanation

Different from previous studies, this study’s focus is on 279 prefecture-level cities between 2012 and 2021, and uses panel data from them. The analysis data are from the “China Urban Statistical Yearbook” and the “China Urban Construction Statistical Yearbook”. Both the China Digital Economy Development and Employment White Paper and the China Digital Economy Development Index White Paper are used to assess the digital economy’s scale and development level. Geographic distances are calculated using the latitudes and longitudes of cities from Baidu maps. Data on geographical distance, economic development, industrial structure, and urbanization are sourced from city statistical yearbooks, while data on internet broadband access numbers are from the “China Communications Yearbook”. The cities with many missing values are excluded, and the interpolation method is used to fill in the few missing values.

Table 2. Descriptive statistics.

Variable	Observed Value	Mean Value	Standard Deviation	Minimum Value	Maximum Value
DEL	2790	0.3341	0.113	0.07	0.80
ECO	2790	10.7886	0.562	9.01	13.06
ISL	2790	0.289	0.209	0.045	1.396
UDL	2790	5.7319	0.9585	0.6831	0.8019
IDL	2790	1.0889	0.6506	0.1679	7.4502
EDU	2790	6.6284	0.9135	3.8394	9.6397
MAL	2790	0.544	0.246	0.396	0.712
TEL	2790	0.003	0.003	0.000	0.063

Note: D is the geographical location difference matrix, calculated by the longitude and latitude of the city. DEL stands for digital economy development level index. The seven variables in the table are calculated to form seven difference matrices of E, S, C, I, H, M, and T in this paper.

displays the descriptive statistical analysis of the variables.

4. Characteristics of the Spatial Association Network in the Chinese Urban Digital Economy

4.1. Overall Trends in Digital Economy Development

As shown in Figure 1, this paper utilizes the trend analysis tool in ArcGIS 10.2 software to visually describe the spatial distribution trend of Chinese digital economy growing. Each vertical line represents the level (height) and position of digital economy progress in each city. In particular, the Z-axis is indicative of the progress of the digital economy. The X-axis moves from west to east, and, from south to north, the Y-axis moves. Both the 2012 and 2021 trend lines are similar; in the north–south direction, there is a rising trend line between the first and third quadrants, while the third and fourth quadrants have a slight U-shaped trend line in the east–west direction. Trend analysis from 2012 to 2021 denotes that year after year, Chinese cities have seen an increase in digital economy development, and these improvements are spatially dispersed, with an important pattern of uneven distribution.

Furthermore, this research paper utilizes the natural discontinuity method to map the spatial distribution of digital economy for 279 prefectural-level cities in China within the development performance between 2012 and 2021, and the results are shown in Figure 2. Overall, from 2012 to 2021, China’s urban digital economy shows an obvious spatial differentiation between the east and the west according to the depth of color level, showing an “unbalanced” situation, and by comparing development level of less-developed western area, the level in eastern coastal cities is much higher. The level of improvement performance for digital economy in various cities is gradually rising, and by 2021, in most cities like East, South and central China, the level of growing performance for digital economy has improved significantly.

4.2. Overall Network Characteristics of China’s Urban Digital Economy

4.2.1. Spatial Association Characteristics

The model of modified gravity was utilized to figure out the spatial associations on the growing performance levels of 279 prefecture-level cities in the digital economy, and a relationship matrix was constructed. Software calculations show that, in 2012, there was a total network density of 0.118 in the digital economy for the urban areas in China, but, in 2021, it showed a rise in network density of 0.123. Comparing the spatial complex network topology maps of these two years (Figure 3), we can see that there are no isolated cities in the intricate network and notable spatial connection linkages in the digital economy development level in Chinese cities. The total scale of network density and network relationships, between 2012 and 2021, showed an upward trend; second, from a regional perspective, the center of the network holds the majority of cities in the eastern and southern China regions. Conversely, the northwest and southwest provinces lie on the outskirts of the network, and this situation has not changed from 2012 to 2021; third, individual cities have experienced significant changes in network centrality and network status from 2012 to 2021; Fourth, cities located on the periphery of the network have a noticeable spillover effect, indicating that a large amount of digital economy resources are flowing out of these areas, posing great challenges to their own development and adversely affecting balanced regional development.

4.2.2. Overall Network Structural Characteristics

This paper calculates each year’s intricate network architecture features utilizing UCINET 6.0 software and creates a dynamic feature map of the structure of the entire complex network (Figure 4). It is apparent from the measurement results that, from 2012 to 2021, the network association degree was consistently 1, indicating that all 279 prefecture-level cities were included in the complex network and maintained good connectivity with direct or indirect relationships. As shown in Figure 4a, there is an upward fluctuating trend in the density of the intricate network and the number of links between cities. Between 2012 and 2021, the number of network relationships rose from 9130 to 9562, and the network density grew from 0.118 to 0.123, depicting a rise in the closeness of spatial associations in the digital economy among cities. Figure 4b shows a generally fluctuating downward trend in network efficiency, indicating an increase in spatial association relationships among cities and rising network stability. There was a significant increase in network hierarchy, from 0.0145 in 2012 to 0.1038 in 2021, suggesting that cities that are developing a better digital economy are increasingly dominating their positions within the complex network.

The accessibility of the complex network of spatial connections that make up the digital economy is typically measured using network small-world characteristics, typically characterized by the average path length and clustering coefficient, as detailed in Figure 4c. Overall, from 2012 to 2021, the spatial association network of cities’ digital economies exhibited significant small-world characteristics. The average path length generally ranged from 2 to 3, indicating that any two city nodes in the network could establish a complete connection through from 2 to 3 intermediary cities. The general trend of the clustering coefficient showed significant fluctuations, indicating frequent contacts and strong mutual influences in the improvement of digital economy in cities.

In order to further examine the structural variations in the digital economies of Chinese cities, this research divides China into seven main regions: North China, Northeast China, Northwest China, East China, South China, Southwest China, and Central China (City classification see Appendix A). As shown in Figure 5a, there is a downward fluctuating trend in the network density and number of connections in North China. This indicates a year-over-year decline in the closeness of the spatial relationship between cities in North China’s digital economy is spatial. The general pattern of network efficiency is upward, but fluctuating, as shown in Figure 5b, indicating fewer spillover paths between cities and a decrease in network structural stability. A less stringent city network hierarchy and a decline in the dominant position of cities that are developing a more efficient digital economy. According to Figure 5c, the overall trend of the clustering coefficient shows a decrease of significant magnitude signifies a decrease in the frequency of contacts, and weaker mutual influence in digital economy development among cities.

Figure 6a indicates an increase in the cities’ digital economy with the closeness of spatial associations. The observation in Figure 6b is that the network’s comprehensive operational efficiency is subject to a variable but generally declining trend, implying that spatial association relationships among cities in the digital economy are increasing and network stability is rising. A consistently stringent city network hierarchy with no significant change in the dominant position of cities with better digital economy development. As seen in Figure 6c, the overall trend of the clustering coefficient shows significant fluctuations, indicating an increase in the frequency of contacts and mutual influence in digital economy development among cities.

As shown in Figure 7a, a rise in the proximity of spatial links in the digital economy between cities is shown by the higher trend in the number of connections and network density in these cities. Figure 7b reflects that the overall network efficiency exhibits a downward trend, suggesting an increase in spatial association relationships among cities and rising network stability. There has been no change in network hierarchy. In Figure 7c, the overall trend of the clustering coefficient shows no significant fluctuations, indicating that the frequency of contacts and mutual influence in digital economy development among cities has not changed significantly.

As shown in Figure 8a, the closeness of spatial associations in the digital economy among cities has essentially remained unchanged. Figure 8b indicates that fewer spillover paths between cities and a decline in network structural stability. It shows an unstable city network hierarchy and an unstable dominant position of cities with better digital economy development in the network. As shown in Figure 8c, the overall trend of the clustering coefficient shows a downward fluctuation, indicating a weakening of contacts and mutual influence in digital economy development among cities.

Figure 9a indicates a decline in the closeness of spatial associations in the digital economy among cities. Figure 9b reflects that the spatial association relationships among cities are reducing in the digital economy, and network stability is declining. There is a gradually more stringent city network hierarchy, with cities that have better digital economy development gaining a dominant position in the network. As shown in Figure 9c, the overall trend of the clustering coefficient shows a fluctuating decrease, indicating a decline in the frequency and mutual influence of digital economy development contacts among cities.

Figure 10a shows an increase in the closeness of spatial associations in the digital economy among cities. Figure 10b reflects an overall fluctuating downward trend in network efficiency and an increase in spatial association relationships among cities and rising network stability. As shown in Figure 10c, the overall trend of the clustering coefficient shows significant fluctuations, indicating frequent contacts and strong mutual influences in digital economy development among cities.

As shown in Figure 11a, the closeness of spatial associations in the digital economy among cities is increasing. Figure 11b reflects an overall fluctuating downward trend in network efficiency, indicating an increase in spatial association relationships among cities and rising network stability. As detailed in Figure 11c, the overall trend of the clustering coefficient exhibits a noticeable decline, indicating a weakening of contacts and mutual influence in digital economy development among cities.

4.3. Analysis of Individual Network Characteristics

4.3.1. Degree Centrality

By analyzing the features of the entire network complexity, this research further uses UCINET software to compute the centrality of degree, betweenness, and closeness of the 279 prefecture-level cities in China in 2021, to discuss the position and responsibility of complex network in each city. Due to space limitations, only the top fifty and the bottom fifty cities are displayed (See Appendix A for results).

The spatial association network of the digital economy in Chinese cities in 2021 has an overall average degree centrality of 15.348. The top fifty cities have an average degree centrality of 39.583, which is greater than the average for all cities. It indicates that there are more connections of these cities than others and occupy a central spot in relation to the spatial connotation network. The majority of cities in the eastern coastal regions, with high levels of centrality are located, suggesting that cities in these regions have affected the economy with digital technologies in other regions profoundly. Conversely, the average degree centrality of the bottom fifty cities is 2.7144, significantly below the overall average, indicating these cities have fewer connections with other cities and occupy a peripheral position in the complex network. Cities with low level of centrality are mainly in the Northwest and Southwest regions, indicating these cities have less direct impact on the digital economy of other regions (see Figure 12 for details).

The average out-degree of the fifty largest cities is 103.32, according to the latest analysis of out-degree and in-degree, and the average in-degree is 74.54. Among them, 39 cities show dominance in outgoing over incoming interactions, indicating these cities are more connected with other cities, demonstrating stronger dissemination and influence capabilities. The bottom fifty cities have an average out-degree of 2.48 and an in-degree of 7.18, indicating these cities are less connected and have weaker influence, importance, and dissemination capabilities within the complex network.

4.3.2. Betweenness Centrality

In 2021, the network of spatial associations that presented in China’s urban digital economy has an average centrality of 0.355. It can be shown that the average betweenness centrality of the top fifty cities is 1.703, higher than the overall average for Chinese cities (Figure 13). These cities have higher betweenness centrality, demonstrating that they are important nodes that have a controlling influence on the intricate network. These cities establish many connections externally, with noticeable benefit effects, and possess high influence and control within the network, serving as “mediators” and “bridges”. Conversely, the average betweenness centrality of the bottom fifty cities is 0.003, significantly below the overall average, indicating that these cities have fewer digital economy resources, smaller digital economy scales, less noticeable benefit effects, and lesser influence in the digital economy spatial association network.

4.3.3. Closeness Centrality

In network analysis, closeness centrality is employed to assess a node’s average distance to all other nodes. In 2021, the average closeness centrality of the 279 prefecture-level cities in China was 16.980, showing little variation, which denotes that the ability of cities within complex network of spatial associations to connect with other cities has gradually strengthened. According to the calculations shown in Figure 14, the average closeness centrality of the top fifty cities is 17.499. These cities have high closeness centrality, indicating that they can establish connections with other cities quickly and efficiently, and they are at the forefront of the digital economy with network, with strong resource acquisition capabilities. On the other hand, the average closeness centrality of the bottom fifty cities is 15.921. These cities have fewer spatial connections with other cities and are situated around the edges of the digital economy complex network, with lower benefit effects and lacking the capacity to significantly affect other cities.

When examining the degree of centrality, betweenness, and closeness in conjunction, it is evident that the East and South China regions consistently score above the national average and above other regions, occupying central positions in the digital economy’s geographical network. On the other hand, the Northwest and Southwest regions score below the national average, with a significant difference from the East and South China regions, placing them on the periphery.

Cities at the local level with top rankings in all three individual network characteristics include Beijing, Shanghai, Nanjing, Shenzhen, Suzhou, Guangzhou, Changzhou, Wuhan, Hangzhou, and Changsha. The prominence of these cities is due to their robust economic foundations, strong science and education resources, rich talent reserves, advantageous geographic locations with convenient transportation, well-developed digital economy infrastructure, and tight connections with surrounding areas. They exhibit a significant “siphon effect”, attracting substantial external resources, capital, and talent inflows, with clear benefit effects, while also having a technological spillover effect on surrounding cities.

Conversely, cities ranking low in all three individual network characteristics include Urumqi, Hulunbuir, Karamay, Zhongwei, Jixi, Hegang, Lijiang, Jiamusi, Baishan, and Lincang. These cities, due to their remote geographic locations, weak economic foundations, insufficient research investment, and underdeveloped digital economy infrastructure, struggle to attract external resources, information, and talent. This results in fewer spatial connections with other cities, positioning them on the outskirts of the network in the digital economy, with low benefit effects and an inability to significantly influence other cities or establish efficient and close connections. This situation leads to a “Matthew effect” in the spatial network that exists within the urban digital economy of China, where the strong become stronger and the weak become weaker.

4.4. Cohesive Subgroups Analysis of China’s Urban Digital Economy Spatial Network

4.4.1. Block Model Analysis

This study utilizes the CONCOR module, which is a component of the UCINET software module, to investigate the block characteristics of the spatial association network of the urban digital economy. Because of that, discovering spatial clustering characteristics within China’s digital economy association network is allowed. The maximum division was set at 2, and the convergence criteria were 0.2%, which resulted in the spatial network map of 279 prefecture-level cities being divided into four blocks: Block I includes 135 cities, mainly located in North China, Southwest China, and Northeast China. Block II consists of 88 cities, primarily in the Northwest and Central China regions. Block III encompasses 33 cities, mainly from the Central and South China regions. Block IV comprises 23 cities which predominantly in the Southeastern region (See Appendix A).

According to the block model analysis results (

Table 3. Inter-block connections in the urban digital economy’s spatial association network.

Block Type	Relationships Received		Relationships Overflow		Expected Internal Relationship %	Actual Internal Relationship %	Block Type Description
	Internal	External	Internal	External
Block I	814	3777	814	3075	48.20	20.93	Bidirectional Outflow
Block II	306	960	306	358	31.29	40.08	Net Beneficiary
Block III	208	1587	208	1969	11.51	9.83	Broker
Block IV	167	1753	167	2665	7.91	5.90	Net Outflow

Note: The total number of received relationships within a block (outgoing relationships) is calculated as the sum of relationships on the main diagonal of the reception matrix; the sum of the relationships in each column (row) outside of its own block represents the total number of outgoing relationships (received relationships) from outside the block. The formula “(Number of cities within the block − 1)/(Total number of provinces in the network − 1)” is used to determine the expected internal relationship proportion, and “Internal relationships within the block/Total spillover relationships of the block” is used to determine the actual internal relationship proportion.

), the internal relationship percentages within each block are 15.63%, while the inter-block relationship percentages are 84.37%, indicating significant spillover effects in the advancement of the digital economy among cities. The roles of blocks within the Chinese urban digital economy spatial association network are categorized into four types:

• Net Beneficiary Blocks: Members of these blocks both receive relationships from external members and from within the block and have a far higher number of entering relationships than exiting ones. Block II, for instance, has 664 outgoing relationships, 306 internal relationships, and receives 950 relationships from other blocks, qualifying it as a “Net Beneficiary” block.
• Net Outflow Blocks: Compared with what they received, these blocks send out significantly more connections to other blocks. Block IV, with 2832 outgoing relationships, 167 internal relationships, and receiving 1753 from other blocks, is classified as a “Net Outflow” block, where members not only satisfy their own digital economy resources but also provide resources to other regions.
• Bidirectional Outflow Blocks: Members of these blocks both send out and receive relationships, having a comparatively greater quantity of interactions originating from inside the block. According to the definition, Block I is a “Bidirectional Outflow” block, with 3889 outgoing relationships to other blocks and receiving 3777 relationships, having more contacts from within the block.
• Brokerage Blocks: These blocks have fewer internal relationships but play the role of connectors and bridges by both sending out and receiving relationships from other blocks. Block III, with 2177 outgoing relationships, only 208 internal relationships, and receiving 1587 external relationships, has extensive contacts with other blocks, qualifying it as a “Brokerage” block.

In constructing the density matrix for each block, the combined Chinese cities’ total network density in 2021 was 0.123, this value is used as a benchmark to compare the density of each block. Substituting 1 for the corresponding block density occurs when it is higher than or equal to 0.123, otherwise, it is replaced with 0. This creates a likeness matrix for the Chinese urban spatial association network, as it can be seen in

Table 4. Density and likeness matrix between blocks in spatial association network of urban digital economy.

Block Type	Density Matrix				Likeness Matrix
	Block I	Block II	Block III	Block IV	Block I	Block II	Block III	Block IV
Block I	0.045	0.014	0.303	0.502	0	0	1	1
Block II	0.014	0.040	0.036	0.043	0	0	0	0
Block III	0.356	0.095	0.197	0.141	1	0	1	1
Block IV	0.652	0.251	0.175	0.332	1	1	1	1

.

4.4.2. Structural Hole Analysis

To further reveal the spatial clustering characteristics within China’s digital economy complex network, this study uses UCINET software to calculate the structural hole metrics of the Chinese urban digital economy spatial association network (See Appendix A). The results from the years 2012 and 2021 are presented and compared, so SWOT analysis is used to carry out the structural hole.

(1)

Strengths: Dominance of Core Cities in Structural Holes

Major cities, such as Shanghai, Beijing, Shenzhen, Guangzhou, Nanjing, etc., exhibit high effective size indices (an average of 30.03 in 2021, up from 28.35 in 2012), indicating their pivotal roles as structural holes in the digital economy network. These cities act as critical information hubs, facilitating efficient resource integration and exerting significant influence over the network. The rising average efficiency index (from 0.6282 to 0.6425, 2012–2021) further underscores their ability to leverage structural holes for enhanced control and information flow.

The average constraint index decreased from 0.2024 in 2012 to 0.1874 in 2021. Cities with decreasing constraints may occupy more structural hole positions, gaining more opportunities to utilize their positions within the digital economy complex network to acquire more control benefits and information resources.

(2)

Weaknesses: Marginalization of Peripheral Cities

Geographically remote cities like Sanya, Kunming, Yinchuan, Lijiang, Urumqi, Baoshan, etc., face high constraint indices and low effective size/efficiency scores due to underdeveloped digital infrastructure. Their limited connectivity restricts their ability to bridge structural holes, perpetuating their exclusion from key network benefits. These cities struggle with “structural hole isolation”, as evidenced by their inability to establish sufficient connections within the spatial network.

(3)

Opportunities: Dynamic Structural Hole Expansion

The declining constraint index and rising effective size suggest opportunities for emerging cities (e.g., Chengdu, Chongqing) to exploit untapped structural holes. Investments in digital infrastructure could enable these cities to bridge gaps and enhance their network roles. National initiatives like the “East Data West Computing” project could empower western cities (e.g., Yinchuan, Jiuquan) to overcome geographic constraints by improving connectivity and reducing dependency on coastal hubs.

(4)

Threats: Core–Periphery Polarization

The widening gap between core and fringe cities is likely to exacerbate regional disparities. Over-reliance on core cities for information poses systemic risks. Thus, it will spread to the whole digital economy spatial association network. Peripheral cities face difficulties, including insufficient policy support and funding, that limit their ability to develop spatial association networks.

5. Analysis of Factors Driving the Structure of the Digital Economy Spatial Association Network

5.1. QAP Correlation Analysis

To explore the construction mechanisms of China’s urban spatial association network, this study selects the most recent year, 2021, as the representative year and uses an analysis of QAP (Quadratic Assignment Procedure) correlation to examine the relationships between China’s urban digital economy spatial association network and various influencers.

Table 5. QAP correlation analysis results.

Variable	Actual Correlation Coefficient	Significance Level	Mean Coefficient	Standard Deviation	Minimum Value	Maximum Value	p ≥ 0	p ≤ 0
D	−0.076	0.000	0.000	0.011	−0.023	0.066	1.000	0.000
E	0.132	0.000	0.000	0.011	−0.026	0.049	0.000	1.000
S	0.013	0.130	0.000	0.012	−0.025	0.059	0.130	0.871
C	0.001	0.170	0.000	0.012	−0.032	0.049	0.170	0.830
I	0.032	0.008	0.000	0.011	−0.030	0.044	0.008	0.993
H	0.013	0.097	0.000	0.011	−0.025	0.072	0.097	0.903
M	−0.026	0.001	0.000	0.012	−0.027	0.058	1.000	0.001
T	0.074	0.000	0.000	0.013	−0.026	0.070	0.000	1.000

displays the results that indicate that six out of the eight factors passed the significance test, affirming that the development of China’s urban digital economy spatial association network is significantly influenced by these six factors. Specifically, the coefficients for geographical location differences and marketization level differences are negative, suggesting that greater distances between cities and larger disparities in marketization levels are detrimental to the development of the urban digital economy that is being encouraged by the establishment of a spatial association network. The suppression of these factors results in spillover effects within the spatial complex network.

Conversely, the positive coefficients for the other four influencing factors indicate that increases in the disparities of these factors can facilitate the formation of China’s urban digital economy spatial association network. These factors include economic development level differences, information development level differences, human capital differences, and technological innovation differences. Each of these positively correlated factors contributes to strengthening the connectivity and flow of information and resources across cities, enhancing the network’s overall cohesion and effectiveness.

By understanding these relationships, policymakers and urban planners can better strategize on reducing negative impacts while enhancing positive drivers to foster a more interconnected and robust digital economy landscape across various urban areas in China. This strategic approach can lead to more balanced urban development, leveraging digital economic strengths and mitigating weaknesses effectively.

5.2. QAP Regression Analysis

This study used QAP regression analysis to investigate the relationships between the influencing elements and the spatial connection matrix of China’s urban digital economy. The outcomes are presented in

Table 6. QAP regression analysis results.

Variable	Unstandardized Regression Coefficient	Standardized Regression Coefficient	Significance Probability	Probability A	Probability B
D	−0.001	−0.075	0.000	1.000	0.000
E	2.479	0.134	0.000	0.000	1.000
S	0.485	0.006	0.224	0.224	0.776
C	0.065	0.02	0.387	0.387	0.613
I	0.131	0.013	0.070	0.070	0.930
H	0.086	0.016	0.055	0.055	0.945
M	−2.864	−0.041	0.000	1.000	0.000
T	4.608	0.016	0.064	0.064	0.936

. The analysis indicates that a significant negative value exists in the regression coefficient for the geographical distance difference matrix at the 1% level, indicating that the development of a spatial association network for the digital economy is hampered by larger physical distances between cities. This is primarily due to geographical constraints; cities that are geographically closer can more easily form spatial associations, as the cost of digital economic element flow is relatively lower between adjacent cities, leading to tighter spatial associations. Conversely, non-adjacent cities face higher costs in the flow of digital economic elements and less efficient information exchange, resulting in looser spatial associations. Thus, Hypothesis H2 is supported.

The highest and most statistically positive coefficient in the economic development level difference matrix is 0.134, suggesting that growing disparities in economic development levels aid in the growth of the urban digital economy spatial association network This suggests that disparities in economic development can lead to a “siphon effect”, where resources are drawn more towards cities with advanced digital economy, which are mainly distributed in the southeast coastal areas. These economic disparities concentrate various resources in these cities. Hypothesis H1 is verified.

Both the informatization level and technological innovation difference matrix’s regression coefficient have a significant level of positivity at the 10% level, suggesting that advancements in information technology provide efficient channels for information circulation and improve the utilization efficiency of various resources between cities, thereby tightening inter-city connections and promoting the formation of urban digital economy spatial associations. They are key factors influencing digital economy development. Therefore, Hypothesis H3 is supported.

The regression coefficients for the difference matrix between industrial structure and urbanization level are 0.006 and 0.002, respectively, but the factor’s failure to pass the significance test suggests differences in industrial structure and urbanization levels among cities are not a significant factor in the creation of a network spatial associations that exists in China’s digital economy. Therefore, Hypothesis H4 is supported

The regression coefficient of the human capital variance matrix shows a significant positive value. This indicates that the expansion of educational disparities is conducive to the formation of the digital economy spatial association network. This factor significantly enhances the circulation of digital economy elements, promotes the connection of urban digital economy, and thereby facilitates the formation of the network. Therefore, Hypothesis H5 is supported.

Conversely, at the 1% level, the marketization level difference matrix’s regression coefficient has a significant negative impact, which suggests that larger disparities in marketization levels between cities are detrimental in the digital economy to the creation of a spatial association network. The primary motive is that the market is a key player in the digital economy; greater differences in city marketization levels lead to larger disparities in resource allocation, which, in turn, increase differences in innovation and competition between cities, affecting the digital economy’s healthy growth and impeding the establishment of the network. Therefore, Hypothesis H6 is supported.

In this research, we take a closer look at the elements that affect the urban digital economy in China and how the spatial correlation matrix relates to regression analysis. The research breaks down the 279 cities in China that are at the prefecture level into Eastern, Central, Western, and seven distinct regions: China’s North, South, East, Central, Southwest, Northwest, and Northeast regions (See Appendix A). The estimation results are presented in

Table 7. QAP regression analysis of eastern, central, and western cities.

Variable	Eastern City		Central City		Western City
	Standardized Regression Coefficient	Significance Probability	Standardized Regression Coefficient	Significance Probability	Standardized Regression Coefficient	Significance Probability
D	0.000	0.898	0.000	0.048	0.000	0.001
E	0.108	0.267	0.103	0.260	0.319	0.008
S	0.227	0.017	−0.000	0.379	0.152	0.073
C	0.030	0.388	0.045	0.335	0.034	0.365
I	0.260	0.012	0.155	0.094	0.158	0.099
H	0.000	0.050	0.263	0.008	−0.000	0.011
M	0.229	0.036	0.140	0.171	0.118	0.206
T	0.061	0.343	−0.143	0.152	0.096	0.211

.

From Table 7, it is clear that all four levels of industrial structure, informatization, human capital, and marketisation had notably positive regression coefficients at the 10% level. An ideal setting in which the digital economy can take root network for spatial correlation among Eastern region cities, is one in which there are larger variations in these four parameters. Among them, the difference matrix for the informatization development level has the largest impact coefficient, at 0.260, indicating that the expansion of informatization development level differences is the most important factor in fostering the development of the digital economy spatial association network in eastern cities. Cities in the east typically have better geographical locations, higher levels of economic development and urbanization, and advanced technological innovation, so it’s no surprise that these factors failed the significance tests. Hence, the development of the Eastern region’s digital economy spatial correlation network is unaffected by these four elements. The Central area includes 97 cities. With the greatest regression coefficient of 0.263, there is a positive link between human capital and the difference matrices at the 1% level and between geographic location and the amount of informatization development at the 10% level. Out of the seven components that were considered, only three had a statistically significant impact on how cities in the Central region’s digital economy spatial correlation network came to be. The Western area includes 83 cities. While the regression coefficients for the difference matrices of industrial structure and informatization development level are notably positive at the 10% level, there is a noticeable positive trend at the 1% level in the regression coefficients for both geographical location and economic development level, according to the regression results. Amplification of the differences in these four factors supports the formation of a spatial correlation network among cities in the Western region. Here, for the difference matrix of human capital, the regression coefficient is notably negative at 10%, suggesting that a digital economy spatial correlation network would be less feasible if there were more disparities in human capital among the western cities. There was no statistical significance for the other three variables.

In the North China region, the network is mainly influenced by four factors: geographical location, human capital, technological innovation, and the level of informatization. The regression coefficients for the difference matrices of geographical location, human capital, and technological innovation are notably positive at the 10% level, and, at the 1% level, the informatization level’s difference matrix is positively significant. Northern China is most facilitated by the expanding gap in human capital, according to the biggest regression coefficient for human capital (0.275), which is among these factors. According to the regression results, the four factors that contribute to the formation in the East China region are characterized by high levels of economic development, informatization, technological innovation, and human capital. At 0.527, the economic development level holds the most significant regression coefficient, indicating that a greater disparity in economic development is more conducive to the development of the digital economy spatial correlation network. The Central China region’s urban digital economy spatial correlation network is primarily influenced by three factors: geographical location, economic development level, and marketization level. The regression coefficient for the difference matrix of geographical location is notably negative at the 10% level, indicating that there are geographical constraints between cities in the Central China region; the greater the geographical distance differences, the less conducive to the formation. At the 1% level of significance, there is a notably positive regression coefficient associated with the disparity matrix of economic development levels (with the largest coefficient at 0.542), suggesting that the economic development level plays a pivotal role in fostering the growth of the spatial correlation network in the Central China region. The degree of industrialization, the degree of computerization (strongly positive at the 1% level), and the level of marketization (strongly positive at the 10% level) are the three parameters that impact building the urban digital economy’s spatial correlation network in southern China. Like the East China region, the economic development level had the most significant regression coefficient (0.653), indicating that a greater gap encourages the growth of the spatial correlation network for the digital economy. Three factors primarily influence the formation of the urban digital economy spatial correlation network in southwest China: the difference matrices for human capital and informatization level are notably positive at the 1% level, and the regression coefficient for the industrial structure difference matrix is notably positive at the 10% level. The informatization level regression coefficient, at 0.298, is the biggest. The other five forces did not go through the significance test. The factors influencing the spatial association network of the digital economy in cities in the northwest region include industrial structure, human capital, urbanization level and marketization level. The most important influencing factor is industrial structure, with the largest regression coefficient at 0.438. The Northeast China region has the key elements that shaped the development of the urban digital economy network of spatial correlations, with five factors in total. Among these, at the 1% level, the informatization level has the biggest coefficient (0.431), whereas the difference matrices of geographical location, technical innovation, and informatization level all have positive regression coefficients. At the 10% level, the human capital regression coefficient is noticeably positive, but the urbanization level regression coefficient is noticeably negative. This suggests that larger disparities in urbanization level do not help form the digital economy’s spatial correlation structure in the Northeast China region (

Table 8. QAP regression analysis of seven regional cities.

	Regional	D	E	S	C	I	H	M	T
Standardized Regression Coefficient	North China	0.000	0.000	0.000	0.000	0.658	0.275	0.000	0.000
	East China	−0.000	0.527	−0.101	−0.002	0.403	0.129	0.039	0.459
	Central China	−0.000	0.542	−0.298	0.116	0.014	−0.572	0.529	−0.159
	South China	0.000	0.653	−0.025	0.064	0.447	0.391	0.195	0.014
	Northwest	0.000	−0.104	0.438	0.000	0.000	0.000	0.000	0.476
	Southwest	0.000	0.000	0.298	0.000	0.449	0.000	0.000	0.000
	Northeast	0.000	0.072	0.000	−0.224	0.431	0.000	0.000	0.000
Significance Probability	North China	0.036	0.393	0.800	0.651	0.000	0.019	0.336	0.030
	East China	0.336	0.000	0.107	0.500	0.000	0.087	0.351	0.000
	Central China	0.017	0.004	0.008	0.163	0.452	0.000	0.000	0.170
	South China	0.234	0.005	0.416	0.354	0.001	0.014	0.094	0.482
	Northwest	0.506	0.316	0.009	0.094	0.518	0.000	0.090	0.310
	Southwest	0.894	0.481	0.044	0.593	0.005	0.000	0.208	0.210
	Northeast	0.000	0.566	0.218	0.929	0.008	0.055	0.511	0.001

).

5.3. Study Comparison

In terms of digital economy development, compared with previous studies [44] mostly based on the provincial level, this paper studies the development trend and spatial distribution trend of China’s urban digital economy. The statistical data can more accurately present the development status and differentiation of the digital economy.

In terms of spatial correlation research, most studies focus on spatial autocorrelation and the spatial spillover effect of the digital economy [45]. This paper focuses on the analysis of spatial correlation network characteristics of the urban digital economy in China. The block model and structural hole analysis are a new expansion on previous research.

In terms of driving factors, many factors that drive the development of the digital economy also drive the formation and development of the spatial association network, but there are also certain differences. Therefore, compared with previous studies on influencing factors of digital economy [46], this paper analyzes the driving factors of the spatial association network of the digital economy, providing a new perspective for the development of the digital economy.

6. Conclusions and Policy Implications

6.1. Conclusions

This paper examines the spatial distribution and development trends of the digital economy in Chinese cities. While investigating the spatial linkage relationships of digital economies across cities, it also constructs a spatial association network. On this basis, the spatial complex network structural features and its driving factors are studied. The following conclusions are drawn:

First, China’s cities are experiencing a fluctuating growth pattern with significant regional disparities in the economy within digital improvement. Cities in the southeast coastal regions exhibit notably higher levels of development compared to other areas.

Second, cities have established connections with neighboring and even non-neighboring cities, ensuring accessibility and tight linkages, with no isolated cities within the complex network. The closeness of spatial association relationships remains low and needs further enhancement. Cities that occupy central positions within the association network exert strong control over national digital economy resources and notably influence surrounding regions, demonstrating a pronounced “siphon effect”. Conversely, the digital economy spatial association network places cities in the central area primarily in a “bridge” role, with cities in the northwest, northeast, and southwest regions positioning themselves on the network’s periphery. This is a new development on the basis of previous research.

Third, according to cluster analysis, there is a reduction in the number of internal connections within each block, while inter-block connections are tight, showing clear spillover effects and significant regional heterogeneity within the network. From the structural hole analysis, cities like Beijing, Shanghai, Nanjing, Suzhou, Shenzhen, and Guangzhou occupy structural hole positions, underscoring their importance and influence within the digital economy spatial network structure. These cities gain considerable “informational advantages” and “control advantages”. This is a new discovery that has not been found in previous studies.

Fourth, the development level of economic growth significantly impacts the establishment of the association network. Divergences in urbanization levels, human capital, and technological innovation contribute positively to the creation of spatial association networks in the digital economy. Geographical proximity and differences in marketization levels are negatively correlated with network formation, which hinders the construction of a spatial association network. This is a new development on the basis of previous research.

6.2. Policy Implications

As one of the most dynamic economic forms of the 21st century, the digital economy has not only transformed the traditional economic models of cities but has also profoundly influenced their development paths. The spatial association network of the digital economy is crucial in promoting the development of urban digital economies. This study reaches important conclusions at the urban level and, based on these conclusions, proposes the following policy recommendations:

Strengthening regional coordinated development strategies will foster balanced growth across different areas. Given the significant disparities between regions, especially between southeastern coastal cities and other areas, policies should be formulated to promote coordinated regional development and ensure a balanced distribution of digital economic resources across the country. The central and western cities are recommended to act as a “bridge”, enhancing cooperation with the eastern coastal cities to achieve interconnected development in the digital economy.

Enhancing city complex network connectivity contributes to improved collaboration and economic integration. Increasing investment in infrastructure, particularly in the digital economy sector, such as 5G networks and data centers, can improve the complex network connectivity and data transmission efficiency between cities. Strengthening intercity cooperation in the digital economy and promoting the use of resources will help form a more closely-knit network structure.

Optimizing the spillover effect of digital economy hub cities helps distribute benefits more widely: For cities in central positions, such as Beijing, Shanghai, Guangzhou, and Shenzhen, further leverage their spillover effects to spread advanced digital economy technologies and experiences to surrounding areas. These cities should disseminate advanced digital economy technologies and experiences to the surrounding areas. Additionally, long-term stable cooperative relationships should be established between these hub cities and peripheral cities to promote balanced development of the digital economy across the country.

Emphasizing policy guidance and differentiated management ensures tailored approaches that address specific regional needs in order to formulate differentiated digital economy development policies based on the specific characteristics of different regions and cities at various stages of development to ensure the targeted effectiveness of these policies. There has to be clearer policy direction to boost innovation, support digital economy integration with traditional industries, and raise digital economy’s contribution to the national economy.

6.3. Limitations and Further Directions

The spatial association network of China’s urban digital economy and its motivating elements are thoroughly examined in this article; however, there are still many shortcomings and research expansibility.

First of all, future research can further expand the regional scope so that it is no longer limited to cities, but extends specific research areas to city clusters, economic zones and even transnational regions. In addition, we can expand the international perspective and compare the structural differences and evolutionary laws of spatial correlation networks of digital economy in different countries.

Secondly, in terms of industry scalability, the research method of this paper can be applied to the production of digital products, the application of digital technology and other fields. In the future, the spatial association network of each industry should be constructed to analyze the characteristic differences in network structure, node centrality and association strength to enrich the research perspective.

Third, in terms of data, the current research is restricted by data acquisition conditions, the data used in this analysis mostly spans the years 2012–2021, and the urban digital economy’s spatial association network may undergo more modifications over time. Follow-up studies should continue to update the data to track the latest trends and provide a more reliable basis for in-depth analysis.