Research on the Influence of Spatial Structure on Carbon Emission Synergy of Urban Agglomeration—Based on the Development Process of Yangtze River Delta Urban Agglomeration in China

Abstract

Carbon emissions, as an indicator of green economic development in urban agglomerations, are closely related to the degree of coordinated development between cities. Additionally, urban agglomerations, as a highly developed form of urban space, are widely regarded as a more efficient, energy-saving, and land-saving urbanization method. This article constructs an urban agglomeration network based on relevant data from listed companies in the Yangtze River Delta urban agglomeration with practical connections between cities and uses social network analysis methods and a fixed effects model to calculate the impact of overall and individual network indicators of urban agglomerations on urban carbon emissions and collaborative emission reduction of urban agglomerations. The regression results indicate that the centrality of individual cities has a significant negative correlation with the intensity of urban carbon emissions, with a coefficient of −0.067. The centrality of core cities has a significant positive impact on the collaborative emission reduction of urban agglomerations, with a coefficient of 0.0138. The impact of network density on the collaborative emission reduction of urban agglomerations shows an inverted U-shaped curve. Based on the analysis results, the paper explores the spatial structure construction method and industrial development control strategy based on urban agglomeration collaborative emission reduction.

1. Introduction

The formation of the urban agglomeration concept can be traced back to Howard’s exposition of urban agglomeration in the late 19th and early 20th centuries. Its core viewpoint is to study the complementary development of urban and rural areas by using the surrounding areas of cities as research objects [1]. From the perspective of economics, the development of urban agglomeration is a process of forming an industrial economic division and cooperation system. When the industry gathers to a certain extent in a central city, it will aggravate the continuous expansion of costs, competition, etc. in the central city. When the dis-economy of agglomeration exceeds the positive externality brought by agglomeration, the agglomeration will be transformed into diffusion and transfer [2]. The industrial division of labor between large cities and their surrounding cities has gradually formed.

The study of urban agglomerations in China began in the 1980s, which was the result of the disruption of the planned economy system after the reform and opening up and the increasingly close connection between cities due to the role of the market economy. Given that the complementary and integrated internal functions of urban agglomerations have a strong driving effect on the development of individual regional cities [3], in the early 1990s, national and local governments adopted the suggestions of scholars and carried out new levels of urban agglomeration planning in many coastal areas [4]. With the deepening of openness, this urban development model has gradually been accepted by inland areas, and large-scale construction practices have been carried out.

However, China’s urban agglomeration strategy has a strong administrative orientation; that is, urban agglomeration is artificially developed with government intervention rather than a natural result of economic development [1]. The government designates the member cities of the cluster, identifies the central cities, and formulates a series of development policies. Policy-oriented urban agglomeration has an obvious single-center structure, and under this structure, resources and development policies are rapidly concentrated in the central cities. Whether such unconventional urban agglomerations can integrate the superior resources of cities and achieve efficient and coordinated development of various urban agglomerations, especially whether they can achieve coordinated emission reduction in the context of green development, deserves to be studied and verified.

The purpose of this article is to explore the relationship between carbon emissions and the spatial structure of urban agglomerations and to identify directions for optimizing the spatial structure of urban agglomerations based on carbon emission synergy. Currently, research on carbon emissions is mostly focused on regional attributes such as population, development status, industrial structure, and other aspects. There are few articles focusing on interregional linkages, and they are primarily focused on the provincial level [5,6,7,8], with the network structure of spatial correlation of carbon emissions between different provinces being studied using the gravity model and coordinated emission reduction policies being proposed [5,9,10,11,12]. However, neither regional development nor carbon emission reduction can be studied independently from the surrounding environment, ignoring the interaction between regions, and the gravitational model cannot reflect the actual connection between cities. To avoid these research deficiencies, this paper constructs an urban agglomeration network based on enterprise association data with practical connections between cities. Enterprise correlation can directly influence economic relations between cities. According to existing studies, enterprise networks can reflect and influence the structural characteristics of urban spatial networks [13], which is an effective way to discuss the development pattern of urban agglomerations based on economic laws. The number of enterprises is related to a region’s influence and competitiveness, and the degree of enterprise concentration will also change a city’s leadership ability, having a significant impact on economic growth [14,15]. The multilateral network relationship between enterprises is important in unifying the market, optimizing resource allocation and efficient flow, promoting exchanges and cooperation between different places, complementing each other’s advantages, and promoting regional integration [16,17,18,19]. Since enterprises are internal relations and actors in the socioeconomic process, many foreign economic geographers regard enterprises as the realistic foundation of urban agglomeration economies [20]. Under the market economy system, enterprises, as the main body of the market, are the direct actors who break the constraints of administrative boundaries and form industrial chains between cities [21]. Zhang Xiangjian and colleagues investigated the industrial development process in the Yangtze River Delta and concluded that spatial agglomeration and diffusion of enterprise functions, division of labor, and cooperation all promoted spatial agglomeration and diffusion of urban functions, which became the primary driving force for the formation of urban agglomerations [22]. As a result, research on the synergy mechanism of urban agglomeration carbon emissions using enterprise data can take into account the dual goals of urban agglomeration economic development and environmental protection from the start.

At the same time, as urbanization has accelerated, material and information links between cities in urban agglomerations have grown, and city development has demonstrated strong interdependence [23]. As a result, in order to formulate more targeted and coordinated emission reduction policies, it is necessary to fully understand the overall structure of urban agglomerations, the links between cities within urban agglomerations, and the impact of changes in the spatial structure of urban agglomerations on the economy and carbon emissions. This paper draws on the research method of world urban networks based on the distribution of listed companies in the Yangtze River Delta urban agglomeration, takes the city where the listed companies are located as the node, constructs the network of the Yangtze River Delta urban agglomeration, and uses the social network analysis method to calculate the overall network effect and individual centrality of the urban agglomeration. The social network analysis method can quantify the degree of association between individuals and other individuals in the overall network, explore the status, rights, and roles of individuals in the network, and analyze the overall characteristics of the network from both individual and overall levels to analyze related issues [24]. This article first analyzes the relationship between the spatial structure of urban agglomerations and carbon emissions and proposes relevant hypotheses. Next, this article uses UCINET 6.5 software to calculate the firm association network indicators of the Yangtze River Delta urban agglomeration and uses a fixed effects model in STATA 17.0 software to calculate the impact of the corresponding network indicators on carbon emission intensity and synergistic emission reduction effects. Based on the analysis results, this article finally proposes a method for optimizing the spatial structure of urban agglomerations based on collaborative carbon emission reduction.

2. Literature Review and Hypotheses

2.1. The Impact of Enterprise-Related Networks on Urban Carbon Emissions

Multilateral network relationships between enterprises can promote unified markets, optimal allocation, and efficient flow of resource elements and play an important role in promoting exchanges and cooperation across regions, complementing each other’s advantages, and promoting regional integration and development. Using the location of microenterprises, we can more carefully identify the spatial structure of industries within the city [22]. At the same time, the relationship between enterprises at the level of talent exchange, technical cooperation, and research and development reflects the relationship between different cities to some extent. Therefore, this paper takes the connection between enterprises in different cities as the connection between different cities.

The enterprise network will facilitate the orderly and autonomous flow and sharing of technology, knowledge, information, talents, and capital. At the same time, big cities tend to be more attractive to these factors, and the level of these factors is improved through the agglomeration effect. Thus, these cities can obtain a higher degree of centrality in different dimensions of the urban agglomeration network and reach a higher level of development. Cities with a high level of development may have radiation and spillover effects, assisting cities in urban agglomerations with a low level of development to improve their technical level and efficiency while developing their economies [25]. By this logic, cities with a higher degree of centrality tend to have lower carbon emissions.

The degree of centrality measures a city’s position in the network space of its urban agglomeration [26]. The greater its degree of centrality, the more direct links it has with other cities, and the higher its position in the network, the greater its ability to influence other cities and control resource flow between cities [27]. On the one hand, the higher a city’s degree of centrality, the stronger its control over talents, technology, capital, and other elements, and the easier it is to obtain the core resources of green development, such as low-carbon technology. The higher the degree of centrality of an enterprise-related network in an urban agglomeration, the more opportunities there are to communicate with other related enterprises, the closer the relationship, and the greater the scope of enterprise radiation and influence, which is more conducive to the formation of economies of scale, the improvement of technical level, and the improvement of resource utilization. On the other hand, the faster the city develops, the larger the scale, the greater the input and energy consumption, and the greater the carbon emissions [28]. Carbon emission reduction is not positively correlated with capital and low-carbon technology possessed by cities because the quality of urban green development represented by carbon emissions per unit of GDP is ignored. As a result, this paper employs carbon emission intensity to investigate the changing trend of carbon emissions between cities under different development levels and contends that the greater the degree of centrality of a city, the faster the economic growth and the higher the resource utilization rate, and the lower the ratio of carbon emission to GDP, i.e., the carbon emission intensity.

Centrality is normally represented by three indicators in social network analysis: degree centrality, closeness centrality, and betweenness centrality, and all three indicators can be used to represent the rights and status of cities in the network [29]. Degree centrality, for example, examines the number of direct connections between cities but ignores the number of indirect connections. As a result, it is necessary to calculate the importance of cities in terms of network connections by combining closeness centrality and betweenness centrality [30]. The ability of a city to influence the relationship between other cities is reflected in its betweenness centrality. In the process of urban network association, closeness centrality describes the degree to which a city is not affected by other cities. The closer the city is to the center, the more direct the connections between enterprises in this city and those in other cities, and they will act as “central actors” in the network. For example, the closer the two points are, the easier it is to transfer information and other elements, implying that they rely less on other aspects of the transaction and are more likely to be in the network’s center [31]. As a result, the following assumptions are advanced in this paper:

Hypothesis 1. 

In the enterprise-related network, the higher the degree of centrality of a city, the lower the carbon emission intensity.

Hypothesis 2. 

In the enterprise-related network, the higher the closeness centrality of a city, the lower the carbon emission intensity.

Hypothesis 3. 

In the enterprise-related network, the higher the city’s betweenness centrality, the lower the carbon emission intensity.

2.2. The Impact of Enterprise-Related Networks on the Coordinated Emission Reduction Effect of Urban Agglomerations

Each node city in an urban agglomeration is not only the main body of the urban agglomeration’s economic and social development but also the direct driving force to promote carbon reduction and green development in the urban agglomeration. Collaborative emission reduction in urban agglomerations is not only conducive to reducing information asymmetry in the city and improving the enthusiasm and effectiveness of carbon emission investment in each subject, but it is also conducive to lowering the cost of carbon reduction, improving the efficiency of green economic growth in urban agglomerations, and lowering the economic impact of carbon emissions [23].

In the context of carbon emission reduction, the significance of urban agglomeration is to coordinate the functions and positioning of node cities so that the overall structure of urban agglomeration can play a synergistic role in carbon emission reduction. Synergy is defined as consistent behavior caused by the coordination and correlation of subsystems within the context of collective behavior.

The collaborative environment necessitates a high level of exchange demand, and the information and technology of customs clearance exchange interact with the surrounding related systems, self-organizing and evolving, forming an orderly structure and, eventually, a synergistic effect. Synergy is a self-organizing system, and the power of this self-organizing system is formed by competition and cooperation among subsystems [32,33]. First, competition between subsystems causes the system to become unbalanced; second, coordination can cause some motions in a non-equilibrium subsystem to unite and enlarge continuously until it occupies a dominant position, thus dominating the evolution of the entire system. As a result, this paper believes that there are two prerequisites for urban agglomerations’ synergistic emission reduction effect. First, the urban agglomeration is a closely linked group, and the major cities in the urban agglomeration are closely related, giving the cities the desire and opportunity for capital, information, and talent flow, implying that the urban agglomeration requires a close cyberspace structure to promote the exchange and communication of various development factors between cities. Second, the core cities are dominant, and they have the ability to radiate to other cities in the urban agglomeration, which gives cities a certain leadership role and makes cities appear benign and orderly. In this state, various elements flow frequently between cities, the radiation and influence scope of core cities are constantly expanded, city interaction is strengthened, and technological innovation, division of labor, and cooperation have the most primitive possibilities, which effectively promotes the reduction of energy costs and carbon emissions and has a strong relationship with the overall structure of cyberspace.

Network density, network hierarchy, and network efficiency are indicators of the overall structure of cyberspace. Among these, network density reflects the overall compactness of the network structure [34,35]. The greater the network density, the more cities with which the network’s enterprises are actually associated, the closer the economic relationship between cities, the more frequent the flow of factors, and the greater the transmission of information technology. It is worth noting that for urban association networks, it is not necessarily true that the greater the network density, the better. If the network density is too high, there will be more redundant lines in the network, which will reduce the flow efficiency of elements and, to some extent, increase related costs [36]. In this way, the overall development efficiency of urban agglomerations will decline. The interrelationship, interaction, and coordination of the major cities are required for the coordinated development of urban agglomerations. The greater the gap in network status and the more one-way connections, the higher the network hierarchy, which is not conducive to the coordinated development of urban agglomerations. The efficiency of network connections between cities in the urban agglomeration network is reflected in network efficiency. The more cities that are linked together, the more stable the urban network and the lower the network efficiency [23]. In the aspect of network synergy, the excessive redundant correlation between cities reduces the flow efficiency of inter-city elements, which is not conducive to the synergistic effect of urban agglomeration. Therefore, this paper believes that the network hierarchy and efficiency of urban agglomerations have a negative impact on the coordinated emission reduction of urban agglomerations. As a result, the following assumptions are advanced in this paper:

Hypothesis 4. 

Within a certain range, the greater the network density of urban agglomerations, the stronger the collaborative emission reduction efforts.

Hypothesis 5. 

The weaker the network hierarchy of urban agglomeration, the stronger the collaborative emission reduction.

Hypothesis 6. 

Within a certain range, the lower the network efficiency of urban agglomeration, the stronger the collaborative emission reduction.

The effects of agglomeration and diffusion are strongly related to carbon emissions. The greater the centrality of core cities, the greater the importance of urban agglomeration and diffusion effects. Spatial agglomeration and enterprise diffusion have facilitated the spatial diffusion of urban functions and have become important supports for coordinated development within urban agglomerations. Taking the Yangtze River Delta urban agglomeration as an example, Shanghai is very appealing to businesses from neighboring cities, and many major corporations have established subsidiaries or relocated their headquarters to Shanghai. Enterprise groups concentrate on management functions in Shanghai, while production and processing functions are distributed across small and medium-sized cities, providing the initial impetus for the formation and growth of urban agglomerations [22].

Core cities can lead, drive, integrate, and coordinate the development of the entire urban agglomeration, as well as promote integrated urban agglomeration development [37]. From the perspective of the development process in Shanghai, it has been radiating to the surrounding cities. After the reform and opening up, Shanghai took the lead in becoming an international metropolis and has been playing a leading role in economic development. In the Yangtze River Delta city group, Shanghai’s economic development level has always been the highest. Thus, this paper takes Shanghai as the core city of the Yangtze River Delta urban agglomeration.

Improving core cities’ radiation capacity will increase their spatial spillover effect and drive the development of the entire urban agglomeration more efficiently. The radiating role of central cities is mainly played through personnel flow and technical knowledge dissemination, which improve the technological level and innovation ability of surrounding cities and thus promote the efficient and orderly development of the entire urban agglomeration. Since the core cities of urban agglomerations frequently have a high level of economic development accompanied by high environmental regulations, many industries in the core cities are bound to shift to marginal cities with relatively backward economies, and the transfer of industrial structure will deepen the city-to-city carbon emission relationship [23]. At the same time, the urban population with low development levels around the urban agglomeration will gather in the core cities, and the core cities will continue to spread to the surrounding cities due to rising living costs and increasing economic pressure. The carbon emission link will be strengthened as a result of the personnel flow process. Using Shanghai as an example, the Yangtze River Delta urban agglomeration has experienced high urbanization and post-industrial development, and its population is nearing saturation, with little room for energy consumption reduction. Cities on the network’s outskirts, on the other hand, have a lot of room for growth in terms of economic development, population, and energy intensity. As a result of the law of diminishing marginal output, the faster the economy develops, the higher the cost of reducing carbon emissions. Hence, the carbon emission reduction effect obtained by the same input is different for cities with different economic levels; the economic development level is different; and the uneven distribution is also a major factor affecting the overall efficiency of carbon emissions. Feng Dong, for example, studied the coordinated emission reduction of the Beijing–Tianjin–Hebei urban agglomeration and stated that the government will shift some tertiary industries in Beijing to Hebei while also easing the population to cities in Hebei Province, which will not only improve the industrial structure of urban agglomerations, solve the problems of unbalanced development and a large population gap, but also promote the transformation of high-energy-consuming industries [23]. The influence of the radiation effect of the central city on regional carbon emission relationships is reflected through knowledge transmission, personnel flow, and industrial transfer. As a result, the following assumptions are advanced in this paper:

Hypothesis 7. 

The stronger the radiation capacity of central cities, the stronger the synergistic emission reduction effect.

3. Methodology

3.1. Measurement Model

Based on theoretical analysis and assumptions, this paper examines the impact of the Yangtze River Delta enterprise network’s spatial structure on carbon emission intensity and the coordinated emission reduction effect in 26 cities in the Yangtze River Delta urban agglomeration. To reduce heteroscedasticity, the related variables are treated logarithmically. During the data analysis process, the Hausman test was performed, and the results indicated that the fixed effect model should be chosen. According to Yu, J.K. (2020) [38], the double fixed effect of time is chosen for analysis in this paper, and the model is built as follows:

$$the \ln c{o}_2{n}_{it}={\alpha }_0+{\beta }_1\ln degre{e}_{it}+{\beta }_j\sum \ln contro{l}_{it}+{\mu }_i+{\delta }_t+{\epsilon }_{it}$$

(1)

This model studies the influence of three kinds of urban centrality on urban carbon emission intensity. where $c{o}_2{n}_{it}$ denotes the carbon intensity of city $i$ in year $t$. ${degree}_{it}$ denotes the centrality of city $i$ in year $t$, including degree centrality, closeness centrality, and betweenness centrality. ${control}_{it}$ denotes control variables including government intervention, total population at year-end, and GDP per capita, respectively, ${\mu }_i$ denotes individual effects, ${\delta }_t$ denotes time effects, and ${\epsilon }_{it}$ denotes random disturbance terms.

In order to study the influencing factors of collaborative emission reduction, this paper constructs the following model [38]:

$$\ln corrsh{n}_{it}={\alpha }_0+{\beta }_1\ln X_t+{\beta }_j\sum \ln contro{l}_{it}+{\mu }_i+{\delta }_t+{\epsilon }_{it}$$

(2)

In the above model, $corrsh{n}_{it}$ is the degree of carbon intensity synergy between city $i$ and Shanghai in year $t$. $X$ is the independent variable, including Shanghai’s point degree centrality as well as network density, network hierarchy, network efficiency, and average path length, which reflect the overall structure of the network.

Among them, the network density and network efficiency need to be maintained in a certain moderate range before they can have a positive impact on carbon emission reduction, so this paper adds the quadratic coefficient of two indicators, as shown in Formula (3), and the formula is explained as above [38].

$$the \ln corrsh n_{it}={\alpha }_0+{\beta }_1\ln X_t+{\beta }_1\ln X_t^2+{\beta }_j\sum \ln contro{l}_{it}+{\mu }_i+{\delta }_t+{\epsilon }_{it}$$

(3)

3.2. Methods and Data

The social network analysis method is used in this paper to examine the urban network correlation pattern. Social network analysis is a sociological research method as well as a quantitative analysis method based on graph theory, mathematics, and other techniques [39], especially suitable for studying the social environment in which an individual is located [15]. From the perspective of its applicable research objects, the social network analysis method has a high degree of matching with the research on the position and functions of individual cities in the spatial structure of urban agglomerations. This paper employs the following analysis indices that can characterize the relationship between cities and urban agglomeration networks: centrality, network density, average path length, network hierarchy, and network efficiency. The fixed effect model is used after obtaining the network indicators to analyze the impact of each network indicator on carbon emissions and coordinated emission reduction.

An adjacency matrix of [26 × 26] is established in this paper based on 26 urban administrative units in the Yangtze River Delta urban agglomeration, with the city on the ordinate as the city where the sample enterprises’ listed companies are located and the city on the abscissa as the city where the sample enterprises’ affiliated enterprises are located. Exclude information where the headquarters and branches are in the same city. Add up all of the sample enterprises to get the multi-valued network adjacency matrix of the inter-city enterprise network.

The enterprise data is derived from the China stock market and accounting research database (CSMAR). This database contains all kinds of economic development data and enterprise data released by the Chinese government and enterprises, such as the city’s GDP, population, location, size, and affiliated enterprises of enterprises, etc., with strong data reliability. Xiao (2022) and Cao (2022) have made use of the basic information data of listed companies and the macroeconomic data in the CSMAR database, respectively, to study the impact of enterprises’ digital transformation on the share of labor income and the impact of the adjustment of local governments’ unemployment targets on the employment quality of enterprises [40,41]. The database provides effective support for relevant research. This paper selects a database of affiliated enterprises, and the basic files of listed companies and affiliated companies are merged to obtain the name and location of enterprises as well as the name and location of affiliated companies. The sample period runs from 2001 to 2019, with a total of 26,058 samples. Data on carbon emissions is provided by the China Carbon Accounting Database, and other variables are provided by the CSMAR Macroeconomic Database.

3.3. Variables

The variables in this paper are divided into two categories. One is the variable describing urban characteristics, including urban size, urban development level, industrial structure, and government intervention. The size of a city is represented by its population [42]. According to the research of Zhang H. [43], compared with GDP, per capita GDP can better reflect the impact of urban economic development levels on carbon emissions. Therefore, this paper chooses GDP per capita to represent the urban development level. China’s economy is more dependent on secondary industries, which are energy- and carbon-intensive [44,45], which is the main source of carbon emissions. The larger the proportion of tertiary industry, the more optimized the industrial structure. Thus, in this paper, the ratio of secondary and tertiary industries [45] is used to characterize the industrial structure. Government intervention refers to the influence of government actions on economic development. According to Lu Z. et al., the level of fiscal expenditure directly reflects the number of various resources available to local governments and thus determines the extent to which government departments can provide support for local industrial development [46]. Thus, this paper uses the ratio of local fiscal expenditure to GDP to measure the level of government intervention [47]. Another type of variable is one describing the characteristics of the spatial structure of the network, including network density, network hierarchy, network efficiency, network distance, degree centrality, betweenness centrality, and closeness centrality.

Network density: the ratio of the actual number of associations in the network to the maximum possible number of associations; it reflects the correlation strength of each node in the network and is often used to study the correlation strength of information and material among network nodes [48].

Network hierarchy reflects the degree of differentiation of city status in the network, and the calculation method is shown in Formula (4), where $P$ is the logarithm of symmetrically accessible points in the network and $max\left(P\right)$ refers to the maximum possible logarithm of symmetrically accessible points.

$$H=1-P/max\left(P\right)$$

(4)

Network efficiency is a measure of the degree to which the number of redundant relationships in a spatially associated network degrades the network’s stability [49]. Network efficiency refers to the effective correlation efficiency between cities, and the calculation method is shown in Formula (5), where $N$ is the redundant correlation number between cities in the network and $max\left(N\right)$ refers to the maximum redundant correlation number between cities in the network.

$$E=1-N/max\left(N\right)$$

(5)

Network distance is expressed by the average path length, and the calculation method is as shown in Formula (6), where $d_{ij}$ represents the shortest path from city $i$ to city $j$.

$$D=\frac{2}{n\left(n-1\right)}\sum d_{ij}$$

(6)

Degree centrality measures the degree to which a node city is at the center of the urban agglomeration network structure. The higher the value, the higher the centrality of the city and the more connections it has with other cities. The calculation method is shown in Formula (7), where $X_{ij}$ is the correlation number between the city $i$ and $j$.

$$C_D\left(i\right)={{\displaystyle \sum }}_{j=1}^i{X}_{ij}$$

(7)

Betweenness centrality measures the intermediary position of a city in the network structure and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest [50]. A higher value indicates that the city is better able to control the carbon emission synergy of other cities. The calculation method is shown in Formula (8), where $s_{jk}$ is the shortcut correlation number between $i$ and $j$.

$$C_D\left(i\right)={{\displaystyle \sum }}_j^n{{\displaystyle \sum }}_k^n\frac{s_{jk}\left(i\right)}{s_{jk}}$$

(8)

Closeness centrality: In network structure, proximity centrality is an indicator of the difficulty of connecting cities [51]. The calculation method is shown in Formula (9), which $d\left(i,j\right)$ indicates the connecting distance between $i$ and $j$.

$$C_D\left(i\right)={\left[{{\displaystyle \sum }}_{j=1}^{n}d\left(i,j\right)\right]}^{-1}$$

(9)

In this paper, enterprise correlation data is used to build a city correlation network, which can offset the lack of actual correlation of carbon emissions between cities when the city correlation network is constructed simply by means of transportation [52] and a gravity model [12]. Meanwhile, urban factors such as city size, city development level, industrial structure, and government intervention are introduced into the regression model. The comprehensive influence of urban factors and city correlation network connections on collaborative emission reduction was analyzed so that the model could reflect the real state of the spatial network on carbon emission intensity and emission reduction coordination degree under specific urban conditions as much as possible.

Synergy: The degree of synergy represents the ability of cities to cooperate in collaborative emission reduction. Relevant research shows that only when the cities with low emission levels are used as the inflow places of factors and the cities with high emission levels are used as the export places of factors, the synergistic emission reduction effect may occur [23,53]. There is a synergistic emission reduction effect when the carbon emission intensity changes in the same direction and in a similar range between the cities where the factors flow and other cities. Generally speaking, the higher the centrality, the more likely it is to become an inflow point for factors. For the Yangtze River Delta urban agglomeration, Shanghai has been in first place in terms of degree centrality, betweenness centrality, and closeness centrality since 2001, and it is the main inflow city for various elements. Therefore, Shanghai is regarded as a benchmark city to measure the carbon emission reduction synergy of the Yangtze River Delta urban agglomeration. Drawing on the research method of Feng Dong (2020), the formula is as follows [54]:

$$synsh{n}_{it}=1-\frac{1}{2}{\left[\frac{\left(c_{st}-\overline{c_s}\right)}{\sqrt{\frac{1}{t}{{\displaystyle \sum }}_1^t{\left(c_{st}-\overline{c_s}\right)}^2}}-\frac{\left(c_{it}-\overline{c_i}\right)}{\sqrt{\frac{1}{t}{{\displaystyle \sum }}_1^t{\left(c_{it}-\overline{c_i}\right)}^2}}\right]}^2$$

(10)

Among them, $synsh{n}_{it}$ refers to the carbon emission synergy between the city $i$ and Shanghai in $t$, $c_{st}$ refers to the carbon emission intensity of Shanghai in $t$, $\overline{c_s }$ refers to the average carbon emission intensity of Shanghai, $c_{it}$ refers to the carbon emission intensity of the city $i$ in $t$ and $\overline{c_i}$ refers to the average carbon emission intensity of the city $i$.

4. Results and Discussion

4.1. The Changes of Enterprise Network Spatial Structure in Yangtze River Delta Urban Agglomeration

From 2001 to 2009, as shown in Figure 1, the correlation quantity and correlation intensity of each node city in the spatial network of the Yangtze River Delta urban agglomeration showed an increasing trend. The Yangtze River Delta urban agglomeration, on the other hand, shows a trend of marginalization, with more and more connections concentrated in central cities such as Shanghai, Nanjing, and Hangzhou, while connectivity between surrounding cities such as Chuzhou, Taizhou, Anqing, and Xuancheng is low, and they only accept central city connections in one direction, lacking city interaction. From the perspective of the overall network structure, a large number of network connections are concentrated between Shanghai and other provincial capitals with higher administrative levels. The participation of edge cities in the coordinated development of urban agglomeration is low, and the polarization of node-city centrality is obvious. Strengthening the effective correlation between edge cities, central cities, and sub-central cities is a key issue that the government should pay attention to in the macro-control of urban agglomeration development strategy.

From 2001 to 2019, Figure 2 depicts the spatial network of enterprise associations in the Yangtze River Delta urban agglomeration. According to the image, network density has shown a significant upward trend overall, particularly around 2014. Network density has accelerated and has a continuous upward trend. This demonstrates that in the Yangtze River Delta urban agglomeration, economic ties between cities are becoming increasingly close, and the degree of closeness is increasing over time. On the one hand, it provides a favorable external environment for collaborative emission reduction; on the other hand, the high network density will increase the number of redundant lines in the network, raising costs, decreasing factor utilization efficiency, and having a negative impact on collaborative emission reduction. The network hierarchy fell from 0.69 in 2001 to around 0.25 in 2004, after which it stabilized. Based on relevant studies, the network hierarchy of the Yangtze River Delta urban agglomeration is reduced from a high level to a low level [55], which indicates that the degree of differentiation of cities in the Yangtze River Delta urban agglomeration is gradually reduced, the development gap between cities is decreasing, and the promoting effect of urban agglomeration development strategy on regional coordinated development begins to emerge. The network efficiency decreases slowly and does not show a stable trend, which indicates that the redundant correlation among the nodes of the spatial network is constantly increasing, the correlation relationships within the Yangtze River Delta urban agglomeration are constantly strengthening and increasing, and the Yangtze River Delta urban agglomeration is still in the process of development and improvement. Overall, the average path length shows a downward trend, indicating that city accessibility is gradually improving and the degree of separation between cities is decreasing. This fully demonstrates China’s urban networks’ high spatial organization efficiency and transmission efficiency.

Figure 3a–c shows cities’ degree centrality in 2001, 2010, and 2019, respectively, to show the changing trend of cities’ degree centrality. It can be seen that the degree of centrality of most of the cities in the Yangtze River Delta urban agglomeration increased, especially the ones close to Shanghai. As for the trend of centrality changes in individual cities, this article selected 2001, 2010, and 2019 as representative years to draw centrality maps in order to more clearly display the network status of different cities in that year and the trend of changes over the past nineteen years. From the perspective of urban agglomeration as a whole, Shanghai has ranked first in terms of centrality since 2001, with strong connections and influence with other cities. Over time, the centrality of all cities has improved, but only the cities around Shanghai and along the Yangtze River have developed rapidly and strengthened connections, while the improvement in the centrality of other cities is not significant. This indicates that the radiating driving effect of central cities on surrounding cities is limited by the spatial distance between central cities and edge cities, as well as whether there are convenient transportation links between them. This is what policy-oriented urban agglomerations should focus on when determining their scope and scale and selecting central cities.

This indicates that Shanghai has played a certain radiation role and may radiate along the Yangtze River, but its role in the surrounding cities of the urban agglomeration is limited. This article also uses the same method to demonstrate the trend of collaborative carbon emission reduction in the Yangtze River Delta. We can see from Figure 3d–f that, unlike centrality, the development trend of carbon emission synergy has fluctuated significantly. According to the selected three years, the synergy first increased and then decreased. At the same time, we can see that unlike the carbon emissions that change in the same direction as the city’s centrality, the magnitude of the carbon emissions synergy has little to do with the centrality of each city. Therefore, the research on carbon emission synergy should be viewed from the perspective of the overall network structure of urban agglomerations and the centrality of core cities.

Figure 4 gives a closer look at the development trend of the carbon emission reduction synergy degree. It shows the average value of carbon emission reduction synergy degree and Shanghai’s degree centrality from 2001 to 2019. It can be seen from Figure 4 that, from 2004 to 2009, the average value of carbon emission reduction synergy fluctuated greatly, with a downward trend. The trend of average carbon emission synergy is consistent with that of Shanghai’s point centrality. The degree of synergy increased from 2009 to 2014 and then decreased after 2014. This trend is consistent with the increase in the number of intercity connections characterized by network density and network efficiency, as shown in Figure 2.

The centrality of Shanghai varies greatly, but the overall trend is upward. Since 2000, Shanghai has implemented a series of industrial structure changes aimed at reducing quantity while increasing quality [56]. The cooperative relationship between Shanghai as a central city and other cities in the urban agglomeration based on enterprise links has been broken and reorganized during the adjustment process, and the urban agglomeration’s synergistic emission reduction effect has fluctuated, but it has continued to rise and remains stable at a certain level after the establishment of the new cooperative relationship. This phenomenon also demonstrates that the synergistic emission reduction effect of urban agglomeration is heavily influenced by urban agglomeration development policy and is closely related to the city’s individual development state. The next part of the paper will analyze factors that influence cities’ carbon emission intensity and carbon emission reduction synergy degree, correlation matrix of all the variables used in the models are shown in

Table 1. Correlation matrix.

	Degree Centrality	Closeness Centrality	Betweenness Centrality	Network Hierarchy	Network Efficiency	Network Dencity	Average Distance	Degree Centrality	Government Intervention	Size	Development	Industrial Structure
degree centrality	1
closeness centrality	0.7246	1
betweenness centrality	0.5957	0.1765	1
network hierarchy	−0.2529	−0.3954	0.0973	1
network efficiency	−0.5313	−0.6929	0.1344	0.4835	1
network dencity	0.5265	0.7361	−0.1319	−0.4726	−0.9887	1
averagedistance	−0.4844	−0.6614	0.1212	0.2106	0.9135	−0.919	1
shdegree centrality	0.4673	0.7093	−0.1316	−0.3776	−0.885	0.8652	−0.8761	1
government intervention	0.1428	0.3419	0.0855	−0.1975	−0.4244	0.4262	−0.4015	0.4376	1
size	0.4574	0.1873	0.5829	0.0183	−0.0125	0.0036	−0.0127	−0.0039	0.0566	1
development	0.6813	0.7125	0.0854	−0.3328	−0.7148	0.7129	−0.6646	0.6653	0.0491	0.1715	1
industrial structure	−0.4855	−0.3749	−0.3231	0.1378	0.3896	−0.3905	0.366	−0.2867	−0.2282	−0.4405	−0.4281	1

.

4.2. The Influence of the Centralities of Enterprise Network Spatial Structure on Carbon Emissions in the Yangtze River Delta Urban Agglomeration

Based on assumptions 1–3 and using carbon emission intensity as an independent variable, the relationship between centrality and carbon emission intensity is investigated using the fixed effect analysis method, and the results are shown in

Table 2. Fixed effect analysis of influencing factors of carbon emission.

	Variable	Model 1	Model 2	Model 3
independent variable	degree centrality	−0.0677 ***	——	——
	closeness centrality	——	−0.0592 **	——
	betweenness centrality	——	——	−0.0861
control variable	government intervention	−0.00562 ***	−0.00501 ***	−0.00602 ***
	size	−0.033 ***	−0.0362 ***	−0.0397 ***
	development	−0.0000434 ***	−0.0000365 **	−0.0000645 ***
	industrial structure	0.059005 ***	0.06387 ***	0.063467 ***
	_cons	0.039002 ***	0.0395916 ***	0.0412265 ***
	R	0.5413	0.5356	0.2097
	Prob > F	0.0000	0.0000	0.0000

Number of observations = 560; ** p < 0.05; *** p < 0.01.

.

As shown in Table 2, there is a significant negative correlation between urban degree centrality and carbon emission intensity, implying that the greater a city’s degree centrality, the lower its carbon emission intensity. In other words, when both carbon emissions and GDP increase, the growth rate of carbon emissions is lower in cities with a higher degree of centrality. The result is in line with Hypothesis 1. This is due to the city’s numerous direct connections with other cities, strong influence over other cities and control over resource flow between cities, rapid economic development, and strong access to resources required for low-carbon development. This result is consistent with Zheng and Ye (2022): the higher the centrality of a city, the closer it is connected to other cities, the fewer obstacles it has to engage in low-carbon development and communication with other cities, the lower the cost of resource flow, and the more low-carbon capital it possesses, as well as the talent resources needed for technological innovation, the more it can reduce carbon emissions and accelerate economic development [36]. As a result, increasing the degree of centrality promotes economic growth in the city while decreasing the growth rate of carbon emissions and lowering their intensity. Similarly, there is a significant negative correlation between closeness centrality and carbon emission intensity, indicating that increased factor mobility aids in slowing the rate of carbon emission growth and lowering carbon emission intensity. The result of betweenness centrality is insignificant, indicating that it has little influence on carbon emissions.

From the perspective of carbon emission reduction in urban agglomerations, the increase in the number of connections between cities and other cities and the reduction of the difficulty of achieving effective connections can significantly reduce the carbon emission intensity, and the interaction terms between the two also show an obvious negative correlation with the carbon emission intensity (p < 0.01). In view of this, the establishment of extensive connections between cities from the perspectives of enterprises, population, science and technology, culture, and other aspects, and the facilitation of effective connections between cities through the construction of rapid transportation and information networks and science and technology cooperation mechanisms and platforms [1], can provide support for science and technology, talent, facilities, and funds for carbon emission reduction, so as to reduce carbon emission intensity.

4.3. The Influence of Enterprise Network Spatial Structure on Coordinated Emission Reduction of Urban Agglomerations

Taking the indicators of the overall network structure as independent variables and the carbon emission reduction synergy as dependent variables, Assumption 4–7 investigates the relationship between the indicators of the overall network structure and the carbon emission reduction synergy using the fixed effect analysis method, with the results shown in

Table 3. Fixed effect analysis of influencing factors of carbon emission synergy degree.

Variable	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10
shdegree centrality	0.0138855 ***	——	——	——	——	——	——
network dencity	——	0.708898 *	5.239875 ***	——	——	——	——
network dencity 2	——	——	−6.774384 ***	——	——	——	——
network hierarchy	——	——	——	−0.5097718 ***	——	——	——
network efficiency	——	——	——	——	−0.8478781 ***	4.591697 ***	——
network efficiency 2	——	——	——	——	——	−4.704012 ***	——
averagedistance	——	——	——	——	——		−0.1538672
government intervention	0.0002054 ***	0.00031 ***	0.0001279	0.000353 ***	0.0002634 ***	0.000093	0.0003419 ***
size	0.0007068 *	0.000889 **	0.0006216	0.000979 **	0.0007846 **	0.000511	0.0009481 **
development	−0.00000344 ***	−0.00000207 **	−0.00000393 ***	−0.00000136 **	−0.00000282 ***	−0.00000429 ***	−0.00000137 *
industrial structure	−0.0942591	−0.0558	−0.0476944	−0.10295 *	−0.0277724	−0.054592	−0.0811333
_cons	−0.6257002 **	0.047239	−0.118866	0.27831	0.8980362 ***	−0.0821504	0.4303291
R	0.2097	0.1651	0.1962	0.1863	0.1778	0.2297	0.1615
Prob > F	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

Number of observations = 560; * p < 0.1; ** p < 0.05; *** p < 0.01; network dencity ² indicates squared value of network density; network efficiency ² indicates squared value of network efficiency.

.

The spatial network indexes associated with enterprises, according to Table 3, have a significant impact on the synergistic effect of carbon emission reduction. According to Model 4, the correlation coefficient between Shanghai’s centrality as a core city and the synergy of carbon emission reduction is 0.0138, which is significantly positive and supports Hypothesis 4. The higher the centrality of enterprise networks in urban agglomerations, the more opportunities there are for communication with other related enterprises, the closer the relationship, and the greater the radiation and influence scope of enterprises, which is more conducive to the formation of economies of scale, the improvement of technical level, and the improvement of resource utilization. As a result, as the centrality of core cities increases, so do their rights and status and their radiation-driven ability, which has played a positive role in coordinated emission reduction through technology spillover and industrial transfer. This radiative driving effect is also reflected in the collaborative innovation and promotion of renewable energy utilization technology [57] and performance improvement technology for renewable energy equipment [58], which can directly reduce the consumption of fossil fuels within urban agglomerations, thereby promoting the reduction of carbon emissions.

The effect of network density on coordinated emission reduction is inverted U-shaped, as shown by models 5 and 6. In order to verify the accuracy of an inverted U-shaped curve, the u-test was adopted to test the results. The test results passed and showed the extreme point as 0.39. As time passes, network density increases, and more and more cities in urban agglomerations participate in urban agglomeration economic interaction, which plays a positive role in coordinated emission reduction. The increase in network density helps to limit and narrow the spatial differences between cities in the network, but when the network density exceeds 0.39, the correlation between network density and carbon emission reduction becomes negative. It demonstrates that network density has surpassed the optimal range and that there are numerous redundant connections. The majority of city connections are concentrated in core cities, and the differences in economic relevance between cities are gradually increasing. This result is in line with previous studies. Fan and Ma 2022 find out that redundant connections between core cities have had a negative impact on the flow of factors, information transmission, and resource efficiency, affecting industrial optimization and transfer, increasing regional differences, slowing the process of regional integration, and negatively impacting coordinated emission reduction [59]. Wang et al. (2022) discovered that cities are too closely connected and have structural imbalances. Cities such as Shanghai, Nanjing, Suzhou, and Wuxi have long been dominant, resulting in a regional network of connections centered around Shanghai [55]. At the same time, the network density inflection point is 0.39, indicating that the network is not a very tight network form, the network structure is relatively loose, many peripheral cities have not fully participated in economic interaction, and spatial cooperation and economic relations between cities need to be strengthened. Wang Xiaoping et al. believe that the spatial distance between cities is negatively correlated with the degree of carbon emission coordination [52]. In the case of fixed distances between cities, reducing the time and cost of intercity connections [1] is an effective way to strengthen urban connections and improve the degree of carbon emission coordination, which can be promoted by the construction of a rapid transit network.

The network hierarchy’s decline has gradually broken the hierarchical structure among cities in the network, which means that cities with lower subordinate and marginal status will have more right to speak, and mutual influence between cities will gradually increase. The potential difference that can form factor flow between cities is decreasing, and factor flow between cities is slowing down. As a result, it has a negative effect on coordinated emission reduction. In the context of urban development rights, the improvement of the network level of urban agglomerations cannot be achieved by inhibiting the development of some cities. Differentiated development becomes an effective way to provide network level in multiple dimensions, which is often accompanied by the adjustment of urban industrial structure and the formation of inter-city division of labor and cooperation [60]. The average path length of model 7 is negative, indicating that city accessibility is gradually improving and the degree of separation between cities is decreasing, which has a positive effect on coordinated emission reduction but is not significant. The reason for this is that an analysis of city accessibility based on enterprise-related data ignores the multiple effects of passive loss and active enhancement in the process of factor flow between enterprises.

According to models 8 and 9, there is an inverted U-shaped relationship between network efficiency and carbon emission reduction synergy; that is, carbon emission reduction synergy increases with the decrease of network efficiency and decreases with the decrease of network efficiency after reaching an extreme value, which is 0.48 according to the calculated results. According to the development trend of spatial network efficiency in the Yangtze River Delta urban agglomeration (Figure 1), the network efficiency reached 0.42 in 2019, and there was a negative correlation between network efficiency and carbon emission reduction synergy. The network efficiency is defined by the redundant association of spatial network nodes; that is, the redundant association among node cities in the Yangtze River Delta urban agglomeration is at a high level. Combined with the calculation results of network density, it can be seen that, as one of the correlation types between cities, redundant correlation can balance the obstacles of some emergencies to the effective correlation between cities in the early stage of the formation of the network, so that the inter-city correlation network is always in a state that guarantees the free flow of elements; that is, the network structure is more stable. However, with the increase in the number of redundant correlations, the contribution degree of redundant correlation to network stability is lower than its hindrance degree to inter-network factor flow efficiency, and network efficiency begins to have a negative impact on the carbon reduction synergy degree.

From the perspective of the green development of urban agglomerations, the stability of the spatial network can be improved by increasing redundant correlation at the initial stage of its formation. For example, homogeneity of industrial development between cities is allowed instead of explicit division of labor and cooperation. It is easier for homogenous enterprises to generate cognitive and technological identities, which are more conducive to the establishment of scientific and technological cooperation networks [61], which then increases the number of network connections and improves network stability. On the other hand, it also contributes to the accumulation of the original capital of cities, thus forming the economic basis for the coordinated development of carbon emission reduction in urban agglomerations. When the redundant correlation of urban agglomerations exceeds the extreme value in the late stage of urban agglomeration development, the industrial structure of urban agglomerations should be adjusted and some repetitive industries should be transferred to peripheral cities or cities outside the urban agglomerations to reduce the redundant correlation of the urban agglomeration network and improve the efficiency of the urban agglomeration spatial network and the degree of cooperation in carbon emission reduction.

5. Conclusions

This paper uses the relevant data of enterprises that hold huge resource allocation rights and are also the main source of energy consumption and carbon emissions to build an inter-city enterprise association network, avoiding the disadvantage that the gravity model cannot study the actual links between cities. This article analyzes the evolution process of urban agglomeration network structure through enterprise data over the past twenty years and combines social network analysis methods and fixed effects models to identify the influencing factors of carbon emissions and collaborative emission reduction based on inter-city connections.

The regression results indicate that the centrality of individual cities has a significant negative correlation with the intensity of urban carbon emissions, with a coefficient of −0.067. The centrality of core cities has a significant positive impact on the collaborative emission reduction of urban agglomerations, with a coefficient of 0.0138. The greater the centrality of cities in urban agglomerations, including core cities, the lower the intensity of urban agglomeration carbon emissions. This is contrary to the single-center development strategy adopted by the vast urban agglomerations in China. The single-center urban agglomeration structure may rapidly improve the economic development level of urban agglomerations, but it is not conducive to coordinated emission reduction. In future urban agglomeration development policies and planning, more cities should be positioned as sub-regional centers, and priority should be given to the development of infrastructure, development land, and industrial support so that the centrality of more cities can be effectively improved and the network hierarchy can be lowered, reducing the carbon emission intensity of urban agglomeration and promoting carbon emission reduction synergy.

The research results show that there is a strong relationship between regional development and carbon emission reduction. Carbon emissions reduction is not only influenced by factors such as the economic development of the city but is also closely related to the connections between other surrounding cities, especially economic connections. The impact of network density on the collaborative emission reduction of urban agglomerations shows an inverted U-shaped curve. The spatial network density and network efficiency of urban agglomerations are related through the redundant correlation between cities. The effective correlation between cities is coupled, and a new correlation relationship is generated, which becomes the redundant correlation. There is a problem of excessive concentration of enterprises and redundant connections in the Yangtze River Delta urban agglomeration. The redundant correlation between cities can improve the network density and reduce the network efficiency of the spatial network, which has a dual effect on the degree of cooperation in carbon emission reduction in urban agglomerations. On the one hand, in the initial stage of urban agglomeration construction, redundant correlation can enhance the synergy degree of carbon emission reduction by improving the stability of the network; on the other hand, when the network structure of urban agglomeration becomes mature, the synergistic effect of carbon emission reduction will be affected by the negative effect on the network efficiency. The development and construction of urban agglomerations can be based on this dual role, and different redundancy and correlation treatment measures can be adopted at different development stages to ensure the synergistic effect of carbon emissions in urban agglomerations.