Analysis of network patterns and its influencing factors in Chengdu-Chongqing urban agglomeration based on multi-flow

Abstract

With the strengthening of the cross-regional flows of the economy, information, innovation, and population, this paper constructs a network model of multi-flow integration and analyzes the spatial pattern and influencing factors of urban networks in Chengdu-Chongqing Urban Agglomeration using social network analysis and spatial analysis technology. The main conclusions are as follows. (1) The density and efficiency are in the transition stage from the primary level to the medium level in the comprehensive network. (2) The overall pattern keeps a polyhedral pyramid structure with Chengdu ↔ Chongqing as the core axis, and the grade of each axis has been significantly raised. (3) Four groups are formed using the social network method and show a geographic proximity effect. In addition, the connections within each group are relatively close, but the connections between the groups are significantly different. (4) Location conditions, economic development level, enterprise development level, scientific research investment, scientific and technological development level, and government support have a greater impact on the formation of the comprehensive network of Chengdu-Chongqing urban agglomeration. Information application level and transportation accessibility show a small impact and human capital level has not yet produced a significant impact.

1. Introduction

Urban agglomerations, serving as a pivotal engine for national and regional economic development, play an increasingly significant role in the process of urbanization and regional integration against the backdrop of globalization. With the rapid advancement of economic globalization and information technology, the connections between cities have become more intertwined, forming a complex network system characterized by the multifaceted flow of population, capital, and information. These comprehensive flows not only facilitate resource sharing and complementarity within urban agglomerations but also reshape the spatial structure and functional positioning of urban agglomerations, further influencing the formation and development of urban network characteristics. With the evolution of big data and network analysis technologies, scholars are now able to analyze the internal network connectivity, centrality, and mobility features of urban agglomerations from a more macroscopic and refined perspective, thereby providing a scientific basis for the process of urban-regional integration and promoting balanced regional development. Early scholars primarily focused their research on the network spatial structure of urban agglomerations based on the concept of flow space [1], utilizing data on high-end service industry flows between cities, transportation flows such as air and freight volumes, and information flows to uncover the functional connections [2]and network relationships between cities [3]. The Globalization and World Cities (GaWC) research network has developed a mature body of work on the study of the world city network, constructing a global city network based on the distribution characteristics of productive service industry corporations' headquarters, regional centers, and local offices within the urban system [4]. Taylor developed a “chain network model” for the top 100 advanced productive service industry corporations to measure network characteristics. As spatial connections between cities become increasingly tight, research on inter-city network connections has also deepened significantly [5]. In terms of research content, most studies analyzed the structural features of urban networks [[6], [7], [8]] and explained the driving mechanism [[9], [10], [11]] by some quantitative model [12,13], and put forward some strategies for optimizing urban systems [14]. From the data source of flow, most scholars used the single indicator such as economy [15], transportation [16], information [17], population [18], and knowledge [19]to analyze the urban network, some scholars used the comprehensive index [18,19] with the combination of the flow of population and economy. In the method, traditional research mostly used the classic methods of the gravity model, interlocking model, and urban flow model to measure network connection. However, owing to the static characteristics of the data such as overall population and GDP, many studies believe that the flow space cannot be truly reflected. With the advantages of flow data such as traffic flow and information flow, many current studies use social network methods [20] to conduct an in-depth analysis of urban centrality, correlated strength, and cohesive groups. In addition, some scholars used the dominant flow method to analyze the optimal paths and the core axes of the regional economy. Regarding the methods of influencing factors, in addition to some qualitative explanations, most scholars used modes such as Quadratic Assignment Procedure (QAP) analysis [21,22], and GeoDetector [23] to measure the structural characteristics of urban networks. In summary, compared to earlier studies that mainly focused on urban networks under the single-element flow framework, current research has begun to explore comparative studies of multiple networks. However, these studies primarily contrast different types of transportation and information flows, lacking comprehensive research on urban networks involving multiple elements' flows. In terms of methodology, besides utilizing social network analysis for spatial structure studies, scholars have attempted to employ statistical analysis methods in conjunction with social network analysis to investigate the mechanisms behind urban network spatial structures. Given this context, conducting temporal and spatial comparative analyses of various urban networks from a multi-dimensional element flow perspective can more comprehensively reveal the developmental characteristics of urban networks. This approach holds significant contemporary relevance by providing a more rational theoretical basis for urban planning.

Cities are complex, multifaceted systems where various element flows are interdependent and mutually influential; a singular element flow cannot fully reveal a city's developmental state and trends. Comprehensive and long-term comparative analysis of multiple flows can offer us a thorough and deep perspective to understand the dynamics and evolutionary patterns of urban development. Additionally, it can identify key elements and potential obstacles driving urban development, providing a scientific basis for urban planning and policy-making. Furthermore, this analysis can enhance our understanding of cities as complex systems, further exploring the interactions and dependencies between urban agglomerations internally and with their external environments. Therefore, this paper considers the advantages and disadvantages of traditional data and big data. This study conducts the urban networks based on the combination of multi-flow, constructs a comprehensive model, and analyzes the characteristics and influencing factors of urban networks in Chengdu-Chongqing Urban Agglomeration using the methods of social network analysis, spatial analysis technology, and other methods.

2. Materials and methods

2.1. Study area

The Chengdu-Chongqing urban agglomeration, located in western China, stands as a pivotal region within the national “Belt and Road” initiative and the Yangtze River Economic Belt strategy. In recent years, driven by policy support and economic forces, the Chengdu-Chongqing urban agglomeration has undergone rapid development and transformation, with significant enhancements in inter-city connectivity and overall competitiveness. However, the development of this urban agglomeration also faces challenges such as uneven resource allocation and a low level of regional integration. These issues are largely tied to the internal comprehensive mobility and urban network characteristics within the urban agglomeration. Therefore, a detailed analysis of the network characteristics and influencing factors of the Chengdu-Chongqing urban agglomeration, based on multiple comprehensive flows, is not only crucial for revealing its internal development mechanisms and interaction patterns but also for optimizing regional development layouts and promoting high-quality development. Since 2015, the Chinese government has intensified its focus on regional coordinated development, particularly through the deep implementation of the Western Development Strategy and the advancement of national-level urban agglomeration development plans. As a crucial component of the national “Belt and Road” initiative and the Yangtze River Economic Belt development strategy, the Chengdu-Chongqing urban agglomeration has experienced significant policy-driven development. Between 2015 and 2020, the Chengdu-Chongqing urban agglomeration underwent a rapid urbanization process, with a notable increase in urbanization rates. Urbanization not only altered the population distribution and structure of the region but also facilitated the accelerated exchange of economic flows, human mobility, and information flows within the region and with external entities. Therefore, selecting the period from 2015 to 2020 for study aims to analyze the characteristics and trends of network evolution within the Chengdu-Chongqing urban agglomeration during this critical period, to gain a deeper understanding of its development dynamics, evolutionary patterns, and future growth potential. This not only provides a scientific basis for the planning and management of urban agglomerations but also holds significant theoretical and practical implications for understanding the development of urban agglomerations in China and globally.

2.2. Research methods

2.2.1. Multi-flow network model

• (1)Economic flow network

The gravity model is commonly used for analyzing spatial interactions, so we use it to measure the strength of the urban economic flow network [23,24]. The models are set as follows in equation (1)- (4):

$$F_{i\to j}=K_{ij}\frac{\sqrt{G_i{P}_i}\sqrt{G_j{P}_j}}{r^2}$$ (1)

$$K_{ij}=\frac{G_i}{G_i+G_j}$$ (2)

$$F_{ij}=\frac{F_{i\to j}+F_{j\to i}}{2}$$ (3)

$${F_i}^{\prime }=\sum _j{F}_{ij}$$ (4)

Where $F_{i\to j}$ represents the intensity of economic connection from city i to city j; $F_{j\to i}$ represents the intensity of economic connection from city j to city i; K_ij represents the correlated coefficient from city i to city j; P_i, P _j represent the resident population of city i and city j respectively; G_i, G_j represent the per capita gross regional product of city i and j respectively; r_ij represents the shortest distance of road transport from city i to j; F_ij represents the intensity of economic flow from city i to city j; F_i＇represents the total economic strength.

• (2)Information flow network

Baidu Index is a statistical index for analyzing information networks. It not only reflects the netizens' attention but also reflects the internet influencing force by other cities’ residents [25]. Therefore, we use the daily average of the Baidu index to measure the strength of information connection. We constructed models (5)–(6)：

$$S_{ij}=0.5S_i+0.5S_j$$ (5)

$${S_i}^{\prime }=\sum _j{S}_{ij}$$ (6)

Where S_ij represents the strength of information from city i to city j; S_i represents the daily average of Baidu index for city j by internet users in city i; S_j represents the daily average of Baidu index for city i by internet users in city j; S_i' represents the total amount of information connection.

• (3)Innovation flow network

Co-authored papers and co-patents are the joint labor of scientific and technological workers, which can effectively reflect the innovation network. Therefore, this study uses these two indicators to measure the strength of innovation. We constructed models (7)–(8)：

$$E_{ij}=0.5U_{ij}+0.5V_{ij}$$ (7)

$${E_i}^{\prime }=\sum _j{E}_{ij}$$ (8)

Where E_ij represents the strength of the innovative connection from city i to city j; U_ij represents the co-authored papers between city i and city j; V_ij represents the co-patents between city i and city j; Ei' represents the innovation between city i and other cities total amount of contacts.

• (4)Population flow network

Big data of Tencent Location (https://heat.qq.com/bigdata/index.html) are based on the positioning function software of cell phones, it can calculate the flow of different traffic such as high-speed rail, ordinary railway, and aviation. Therefore, we use this big data to measure the strength of the population flow. We constructed models (9)–(10):

$$T_{ij}=\frac{T_{i\to j}+T_{j\to i}}{n}$$ (9)

$${T_i}^{\prime }=\sum _j{T}_{ij}$$ (10)

Where T_ij represents the strength of population flow from city i to city j; $T_{i\to j}$ represents the flow of population from city i to city j; $T_{j\to i}{T}_{j\to i}$ represents the flow of population from city j to city i; n represents the number of days; T_i' represents the total amount of population flow.

• (5)Comprehensive flow network

Limited by the one-sidedness of a single flow, whether the population flow or traffic flow cannot fully reflect the state of urban connection. Referring to related studies, it is considered that each elemental flow is equally important in the spatial structure system of urban agglomerations [26], therefore, the values of each single flow element are accumulated to find the mean value as the comprehensive flow matrix. We constructed models (11)–(12):

$$Z_{ij}=\frac{{F_{ij}}^{\prime }+{S_{ij}}^{\prime }+{E_{ij}}^{\prime }+{T_{ij}}^{\prime }}{4}$$ (11)

$${Z_i}^{\prime }=\sum _j{Z}_{ij}$$ (12)

Where Z_ij represents the comprehensive correlated strength from city i to city j; F_ij', S_ij', E_ij' and T_ij' represent the normalized values of correlated strength of the economy, information, innovation and population from city i to city j respectively; Z_i' represents the total amount of comprehensive strength.

2.2.2. Social network model

• (1)Network index

The network index is used to indicate the centrality of network nodes in the research area [27]. If the index is at a high level, indicating that the centrality of the city is more prominent in the overall network, and vice versa. The model is set as follows:

$$D=\frac{2l}{n\left(n-1\right)}$$ (13)

Where D represents the network index; l represents the number of connected lines among nodes; n represents the number of urban nodes.

The correlated degree is used to indicate the close connection status among cities. If the degree of a city is at a high level, indicating that the network cooperation is stronger than other cities’ correlation. The model is set as follows in equation (14):

$$C=1-\frac{V}{N\left(N-1\right)/2}$$ (14)

Where C represents the correlated degree; V represents the number of unreachable nodes in the network; N represents the network size.

The average efficiency is used to represent the connectivity degree among cities. If the value is at a low level, reflecting that the research area has relatively more channels and the overall network is more stable. The model is set as follows in equation (15):

$$E=\frac{1}{n\left(n-1\right)}\sum \frac{1}{d_{ij}}$$ (15)

Where E represents the average efficiency of the network; n represents the number of city nodes; d_ij represents the shortest distance from city i to city j.

• (2)Node index

Node index including AC_i and AP_i is used to measure exchangeability and dominant force of regional resources, it reveals the node role of transition and central control of cities. Therefore, we used these two indices to measure the roles of the network node. We constructed models (16)–(17)：

$$A{C}_i=\sum _j{R}_{ij}\times D{C}_j$$ (16)

$$A{P}_i=\sum _j\frac{R_{ij}}{D{C}_j}$$ (17)

Where AC_i represents the transformation centrality of the network node; AP_i represents the control power of the network node; R_ij represents the correlated strength from city i to city j; DC_j represents the centrality of city j.

• (3)Cohesive group

Cohesive group analysis is mainly based on the cluster method to explore the local urban assemblage, it can reveal the cities’ alliance status of geographical combination. Therefore, we use the Concor method to analyze the cohesive and close status of the urban agglomeration.

• (4)Quadratic Assignment Procedure (QAP)

QAP analysis is a non-parametric estimation method for analyzing matrix similarity comparison; it is mainly used to measure the correlated strength and regression coefficients [28]. Compared with other regression methods, this method can perform an effective non-parametric test, and can better solve the multi-collinearity problem.

2.3. Data sources

The data on GDP, total resident population, and the distance of the shortest road, were obtained from the Statistical Yearbook, Economic Statistics Bulletin, and Baidu Maps website (https://map.baidu.com). The daily average data of the Baidu index was obtained from the Baidu index website (https://index.baidu.com). The data of co-authored papers and co-patents were obtained from the Web of Science website (https://www.webofscience.com) and the State Intellectual Property Office website (https://www.cnipa.gov.cn). The data on population flow were obtained from the Tencent Location Big Data website (https://heat.qq.com). Due to the large sample size, the 10th-16th day of each month in 2015 and 2020 were selected separately. The statistical indicators of influencing factors were obtained from statistical yearbooks and the statistical bulletin of national and local statistical offices. In addition, the data on geographical proximity was derived from the Baidu Maps website (see Fig. 1).

Fig. 1.

The map of the region site (a) and research unit (b).

3. Results

3.1. Network pattern

The social network method was used to calculate the network index and average efficiency. The results are shown in Fig. 2. The network index increased from 0.47 to 0.52 but deviated greatly from the ideal value of 1. Therefore, there is still room for further improvement. The correlated degree was 1 in 2015 and 2020, indicating that a direct or indirect relationship has been established and a coordinated model has formed. The network efficiency decreased from 0.65 to 0.55 in the research period, reflecting the continued expansion of the channels of circulation and improvement of correlated stability. With the continuous enhancement of network density and network efficiency, the comprehensive flow network has gradually developed to the middle stage of coupling integration. However, the network efficiency of the overall pattern of Chengdu-Chongqing Urban Agglomeration is still not high, so it is necessary to improve the integration of various flows. Therefore, the state and local governments has implemented several policies and measures to improve network efficiency. To be specific, since the Plan was issued in 2016, the government of Sichuan and Chongqing Province responded quickly to the Plan and put forward some specific measures such as constructing the modern urban system, establishing some cooperative organizations, and signing several strategic agreements. These policies and measures not only have speeded up the construction pace of a comprehensive transportation network, but also enhanced the radiation of the dual-core cities of Chengdu and Chongqing, and further deepened regional economic cooperation.

Fig. 2.

The overall index of comprehensive network (a) and single flow network (b).

Due to the comprehensive flow network being composed of four flows, analyzing the single-flow network can further reveal the existing problems. Correlated degrees of economy, information, innovation, and population are all 1, similar to the overall flow network. Therefore, in the future, four flows should be highly integrated and form a close interactive combination to support the urban networks. The network density of economy, information, innovation, and population, increased from 0.33 to 0.44, 0.53 to 0.61, 0.34 to 0.42, and 0.30 to 0.41 respectively. It shows that the increment of network density of information flow is the highest, so the cities need to strengthen the cohesive role of economic correlation, innovative cooperation, and population flow in Chengdu-Chong Urban Agglomeration. The average efficiency of information, innovation, and population, decreased from 0.76 to 0.64, 0.54 to 0.45, 0.75 to 0.66, and 0.8 to 0.67 respectively. Although it showed a downward trend, the values of the economic flow, innovative flow, and population flow are still higher than the overall network. Therefore, it is necessary to balance the circulation efficiency of different flows and promote the overall efficiency to a higher level.

3.2. Network connection

Based on the matching relationship of AC_i and AP_i, we calculate the centrality of urban nodes of the overall network (Fig. 3.) and divide them into six levels using natural breaking classification (Fig. 4.).

Fig. 3.

Transformation centrality, transformation control force, and position of each city in the comprehensive network.

Fig. 4.

The Connection grade of comprehensive network and single element network.

From 2015 to 2020(Fig. 4a and b), the overall pattern has not changed significantly, but the grade of axes especially in the last four levels has been raised. The grade of Chengdu-Chongqing has been raised from level 2 to level 1, so this axis is regarded as the core correlated channel. From the perspective of actual development, relying on the core and sub-core roles of Chengdu and Chongqing, this axis of Chengdu↔Chongqing has a strong centripetal force to gather and dominate resources. Therefore, it undertakes the function of driving the co-development of the urban agglomeration. The grades of Chengdu↔Meishan, Chengdu↔Deyang, and Chengdu↔Mianyang have increased from level 4 to level 3, and Chengdu↔Leshan, Chengdu↔Ziyang, Chengdu↔Nanchong, and Chongqing↔Guang'an increased from level 5 to level 3, which can be called for sub-core axes. From the spatial pattern, we can see that the radial network was formed by the axes of Chengdu↔Leshan, Chengdu↔Ziyang, and Chengdu↔Nachong, indicating that Chengdu has a strong radiation force in the north-western Sichuan. However, except for the axis of Chongqing↔Guang'an, Chongqing has not formed a strong force of radiation role in its immediate vicinity.

Although the grade of Chengdu↔Ya'an, Chengdu↔Yibin, Chengdu↔Neijiang, Chongqing↔ Dazhou, Chongqing↔Nanchong, and Chongqing↔Yibin have increased from level 5 to level 4, and some low-level cities with weak economic strength have in the central area of Chengdu-Chongqing Urban Agglomeration increased from level 6 to level 5, they are still at a low level. Apart from the above axes, the remaining axes at level 6 are mainly composed of edge cities interconnecting with each other. Due to the low-level cities being away from core cities and their ability to concentrate resources is not high, the support for the overall network is insufficient and needs to be optimized.

Since the integrated network is composed of four flows, we analyze the four single-flow networks to reveal the problems in urban networks. From Fig. 4c, e, g, i and 4(d, f, h, J), it can be seen that the network patterns of single-flow did not change significantly, but the grade of axes is significantly different from 2015 to 2020. Specifically, in the four networks of single-flow, the grade of the Chengdu ↔Chongqing all jumped to level 1, which is similar to the comprehensive network, showing that the close cooperation of various elements between Chengdu and Chongqing is the main force for shaping the overall network. Therefore, based on the cooperative advantages of various elements, Chengdu and Chongqing should strengthen the development of manufacturing clusters along the key axes, improve the population agglomeration of core cities, and lead the network degree and correlated level of overall pattern to a high level.

In addition, affected by differences in spatial distance, industrial direction, technical field, and urban infrastructure, the grade of the single-flow network around the core city of Chengdu and Chongqing is significantly different. Specifically, the cities around the core cities formed a local network of 1–5 levels in the innovative network, economic network, and population network. However, the cities around the core cities have formed a global network of information networks with the rapid construction of infrastructure. In short, in the future, the government should pay more attention to the cooperation of the industrial chain, scientific research projects, and construction of the cross-city facility, to enhance the driving force of the core cities of Chengdu and Chongqing to the peripheral cities.

3.3. Network group

Network group is used to reveal the sub-structures and their interrelationships within the integrated and single-factor networks, which are used to identify which cities within the Chengdu-Chongqing urban agglomeration have relatively strong ties. Firstly, the Concor algorithm in Ucinet software is applied to divide the integrated network subgroups (Table 1), which will be integrated and get the density of connections within and between subgroups; Secondly, the subgroups densities of the integrated and single-element networks were converted into a matrix of correlation coefficients, using the average network density as a benchmark; Use the correlation coefficient matrix as an input matrix and continue the correlation coefficients between the rows or columns of this matrix to obtain a new correlation coefficient matrix; After several iterations of calculation, the final matrix was obtained (Table 2). Finally, ArcGIS was applied to represent the spatial visualization of the cohesive subgroups of the integrated network (Fig. 5). Considering the similarity of the results for the 2015 and 2020 time sections, only the 2020 subgroup is analyzed below. Fig. 5 shows that the comprehensive network has formed four groups, and we named I, II, III, and IV.

Table 1.

Composition of cities in different groups.

Comprehensive Network	I	Chengdu	III	Luzhou, Yibin, Zigong, Neijiang
	II	Meishan, Ziyang, Deyang、 Mianyang, Leshan,Ya ’an	IV	Guang'an, Nanchong, Suining, Dazhou, Chongqing
Economy Network	I	Chengdu, Meishan, Ziyang, Leshan, Ya ’an	III	Luzhou, Yibin, Zigong, Neijiang
	II	Mianyang, Deyang	IV	Guang'an, Nanchong, Suining, Dazhou, Chongqing
Information Network	I	Chengdu	III	Luzhou, Yibin, Zigong, Neijiang
	II	Suining, Dazhou, Nanchong, Guang ’an	IV	Leshan, Meishan, Deyang, Mianyang, Ya ‘an, Ziyang, Chongqing
Innovation Network	I	Chengdu, Meishan	III	Neijiang, Mianyang, Ya ’an、Yibin, Ziyang, Chongqing, Guang'an
	II	Luzhou, Deyang, Dazhou, Zigong, Leshan	IV	Nanchong, Suining
population network	I	Chengdu	III	Luzhou, Zigong
	II	Meishan, Neijiang, Deyang, Mianyang, Suining, Ziyang, Leshan, Nanchong, Chongqing, Ya ’an	IV	Dazhou, Yibin, Guang'an

Table 2.

Image matrix of the cohesive group in 2020.

Comprehensive Network	I	II	III	IV	Economy Network		I	II	III	IV	Information Network	I	II	III	IV
I	–	1	1	1		I	1	1	0	0	I	0	1	1	1
II	1	0	0	0		II	1	1	0	0	II	1	0	0	0
III	1	0	0	0		III	0	0	1	0	III	1	0	0	0
IV	1	0	0	1		IV	0	0	0	1	IV	1	0	0	0

Innovation Network	I	II	III	IV	Population flow network	I	II	III	IV
I	1	1	1	1	I	0	1	1	1
II	1	0	0	0	II	1	0	0	0
III	1	0	0	0	III	1	0	0	0
IV	1	0	0	0	IV	1	0	0	0

Fig. 5.

Cohesive groups of the comprehensive network in 2015(a), 2020(b).

Specifically, in the comprehensive network, group I covers only Chengdu, and group II covers 6 cities including Mianyang, Deyang, Ziyang, Meishan, Leshan, and Ya'an. As an important aisle for the urban agglomeration to open to the western province, these cities in group II show a geographic proximity effect around the core city of Chengdu in the northwest. Group III covers four cities including Neijiang, Zigong, Yibin, and Luzhou, showing a significant geographical proximity effect in the south. As a key demonstration area for the cross-regional coordination of the urban agglomeration, group IV covers five cities including Guang'an, Nanchong, Suining, Dazhou, and Chongqing, showing a significant geographical proximity effect of aggregation in the northeast. In addition, Table 1, Table 2 show that the correlated strength of the four groups is relatively consistent, but the internal gap is significantly different from the comprehensive network. Specifically, the group I has only Chengdu, so there is no internal connection, but it is closely related to the cities in groups II, III, and IV, indicating that Chengdu has a strong driving effect on other groups. The cities in Group II and III have lower correlated strength than the average value, indicating that the urban connections between group II and III are not close. However, the correlated strength in group IV is greater than the average value, indicating that internal urban connections in this group are relatively close.

As the comprehensive network is composed of four flows of the economy, information, innovation, and population, we analyze the single-flow network to further reveal underlying laws. Although the internal correlated strength of group II in the comprehensive network is not close, have established relatively close connections with the core city of Chengdu in the single-flow network of economy, information, population, and innovation, showing that the cities in group II have formed a medium-strength correlated axis with the core city. Under the leadership of the core city, group II should give full play to this advantage adjacent to the core city, and promote its comprehensive force to a high level. The cities in group III of the comprehensive network, not only form a close connection of economic network, but also have a close interaction with the core city of Chengdu in the network of economy, innovation, and information. Therefore, based on the internal and external advantages of group III, the government should focus on strengthening the economic cooperation of internal cities, and simultaneously strengthening the external cooperation relationship with the core city of Chengdu, to enhance its comprehensive strength to a higher level. The cities of group IV, not only formed a close interaction with the core city of Chongqing and break the administrative barriers, but also formed an internal network of information, innovation, and population. Therefore, similar to group III, the future focus of Group IV needs to strengthen its internal links and external cooperation.

4. Influencing factor

Based on previous studies [[9], [10], [11], [12]], we used QAP for regression analyses. Since QAP is a randomization test (Randomization Test) method for comparing the values of individual elements corresponding to two or more square matrices, it gives the correlation coefficients between two matrices by comparing the values corresponding to individual square matrices, as well as performing a non-parametric test on the coefficients. consequently，we construct an influencing factors matrix including the economic gap, human capital difference, the gap in information technology, the gap in scientific investment, geographical proximity effect, and the relationship of administrative affiliation (see Table 3). Economic gaps directly reflect the uneven development among cities within an urban agglomeration, with the gap in per capita GDP accurately depicting the variations in economic development levels between cities. These differences impact the flow of people, capital, and the geographic distribution of economic activities, thereby affecting the network structure and evolutionary characteristics of the urban agglomeration. Human capital, as a key resource driving urban development, is indicated by the disparity in employment numbers, reflecting differences in human resource allocation between cities. Information technology, fundamental to modern society, profoundly influences economic activities, social interactions, and knowledge dissemination. The gap in the number of internet users mirrors the variations in the prevalence and application of information technology between cities, affecting the speed and breadth of information flows, and consequently, the internal information exchange capacity and overall network connectivity within the urban agglomeration. Investment in science and technology is a critical factor for fostering urban innovation and technological advancement, with the level of R&D funding directly impacting a city's innovation capability and technological outputs. Administrative affiliation affects inter-city policy coordination, resource distribution, and cooperation mechanisms. Cities within the same province may exhibit higher efficiency and closer ties in administrative coordination, policy formulation, and resource sharing, significantly influencing the formation and evolution of the internal network of the urban agglomeration. Therefore, the economic gap is represented by the gap in the per capita GDP; the human capital difference is represented by the number gap of employees; the gap in information technology is represented by the number gap of internet users, and the gap in scientific investment is represented by the gap of R&D founding, the relationship of administrative affiliation is represented by whether cities belong to the same province(see Table 3).

Table 3.

The analysis of influence factors with the QAP method.

Independent Variables	Specific Indicators	Dependent Variable （in 2015 ）		Dependent Variable （ in 2020）
		Correlation Analysis	Regression Analysis	Correlation Analysis	Regression Analysis
Economic Gap	Per Capita GDP Gap/Yuan	0.402c	0.304c	0.420c	0.284c
The Gap in Information Technology	The Number Gap of Internet Users/%	−0.259b	−0.185b	−0.170b	−0.229b
The Gap in Scientific Investment	R&D Funding Gap/100 million Yuan	−0.256b	−0.147a	−0.264b	−0.045a
The Gap in Human Capital	The Gap in Employees	−0.285b	−0.153a	−0.225b	−0.247a
Geographical Proximity Effect	Adjacency is 1/Otherwise 0	−0.417c	−0.382c	−0.412c	−0.375c
The Relationship of Administrative Affiliation Relation	1 in the Same Province/Otherwise 0	−0.288a	−0.257a	−0.104	−0.120
R2			0.336a		0.322a
Adjusted R2			0.312a		0.301a

Note.

^ap < 0.10.

^bp < 0.05.

^cp < 0.01.

4.1. Economic force

The regression coefficient of the economic gap is significant at the 1 % level, reflecting that economic strength is the core factor for the urban correlation. From the spatial structure, the axes of strong economic connections are in the small scope with Chengdu and Chongqing, which just confirms the gap in economic force. In reality, cities with high economic strength have the technical advantages to develop products, while cities with low strength have the advantage of an adequate supply of raw materials and the cheap cost of labor. Therefore, the cities with a large economic gap will undertake different functions and form complementary industrial chains, to pursue the maximization of profit. However, with the rapid growth of low-level cities, they will reduce their technological dependence on high-level cities, and their internal interaction with adjacent areas will enhance, so their impact on the comprehensive network will be reduced. In contrast, the cooperative relationship of low-level cities with weak axes on the fringes not obvious in 2015 such as Deyang-Mianyang, Suining-Nanchong, and Neijiang-Zigong, but it is strengthened by the enhancement of economic strength and economic ties in 2020 which are in line with the regression coefficient and reduced evolution characteristics.

4.2. Information technology

The regression coefficient of the gap in information technology is negative and significant at the 5 % level, showing that information technology plays an important role in the comprehensive network. The absolute value of the regression coefficient increased from 0.185 to 0.229, indicating that cities with a small gap in information technology are easily correlated by shaping networks. With the acceleration of the technological and digitalization process, information technology has gradually become a crucial carrier of enhancing the efficiency of communication and producing close connections in the fields of medical care, education, finance, and government services. It is worth mentioning the level of information technology of Ya'an, Luzhou, and Nanchong is still at a grade, while other cities have gradually improving from 2015 to 2019, indicating that they are not closely connected to cities in the surrounding area. Under these circumstances, the correlated strength showed a downward trend of Ya'an↔Chengdu, Ya'an↔Mianyang, Luzhou↔Chongqing, Luzhou↔Chengdu, Nanchong↔Chengdu, and Nanchong↔Dazhou. In addition, with the rapid improvement of the level of information technology in Mianyang, the gap between it and Chongqing has been continuously narrowed, which can be proven by the change in the regression coefficient.

4.3. Scientific investment

The regression coefficient of the gap in scientific investment is significant at the 10 % level and its absolute value decreased from 0.147 to 0.045, which means that cities with a small gap in scientific investment are more likely to form close innovative networks. In theory, unlike other flow networks, the network of scientific investment mainly relies on intellectual resources such as patents and papers to establish a cooperative network. Therefore, it doesn't require much cost of urban connection and it is easier to form a balanced relationship of regional cooperation. In 2015, the pattern of scientific investment in the Chengdu-Chongqing Urban Agglomeration showed obvious heterogeneity, indicating that the core cities have concentrated more resources such as scientific research institutes and high-tech enterprises. Therefore, to establish a scientific network, the Plan proposed that the government should give full play to the advantages of the scientific and technological resources of Chongqing and Chengdu, and accelerate the construction of regional innovation platforms. In 2020, the sixth meeting of the Central Financial and Economic Commission of China emphasized that the Chengdu-Chongqing Region should become an important growth pole of China's science and technology innovation core, so the policies provide strong support for entrepreneurship innovation, and the transformation of scientific and technological achievements.

4.4. Human resources

The regression coefficient of the number gap of employees decreased from −0.153 to −0.247 and it passes the significant test at the 1 % level, indicating that the difference in human resources has a positive effect on shaping the comprehensive network. It can be found that the large gap in human resources in different cities will speed up the frequency of population flow, and accelerate the process of urbanization, industrialization, and information action. Compared with 2015, the absolute value of the regression coefficient in 2020 has increased, which mean that population agglomeration provides a basic guarantee for the smooth flow of a comprehensive network with the scale-up of the gap in human resources. From the changes in recent years, driven by the improvement of economic force, social progress, and innovative development, the high-quality talent demand of enterprises and R&D departments has been increasing. That is, the market of the low-quality labor force can no longer meet the needs of industrial upgrading and urban-rural structural transformation. In reality, the rapid increase of total employees and the weakened growth of high-quality talents led to the proportion imbalance of the structure of human resources in recent years. In this situation, the effect of the large gap in human resources in underdeveloped regions is more obvious, especially in southern Sichuan.

4.4.1. Geographical proximity effect

The geographical proximity effect is significant at the 1 % level, which means that it provides an important deriving force for comprehensive network shaping. In theory, because of low communication costs and high cultural consistency, the efficiency of urban communication at close range will be higher than in further scope. Realistically, Chengdu-Chongqing Urban Agglomeration has not only added multiple integrated transportations such as high-speed railways, intercity railways, expressways, and railway sites, but also built multiple hubs such as railway stations, commercial ports, and airports, which greatly alter the negative effects of distance on network formation. At the same time, tributary waterways such as Wujiang, Jialing, and Minjiang have been constructed in recent years. With the construction of a rapid transportation system, the cost of time and transportation of urban connections have been greatly reduced.

4.4.1.1. 6Policies and institutions

The absolute value of the regression coefficient decreased from 0.257 to 0.120, indicating that the influencing role of administrative affiliation is gradually decreasing. In 2015, due to some administrative barriers between Chongqing and Sichuan Province, cross-provincial urban exchanges were hindered to some extent, so the correlated strength of some border cities was not smooth, and local cooperation was difficult. However, since the implementation of the Plan, a regional alliance was established by a joint conference of economic integrated development co-organized by Sichuan and Chongqing. With the regional cooperation and boundary-breaking measures accompanied by regional alliances, the governments of Sichuan and Chongqing have signed several cooperation agreements such as cultural relics protection and ecological co-construction, which have further promoted economic integration, optimal allocation of resources, cultural exchange, information sharing and integrated construction of service facilities. From the calculation results of the correlated strength, some axes from Chongqing to some border cities in Sichuan province have increased such as Chengqing↔Dazhou and Chengqing↔Guang'an.

5. Discussion and conclusions

5.1. Discussion

In the context of the information age, the organizational connections between cities have shifted towards dynamic networks of elemental connections, with the deep implementation of flow space providing new perspectives and momentum for studying regional spatial patterns. This study, grounded in big data, employs a comprehensive approach by utilizing diverse flow elements such as economic, information, innovation, and human flows to investigate the network characteristics of the Chengdu-Chongqing urban agglomeration. This contrasts sharply with traditional studies that focus on a single flow element, offering a more holistic and integrated analytical framework to explore the development and evolutionary traits of urban networks. Simultaneously, we have uncovered that the urban network is transitioning from a primary to an intermediate stage in terms of density and efficiency, not only highlighting the dynamism of the Chengdu-Chongqing urban agglomeration but also its immense potential for development as a whole. Furthermore, this study makes significant findings regarding the spatial structure of the Chengdu-Chongqing urban agglomeration, identifying a polyhedral pyramid structure centered around Chengdu and Chongqing. This contrasts with the mature, concentrated network structures of urban agglomerations in Eastern China, reflecting differences in regional development levels, policy support, and historical-cultural backgrounds. Moreover, the identification of four clusters and their geographical proximity effects through social network analysis aligns with the general notion of urban network geographical clustering. By revealing the tight connections within clusters and the clear differences between them, this study adds new perspectives and depth to the field of urban network research. However, this study finds that under the leading goal of regional integrated and collaborative development, the spatial network of the Chengdu-Chongqing urban agglomeration is not yet mature. The research results can be summarized into the following main issues: Firstly, Chengdu and Chongqing hold significant core positions within the main urban areas, but their capacity to drive development in surrounding areas is insufficient, highlighting a pronounced “core-periphery” issue. Secondly, inter-city connections overly rely on Chengdu and Chongqing, with secondary cities not playing a prominent role. Thirdly, the independent development characteristics of cities are not pronounced, with peripheral cities showing too strong a dependency on core cities. In the future, the Chengdu-Chongqing urban agglomeration should first strengthen the core status of its leading cities and enhance urban comprehensive service capabilities. The core positions of Chengdu and Chongqing should be reinforced, leveraging advantages in information, talent, technology, and capital to improve their competitiveness, enhance the aggregation of element flows, overcome administrative restrictions, attract and drive the development of surrounding districts and counties, and achieve the regional development goal of a “multi-core, dual-center” model. Although Chengdu and Chongqing have always been at the core of the Chengdu-Chongqing urban agglomeration, compared to other core cities in China, their comprehensive strength still needs to be enhanced. They should fully utilize their rich natural resources and geographical positions to improve urban comprehensive service capabilities through multiple channels. Secondly, cultivate key nodal areas within the network and develop secondary center areas. Fully leverage cities with higher centrality, such as Mianyang, to shift from passive to active development and drive the coordinated development of surrounding cities. Use local resources to intensify infrastructure construction, optimize the allocation of high-quality resources, attract enterprise development through relevant preferential policies, encourage innovative development, define development functions, and introduce advanced technology. Lastly, deepen the distinctive functional features of city nodes, fully leveraging their advantages. Peripheral cities should identify their core values, position future development trends, actively interact with core cities, optimize their resource allocation, promote industrial transformation, and form their own regional characteristic development directions. Core and hub cities should effectively play their role in driving development, clarifying regional functional division, strengthening external exchanges, and establishing an efficient system for connecting urban networks across various element flows.

5.2. Conclusions

Based on the perspective of the multi-flow of economy, information, innovation, and population, this paper constructs a comprehensive model. It analyzes the characteristics and influencing factors of urban networks in Chengdu-Chongqing Urban Agglomeration in 2015 and 2020 using the methods of social network analysis, spatial analysis technology, and other methods. The core conclusions are as follows. (1) With the continuous enhancement of density and efficiency of the integration of the various flows, the comprehensive network has evolved into a medium-term stage and achieved some achievements in cross-regional cooperation. However, it is still necessary to focus on breaking through the bottleneck of channels of circulation and enhancing the correlated efficiency of economic, innovative, and population networks, to further improve the overall interactive level. (2) The overall pattern showed a polyhedral pyramid structure with Chengdu ↔ Chongqing as the core axis, the axes around the core cities of Chengdu, and Chongqing as the sub-core axes. Compared with the core city of Chongqing, the radiation force of Chengdu for promoting the co-development of neighboring regions is more prominent. In addition, although the correlated axes in different levels show a significant increasing trend, they still show a significant geospatial constraint phenomenon away from the core cities. (3) Four groups are formed by social network analysis. Group I: Chengdu. Group II: Mianyang, Deyang, Ziyang, Meishan, Leshan, and Ya'an. Group III: Neijiang, Zigong, Yibin, and Luzhou. Group IV: Chongqing, Guang'an, Nanchong, Suining, Dazhou. Except for group I, the cities in other groups all have unbalanced connections away from the core cities. From the internal connection of different groups, the interactive degree of group IV is closer than groups II and III. (4) Human resources provide a basic guarantee for the smooth flow of the comprehensive network and speed up the integrated combination of other flows. In addition, the effect of geographical proximity still exists in the peripheral area, and policies and institutions provide important strategic support and soft environmental guarantees.

Funding statement

This work was supported by the National Natural Science Foundation of China (42271213).

Data availability statement

The authors do not have permission to share data.

CRediT authorship contribution statement

Xiaomin Wang: Writing – review & editing. Zhiwei Ding: Writing – original draft, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.