Chinese Urban Carbon Emission Correlation Network: Construction, Structural Characteristics, and Driving Factors

Abstract

Against the backdrop of carbon reduction and sustainable development, cities play a central role in carbon emissions. These emissions are interconnected through economic, demographic, technological, and other factors, forming a complex network. This study investigates the structural characteristics and driving factors of carbon emission linkages among Chinese cities, with the aim of providing theoretical support and practical guidance for the development of sound regional carbon reduction policies. An improved gravity model was used to measure both the presence and intensity of linkages between cities. Social Network Analysis (SNA) was applied to examine network features such as density, centrality, and hierarchical structure. In addition, the Quadratic Assignment Procedure (QAP) was employed to test the effects of geographical proximity, economic disparities, demographic differences, and technological gaps on carbon emission linkages. Based on these methods, the study constructs the Chinese Carbon Emission Correlation Network (CECN), which shows high connectivity, a clear hierarchical structure, and a strengthened role of core cities. Cities with extensive linkages are mainly located in the eastern coastal region and political centers, forming a spatial pattern with stronger connections in the east than in the west, and more along the coast than inland. The network can also be divided into five distinct sub-groups. Moreover, geographical proximity, population differences, economic affluence, and technological disparities were found to significantly shape the spatial correlation of carbon emissions. These findings offer valuable guidance for designing targeted carbon reduction policies, which are essential for fostering regional coordination and advancing sustainable urban development.

1. Introduction

Climate change is a major global issue, driven mainly by emissions of greenhouse gases such as carbon dioxide. World Bank data show that China has been the largest carbon emitter since 2006, accounting for about 28% of global emissions [1,2]. In response, the nation committed to peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060 [3]. The government explicitly emphasizes the need to actively and prudently advance carbon peaking and carbon neutrality, considering the country’s unique energy and resource endowments. Following the principle of establishing before breaking, the country outlined a planned and stepwise pathway for carbon peaking. This strategic deployment indicates that the green and low-carbon transition has entered a new stage of systematic advancement. In recent years, notable progress has been made in advancing the green transition; however, the overall development pattern remains uneven. Despite multiple government measures to mitigate climate change, reliance on resource-intensive production and fossil fuels remains substantial, creating significant obstacles to rapid short-term emission reductions [4]. At the same time, an inverse spatial agglomeration between economic activity and carbon emissions has emerged, with both emission intensity and total emissions shifting to less developed regions, thereby exacerbating regional environmental inequality. In this context, an in-depth examination of China’s carbon emissions is particularly critical. Such research not only provides robust data support for more targeted and effective mitigation policies, but also contributes to advancing green and low-carbon development in China and worldwide.

China’s carbon emissions show pronounced spatial heterogeneity, largely driven by regional disparities in economic structure, industrial composition, and energy consumption patterns [5]. To better understand the interregional interaction mechanisms of carbon emissions, scholars have increasingly examined their spatial correlation effects. In early research, input–output modeling frameworks were widely applied to study interregional carbon transfer [6,7], carbon leakage [8,9], and embodied carbon emissions [10,11,12], providing important insights into the allocation of interregional carbon responsibilities. However, compiling China’s input–output tables is time-consuming, coarse in resolution, and heavily reliant on sectoral averages, making it difficult to capture intra-industry differences. This limitation may introduce estimation biases and hinder accurate representation of the spatial distribution of carbon emissions. To address these shortcomings, subsequent studies employed spatial econometric models to analyze the spillover effects of carbon emissions and their determinants [13,14,15]. This approach allows for the consideration of spatial dependence while identifying the region-specific drivers of carbon emissions, thereby providing quantitative support for policy design. Nonetheless, such analyses typically rely on spatial adjacency or distance-based weight matrices, which insufficiently capture actual interregional interactions, and fail to reflect the overall structural characteristics of regional linkages [16,17]. Meanwhile, exploratory spatial analysis methods have been widely applied. Using indicators such as the Theil index, Theil coefficient, and coefficient of variation, researchers have revealed regional disparities and spatial agglomeration patterns of carbon emissions at national, provincial, and urban scales [18,19,20,21,22,23,24,25]. Findings suggest that carbon emissions spread across regions via mechanisms such as atmospheric circulation, trade exchanges, and industrial transfer, thereby exhibiting strong spatial correlation and spillover effects. However, most of these studies have primarily analyzed attribute data of carbon emissions, neglecting the advantages of relational data in identifying spatial linkages. Against this backdrop, SNA has been increasingly applied in carbon emission research because of its strengths in characterizing network structures, node relationships, and transmission pathways. Some scholars have constructed spatial correlation networks of carbon emissions to identify interregional linkages, core nodes, and sub-group structures [26,27,28,29]. Early network studies relied on input–output models [30,31,32]; however, their limited timeliness prompted more scholars to adopt gravity models for constructing spatial correlation networks of carbon emissions [33,34,35]. This method provides a flexible analytical framework and enables network analysis from both global and individual perspectives [36,37,38]. Moreover, some scholars have used block models and the Rand-ESU algorithm to further explore internal clustering structures [39,40]. In addition, other studies have examined the determinants and effects of the spatial correlation networks of carbon emissions. For example, panel data models have been applied to assess how attributes such as network structure, population size, and energy structure influence carbon emissions [41,42,43]. Meanwhile, QAP has been employed to investigate the formation mechanisms of carbon emission networks in terms of relational variables such as energy intensity, industrial structure, and technological level [27,29,44].

Existing research has largely focused on the provincial level, with limited systematic investigation of city-level carbon emission networks. Moreover, the few studies conducted at the urban scale typically focus on specific city clusters, making it difficult to provide a comprehensive picture of spatial interactions among cities nationwide. Consequently, the lack of in-depth research on city-level carbon emission networks constrains understanding of fine-grained spatial interaction mechanisms, and hinders the development of more targeted emission reduction policies.

Building upon the above research background and literature review, it is evident that the structural characteristics and driving factors of China’s city-level carbon emission linkages remain insufficiently studied. To fill this gap, this study addresses two core questions: (1) What is the structure of intercity carbon emission linkages in China? (2) What factors shape the spatial association strength of carbon emissions among cities?

This study aimed to systematically identify the structural characteristics and driving factors of city-level carbon emission linkages in China, providing both theoretical foundations and practical guidance for the scientific design of urban carbon reduction policies. To achieve these objectives, an improved gravity model was applied to quantify intercity carbon emission linkages and their intensity. SNA is employed to assess the density, centrality, and hierarchical structure of the carbon emission network. In addition, QAP regression was used to investigate how geographical, demographic, economic, and technological differences influence the formation of intercity carbon emission linkages. The results show that China’s CECN is highly connected and exhibits a clear hierarchical structure, with core cities occupying dominant positions. Cities with extensive carbon emission linkages are mainly concentrated in the eastern coastal region and political centers. This pattern reflects significant regional disparities, characterized by stronger linkages in the east than in the west, and in coastal areas compared to inland regions. Moreover, geographical proximity, population size, economic development, and technological differences significantly influence the spatial associations of carbon emissions. This study deepens theoretical understanding of spatial interactions in carbon emissions and provides critical evidence for designing regional collaborative emission reduction policies. The main contributions of this study are twofold: (1) it applies an improved gravity model to construct a nationwide spatial correlation network of carbon emissions across 284 cities, thereby overcoming the limitation of prior studies that focused mainly on provincial units. This approach provides a more detailed view of the spatial coupling relationships and network structures of intercity carbon emissions. (2) It also introduces QAP regression, which effectively addresses multicollinearity among variables and thereby improves the precision and robustness of factor analysis. This method allows for a deeper exploration of the mechanisms driving the formation of spatial linkages in carbon emissions.

The remainder of this paper is organized as follows. Section 2 provides a literature review and presents the research hypotheses. Section 3 introduces the data sources and the construction of the CECN based on the gravity model. Section 4 analyzes the structural characteristics of the CECN and its driving factors. The final section summarizes the key findings and offers policy implications.

2. Literature Review and Research Hypotheses

In the process of analyzing the spatial interaction mechanisms of carbon emissions across regions, scholars have gradually focused on the spatial correlation effects of carbon emissions. Existing studies have primarily concentrated on the topological characteristics of carbon emission networks, aiming to reveal the connections among regions. Yang et al. (2025) analyzed both global and individual network indicators, finding significant spatial interdependencies among provincial administrative regions [40]. The interactions of carbon emissions depend not only on direct inter-regional connections, but also on the overarching network structure [40]. Meng et al. (2025) proposed a model based on Global Average Structural Entropy (GASE) to evaluate the roles of different nodes within urban carbon emission networks, further revealing the complexity of inter-regional carbon emission networks [45]. In other studies within this field, some scholars have further refined the spatial structural characteristics of carbon emissions, particularly examining the spatial network features of different city clusters and regions. For example, Wang et al. (2018) analyzed the flows of carbon emissions among regions, revealing the network characteristics of carbon emissions in eastern, central, and western China [46]. Overall, most studies attempt to uncover the overall network characteristics of carbon emissions by measuring metrics such as hierarchy, efficiency, and density. However, these analyses often remain at the macro level, lacking in-depth exploration of the underlying regional mechanisms.

To comprehensively understand the formation mechanisms of spatial correlations in carbon emissions, recent studies have gradually shifted toward examining the endogenous and exogenous factors underlying these spatial linkages [47,48]. Existing studies generally suggest that regional economic development levels, differences in industrial structure, and variations in energy efficiency all influence the supply, demand, and flow of carbon emissions. For example, Lv et al. (2019) analyzed the impact of regional economic disparities on carbon emissions, proposing a close link between the efficient use of emissions in economically developed regions and the diffusion of emissions from less developed areas [1]. Xu et al. (2022) explored the effects of differences in energy structure on carbon emission transmission, noting that energy-intensive regions can intensify the spatial correlations of emissions through energy and technology flows [49].

However, existing literature still has limitations in explaining the mechanisms of spatial correlations in carbon emissions. First, most studies attribute spatial linkages to differences in regional attributes, such as economic development, population size, or energy efficiency. This approach overlooks the roles of geographic proximity, factor complementarity, and technology diffusion among cities, making it difficult to fully reveal the generation logic of carbon emission linkages. Second, current methods often rely on different matrices to measure inter-regional disparities; however, this approach only captures quantifiable “static gaps” and fails to reflect dynamic interactions such as geographic distance, population mobility, industrial relocation, and technological cooperation. Third, although a few studies have begun to focus on spatial networks within city clusters, they have not systematically compared the relative roles of different driving factors in shaping spatial carbon emission linkages. Therefore, it is necessary to build on existing research and further examine how external factors across different dimensions promote the formation and strengthening of spatial correlations in carbon emissions.

Geographical distance is a key factor influencing intercity socioeconomic interactions [50]. In the context of carbon emission spatial correlations, neighboring cities can exchange resources, labor, and technologies more conveniently and efficiently due to shorter physical distances. Lower costs of disseminating technology and production factors further strengthen intercity carbon emission linkages [51]. Furthermore, geographical proximity promotes the establishment of regional collaborative emission reduction mechanisms and policy coordination, thereby reinforcing the spatial correlations of carbon emissions [51]. Building on these theoretical and empirical insights, this study proposes the following hypotheses:

H1: 

The smaller the geographical distance between cities, the stronger the intensity of their carbon emission spatial correlation.

Beyond geographical proximity, differences in population size also influence the spatial distribution of carbon emissions. Cities with greater population disparities typically experience more frequent population flows, which foster economic exchanges and transportation activities. These processes increase energy consumption in sectors such as construction and transport, thereby intensifying intercity carbon emission linkages [52]. In addition, complementarities in labor markets and consumption patterns arising from population differences promote industrial collaboration and carbon emission flows across cities. Therefore, this study proposes the following hypothesis:

H2: 

The greater the population size difference between cities, the stronger the intensity of their carbon emission spatial correlation.

Economic disparities further contribute to the formation of intercity carbon emission linkages. In economically advanced cities, industrial upgrading and stricter environmental regulations often result in the relocation of high-carbon industries to less developed regions, thereby generating a spillover effect in carbon emissions [52]. Moreover, complex economic ties and industrial transfer between developed and less developed cities constitute a major driver of spatial carbon linkages [27]. Accordingly, this study proposes the following hypothesis:

H3: 

The greater the economic disparity between cities, the stronger the intensity of their carbon emission spatial correlation.

Finally, technological disparities also play a crucial role in shaping the spatial interactions of carbon emissions. Frequent exchanges and cooperation between technologically advanced and less advanced cities, together with the mobility of technical personnel and complementarity of production factors, facilitate technology diffusion and industrial collaboration, thereby strengthening intercity carbon emission linkages [53]. Moreover, technological disparities create opportunities for complementary advantages, fostering the development of cross-regional green industrial chains and innovation networks that further intensify the spatial coupling of carbon emissions. Hence, this study proposes the following hypothesis:

H4: 

The greater the technological disparity between cities, the stronger the intensity of their carbon emission spatial correlation.

3. Methodology and Data

3.1. Determination of the Spatial Correlation Network of Carbon Emissions

Social Network Analysis is a systematic analytical approach that evaluates the structural characteristics of complex relational networks through relationship data [54]. Establishing a spatial correlation matrix forms the foundation for constructing CECN. In existing literature, methods describing spatial correlations primarily include vector autoregressive models or gravity models [55,56,57]. However, vector autoregressive models are suitable for data spanning longer periods and are overly sensitive to lag-order selection, introducing errors in the spatial correlation of variables [18]. Analyzing spatial correlation networks using the gravity model allows not only for the measurement of overall spatial correlations within regions, but also the measurement of spatial carbon emission flow relationships among individual entities within regions, providing a better assessment of spatial correlations in carbon emissions [44]. In contrast to traditional gravity models that neglect bidirectionality and asymmetry in spatial correlations, this study employs an improved gravity model to construct a directed network of spatial correlations in carbon emissions among Chinese cities. To highlight the directional differences in carbon emission flows in practice [55,56,57], we introduce a directional carbon emission linkage intensity indicator $b_{ij}$ in the model, representing the strength of city $i$’s influence on city $j$’s carbon emissions, while allowing $b_{ij}$ ≠ $b_{j_i}$, thereby reflecting the directionality and asymmetry of carbon emission flows [58]. Specifically, the model constructs a directed network by separately calculating the carbon emission linkage intensity from city $i$ to city $j$ and from city $j$ to city $i$.

Based on this, the modified gravity model in this study is as follows:

$$X_{ij}=b_{ij}{\displaystyle \frac{\sqrt[3]{N_i{c}_i{G}_i}\sqrt[3]{N_j{c}_j{G}_j}}{{\left(\frac{E_{ij}}{a_i-a_j}\right)}^2}},b_{ij}={\displaystyle \frac{c_i}{c_i+c_j}}$$

(1)

In the above, $i$ and $j$ represent cities; $X_{ij}$ represents the carbon emission correlation intensity from city $i$ to city $j$ within various cities in China. The term $b_{ij}$ measures the relative share of emissions of city $i$ in its relationship with city $j$, reflecting city $i$’s proportion of total emissions between the two cities. It is used to assess the “contribution” or “relative importance” of city $i$ in the carbon emission spatial correlation between the two cities; $N$, $c$, $G$, and $a$ represent population size, carbon emissions, GDP, and per capita GDP, respectively; $E_{ij}$ is the geographical distance between city $i$ and city $j$. To simultaneously account for the impact of both economic and geographical distances on carbon emission spatial correlation, the “distance” between cities is determined by the ratio of the geographical distance ($E_{ij}$) to the GDP difference ($a_i-a_j$) between the cities [36].

Formula (1) allows for the computation of the gravity matrix capturing the spatial correlation effects of carbon emissions among various cities in China. Each element in this matrix corresponds to the correlation strength of carbon emissions between two specific cities [58]. However, in the actual network, not all gravity values indicate significant correlations. Therefore, the average value of the matrix is set as a threshold, and the gravity values are binarized to construct a directed, asymmetric binary adjacency matrix [39]. Values greater than or equal to the threshold are assigned a value of 1, indicating the presence of a spatial carbon emission correlation between the corresponding row and column cities. Otherwise, they are assigned a value of 0, indicating the absence of such a correlation. The diagonal elements are set to 0 by default, since carbon emissions cannot interact with themselves; therefore, no spatial correlation exists for a city with itself.

3.2. Characterization of Network Structure

This paper employs four indicators, namely network density, network hierarchy, network efficiency, and network connectedness, to depict the overall structural characteristics of the network. In addition, degree centrality and betweenness centrality are used to describe the structural roles of individual nodes within the network. The Louvain algorithm is applied for cluster analysis, dividing the CECN into several sub-groups. The functional roles of these sub-groups are then identified based on their interrelationships.

3.3. Network Formation Influencing Factors

Both the Quadratic Assignment Procedure (QAP) and multiple regression can be used to analyze how changes in one set of variables correspond to changes in another. A prerequisite for multiple regression analysis is that the explanatory variables are relatively independent. However, because the regression variables represent correlation matrices between cities, multicollinearity may occur. In addition, geographical proximity between cities may also affect the regression results. The QAP employs random permutations of matrix data to compare similarities between two square matrices, thereby assessing the relationships between the original matrices. Compared with multiple regression, QAP is more suitable for analyzing complex network data, such as social network and spatial correlation matrices. It effectively identifies relationship patterns in such networks and provides deeper insights into their structural characteristics.

Based on the above analysis, the model was developed as follows:

$$S=f(D,P,R,T)$$

(2)

In model (2), $S$ represents the carbon emission network relationships among Chinese cities. $D$ represents geographical distance, reflecting the degree of geographical proximity between cities; $P$ represents population differences, measuring the disparity in population size between cities; $R$ represents economic differences, indicating the gap in economic levels between cities; $T$ represents technological differences, reflecting the disparity in technological development between cities. These variables collectively influence the spatial correlation intensity of carbon emissions among city clusters.

In terms of variable measurement, geographical distance, $D$, is represented by whether cities are adjacent to each other, indicating the proximity of their physical locations. Population differences, $P$, are measured by the difference in the total population at the end of the year, calculated using a population disparity matrix. Economic differences, $R$, are represented by the disparity in per capita GDP, calculated through an economic difference matrix. Technological differences, $T$, are assessed using the difference in R&D expenditure, represented by an R&D disparity matrix. These measurements allow for a more precise understanding of how the various dimensions of intercity differences contribute to the spatial correlation of carbon emissions.

3.4. Data Sources

This study selects the period from 2010 to 2021 as the sample window. After accounting for changes in administrative boundaries and missing data, a final sample of 284 cities was selected. Carbon emission data for China’s prefecture-level cities were calculated using the methodology proposed by Cong Jianhui. This method clarifies the extent to which indirect emissions are incorporated into urban carbon accounting guidelines, and more explicitly defines the boundaries of urban carbon accounting. This accounting approach more accurately reflects the actual conditions of Chinese cities. Therefore, this study draws on the methodology adopted in China Population, Resources and Environment [40].

In 2024, China issued the Interim Regulations on the Management of Carbon Emissions Trading, which clarified the disclosure responsibilities of key greenhouse gas emitters. These emitters are required to publicly disclose annual greenhouse gas emission reports, including information on emission volume, emission facilities, and statistical accounting methods. They must also ensure the authenticity, completeness, and accuracy of the reported data. Relevant data were first collected from the China Energy Statistical Yearbook, the China Industrial Statistical Yearbook, and the China Agricultural Statistical Yearbook. Carbon emissions were then calculated using the latest classification system, covering Scope 1, Scope 2, and Scope 3 emissions. The specific accounting standards are outlined as follows:

Scope 1 includes all direct emissions within a city’s administrative boundaries. These primarily arise from transportation, building energy consumption, industrial processes, agriculture, forestry, land use change, and waste management.

Scope 2 covers indirect emissions from energy generated outside the city’s boundaries. These include emissions from externally purchased electricity, heating, and cooling to meet urban demand.

Scope 3 encompasses other indirect emissions from urban activities outside the administrative boundaries, excluding those in Scope 2. These include greenhouse gas emissions from the production, transportation, use, and disposal of goods imported into the city.

For the energy component, energy consumption data by energy type and sector were obtained from the China Energy Statistical Yearbook and statistical yearbooks at various levels. Data on industrial processes and product use were sourced from the China Industrial Statistical Yearbook and other statistical yearbooks. Data on agriculture, forestry, and other land use activities come from the China Agriculture Statistical Yearbook, China Animal Husbandry Yearbook, China Forestry and Grassland Statistical Yearbook, and other statistical yearbooks. Data on waste management are obtained from the China Environmental Statistical Yearbook and other statistical yearbooks. Data on purchased electricity, heating, and cooling are sourced from the China City Statistical Yearbook, the China Energy Statistical Yearbook, and other statistical yearbooks.

Emission factors are based on officially published data, specifically including the Guidelines for Provincial Greenhouse Gas Emission Inventories (Trial) and carbon emission inventory guidelines issued by governments at various levels.

The data for population, economy, technology, and related statistical indicators come from the statistical yearbooks of various provinces and cities.

4. Results and Discussion

4.1. Characterization of the Network

From 2011 to 2021, the Chinese Carbon Emission Correlation Network (CECN) was constructed using a modified gravity model. Figure 1 illustrates the CECN diagrams for 2011, 2016, and 2021. Spatially, carbon emission correlations exhibit a radial diffusion pattern, spreading outward from large cities and provincial capitals to surrounding areas. Core cities such as Beijing, Shanghai, and Shenzhen exert a radiation effect on nearby regions, driven by the agglomeration of industries and economic activities. Urbanization and industrial transfer often drive the outward expansion of carbon emissions from these central regions, reinforcing the spatial radiation effect. In addition, the spatial distribution of carbon emissions exhibits a clear hierarchical structure: linkages are denser among large cities and those in the eastern region, but relatively sparse among small- and medium-sized cities and those in the west. Finally, China’s carbon emissions demonstrate a spatial agglomeration effect. For instance, the Yangtze River Delta and Pearl River Delta, characterized by closely interconnected economies, also exhibit strong carbon emission linkages.

Next, this paper examines the characteristics of the CECN from three perspectives: overall network structure, individual network structure, and regional features, with the aim of uncovering patterns in carbon emission flows.

4.1.1. Characterization of the Overall Network Structure

Figure 2 presents the characteristic indicators of the overall CECN network. The connectedness remains relatively high, ranging from 0.9444 to 0.979, indicating that carbon emission interactions among cities are stable and that the spatial correlation pattern is well established. The hierarchy increased from 0.0215 in 2011 to 0.1081 in 2021, suggesting an enhanced leading role of core cities in the carbon emission network and intensified hierarchical differentiation. Efficiency fluctuates between 0.8763 and 0.8957, indicating that resource allocation efficiency remains stable despite the high level of connectedness. Density remains high, ranging from 0.965 to 0.971, showing that carbon emission correlations among cities have not declined significantly and that the network structure is dense and stable. Overall, the CECN exhibits high connectedness, a rising hierarchy, and a strengthened role of core cities.

4.1.2. Characterization of the Structure of Individual Networks

Figure 3 presents the degree centrality of cities within the CECN for 2011, 2016, and 2021, showing only the top ten cities. Degree centrality reflects the number of carbon emission linkages for each city in the network. Cities with higher degree centrality are predominantly concentrated in eastern coastal areas and political centers. Overall, the pattern can be summarized as “more in the east and less in the west, more along the coast and less inland”. Among them, Beijing, Shanghai, Shenzhen, Guangzhou, and Daqing exhibit particularly high numbers of carbon emission linkages. Possible explanations include the fact that Beijing, Shanghai, Shenzhen, and Guangzhou are economically developed, experience severe traffic congestion, and are undergoing rapid urbanization with substantial infrastructure construction. These factors contribute to increased carbon emissions, resulting in more extensive linkages. In contrast, the industrial structure of Daqing is primarily centered on fossil fuels. As one of China’s major oil-producing areas, Daqing hosts a large-scale oil industry, with significant carbon dioxide emissions generated during extraction, processing, and utilization.

Cities with relatively few carbon emission linkages are mainly concentrated in Lijiang, Xining, Lincang, and Pu’er. This is primarily because urbanization in these cities has progressed relatively slowly, and their industrial structures are dominated by low-carbon sectors such as tourism and agriculture. Compared with heavy and energy-intensive industries, these sectors generate relatively low levels of carbon emission linkages.

From 2011 to 2021, the total number of carbon emission linkages among Chinese cities fluctuated but overall exhibited a downward trend. A possible explanation is that cities have actively implemented carbon emission control policies, including the promotion of clean energy, improvements in energy efficiency, and strengthened emission supervision. These policies have reduced city-level carbon emissions, thereby lowering the number of carbon emission linkages between cities. In addition, with economic development, cities are undergoing structural transformation, with high-energy and high-emission industries gradually being replaced by low-carbon and environmentally friendly sectors.

Figure 4 shows the out-degree and in-degree centrality of cities in the CECN for 2011, 2016, and 2021, with only the top ten cities presented. Out-degree reflects the number of carbon emission outflow linkages, while in-degree reflects the number of inflow linkages for each city. Cities with relatively high outflow linkages include Beijing, Shanghai, and other major cities. A possible explanation is that these cities are among the most economically developed in China, hosting numerous large enterprises and industrial clusters. In addition, they typically have dense populations, high levels of urbanization, and relatively large per capita energy consumption. Population growth and accelerated urbanization often lead to traffic congestion and increased building energy use, thereby generating more carbon emission outflow than inflow linkages. By contrast, cities with relatively high inflow linkages include Daqing, Dongying, and similar cities. One reason is that some of these cities are important national energy bases, where extensive coal mining and thermal power generation result in higher carbon emission inflows than outflows. Furthermore, with economic development and industrial upgrading, these cities may absorb high-energy and high-emission industries relocated from core cities.

Figure 5 presents the betweenness centrality of cities within the CECN in 2011, 2016, and 2021 (only the top ten cities in terms of betweenness centrality are shown). The betweenness centrality mainly reflects to what extent a city is located “in the middle” of other “point pairs”, that is, the degree to which a city acts as a “bridge” between other cities in the CECN.

In the data of 2011, 2016, and 2021, the betweenness centrality of Shenzhen has remained at a relatively high level. This indicates that Shenzhen has been playing an important role in China’s Carbon Emission Correlation Network and is a core node connecting the carbon emission activities of other cities. The betweenness centrality of Beijing was not particularly prominent in 2016. However, by 2021, its betweenness centrality had increased significantly, ranking on a par with Shenzhen. This shows that the influence of Beijing in the carbon emission correlation network has been gradually enhanced, becoming a core city on a par with Shenzhen. Guangzhou has maintained a relatively high betweenness centrality in the data of all three years. Although it has fluctuated, it has always been among the top ten. This indicates that Guangzhou also plays an important role in the carbon emission correlation network and is an important node connecting other cities. Nanjing exhibited a relatively high betweenness centrality in the data of 2021, emerging as one of the newly rising cities with high betweenness centrality. This indicates that the status of Nanjing in the carbon emission correlation network has been gradually elevated, becoming an important bridge connecting other cities. Although the betweenness centrality of Shanghai has fluctuated in different years, it has remained at a relatively high level. As one of China’s economic centers, the role of Shanghai in the carbon emission correlation network cannot be ignored.

The data reveal that large cities with developed economies and dense populations occupy a dominant position in the carbon emission correlation network. Due to their intensive economic activities and high energy consumption, these cities exhibit higher betweenness centrality within the network.

4.1.3. Regional Characterization of the Network

The modularity of the CECN was calculated as 0.248 in 2011, 0.277 in 2016, and 0.284 in 2021. The modularity index measures the cohesion among nodes within a network and the degree of separation between different subnetworks. The observed values, ranging from 0.248 to 0.284, suggest the presence of some community structure. However, the overall structure remains relatively loose, and community divisions are not particularly distinct. In network science, modularity values of 0.3–0.7 are typically considered moderate to high, indicating a distinct community structure, whereas values close to zero suggest an absence of meaningful community organization. Compared with a typical random network, the CECN shows measurable but moderate levels of community organization. The gradual increase in modularity indicates that regional or subnetwork structures within the CECN have become more prominent, accompanied by a stronger regional clustering effect. This implies that the spatial distribution of carbon emissions is beginning to show more distinct regional characteristics, with emission patterns in different regions gradually developing stronger independence and internal connectivity.

The Louvain algorithm was applied to divide the sub-groups of the average network from 2011 to 2021, and the results are shown in Figure 6a. In addition, the sub-groups were visualized on a map of China, as presented in Figure 6b. The first sub-group is centered around Dongying, Hangzhou, Nanjing, Qingdao, and Hefei; the second sub-group is centered around Shenzhen, Guangzhou, Wuhan, and Changsha; the third sub-group is centered around Beijing, Chongqing, Chengdu, Xi’an, and Kunming; the fourth sub-group is centered around Harbin, Changchun, and Shenyang; the fifth sub-group is centered around Nanchang, Zhangzhou, and Huanggang.

The first sub-group is centered on cities including Dongying, Hangzhou, Nanjing, Qingdao, and Hefei, which collectively demonstrate a clustered spatial distribution. In the Yangtze River Delta, cities such as Nanjing, Hangzhou, Suzhou, Wuxi, Changzhou, Nantong, Yangzhou, Zhenjiang, Hefei, Wuhu, and Ma’anshan maintain strong economic linkages. Their coordinated industrial development has reached a high level, resulting in mature urban agglomeration. Consequently, carbon emissions in these cities are mutually influenced and strongly correlated. In the Beijing–Tianjin–Hebei region, although Beijing is not included in the first sub-group, the process of regional integration has intensified spatial carbon emission correlations among cities such as Shijiazhuang, Tangshan, Baoding, Langfang, Cangzhou, and Hengshui, making them more complex and interconnected. In the Shandong Peninsula, cities including Qingdao, Jinan, Yantai, Zibo, Weifang, and Dongying advance jointly in economic development, showing interdependence in industrial growth and infrastructure construction. As a result, their carbon emissions are interrelated and mutually constraining. On the west coast of the Taiwan Strait, cities such as Fuzhou, Xiamen, Quanzhou, Ningde, and Putian engage in frequent economic, trade, and industrial cooperation, leading to strong spatial carbon emission correlations.

The second sub-group is centered on Shenzhen, Guangzhou, Shuozhou, Wuhan, and Changsha. Geographically, it shows both clustered distribution and river-oriented distribution. In the Pearl River Delta, cities such as Shenzhen, Guangzhou, Foshan, Dongguan, Zhongshan, Zhuhai, Jiangmen, and Yangjiang have formed a dense urban agglomeration characterized by strong industrial coordination and close carbon emission linkages. Additionally, the sub-group follows a river-oriented distribution. Cities such as Wuhan, Yueyang, Xiangyang, Yichang, Jingzhou, Changde, Yiyang, Xiangtan, Zhuzhou, and Changsha are located along the Yangtze River or its tributaries. Benefiting from waterway transportation, these cities maintain intensive trade and, consequently, strong carbon emission correlations.

The third sub-group is centered on Beijing and Chongqing, consisting mainly of inland cities located in central and western China, including the Chengdu–Chongqing, Guanzhong, and Central Yunnan urban agglomerations, where spatial carbon emission correlations are particularly close. The fourth sub-group comprises cities from Northeast China, including those in Heilongjiang, Jilin, and Liaoning provinces, as well as eastern Inner Mongolia (e.g., Tongliao and Hulunbuir). The fifth sub-group is distributed across the Poyang Lake Ecological Economic Zone, the West Coast Economic Zone of the Taiwan Strait, and Eastern Hubei. Within China’s extensive and complex spatial carbon emission network, the fourth and fifth sub-groups account for only a small share. They occupy relatively marginal positions and primarily maintain local correlations. Additionally, Karamay and Urumqi, located on China’s northwestern frontier, remain geographically isolated with weak connections to other regions in the carbon emission network.

Table 1. Number of relationships within and between sub-groups.

	Sub-Group 1	Sub-Group 2	Sub-Group 3	Sub-Group 4	Sub-Group 5
Sub-group 1	668.27	150.36	13.82	77.64	58.18
Sub-group 2	146.55	402.91	51.27	24.55	41.55
Sub-group 3	28.91	63.09	124.18	9.82	5.09
Sub-group 4	90.18	41.00	11.73	77.18	10.64
Sub-group 5	53.91	35.18	0.73	6.45	26.82

presents the number of carbon emission relationships within each sub-group and between different sub-groups. The carbon emission outflow from Sub-group 1 to Sub-group 2 amounts to 150.36, while it receives a carbon emission inflow of 146.55 from Sub-group 2. This indicates that the amount of carbon emissions output by Sub-group 1 to Sub-group 2 is slightly more than that received from Sub-group 2, demonstrating a certain trend of net carbon emission outflow. The carbon emission outflow from Sub-group 1 to Sub-group 3 is 13.82, and it receives a carbon emission inflow of 28.91 from Sub-group 3, thus showing a situation of net carbon emission inflow. The carbon emission outflow from Sub-group 1 to Sub-group 4 is 77.64, and it receives a carbon emission inflow of 90.18 from Sub-group 4. The phenomenon of net carbon emission inflow also occurs here. The carbon emission outflow from Sub-group 1 to Sub-group 5 is 58.18, and it receives a carbon emission inflow of 53.91 from Sub-group 5. The difference between the two is relatively small, suggesting that the two-way flow in terms of carbon emissions is in a balanced state. The carbon emission outflow from Sub-group 2 to Sub-group 3 is 51.27, and it receives a carbon emission inflow of 63.09 from Sub-group 3, presenting a situation of net carbon emission inflow. The carbon emission outflow from Sub-group 2 to Sub-group 4 is 24.55, and it receives a carbon emission inflow of 41.00 from Sub-group 4. The situation of net carbon emission inflow also exists here. The carbon emission outflow from Sub-group 2 to Sub-group 5 is 41.55, and it receives a carbon emission inflow of 35.18 from Sub-group 5, showing a trend of net carbon emission outflow from Sub-group 2 to Sub-group 5. The carbon emission outflow from Sub-group 3 to Sub-group 4 is 9.82, and it receives a carbon emission inflow of 11.73 from Sub-group 4. The difference between the carbon emission outflow and inflow here is not significant, indicating that the two-way flow in terms of carbon emissions is in a balanced state. The carbon emission outflow from Sub-group 3 to Sub-group 5 is 5.09, and it receives a carbon emission inflow of 0.73 from Sub-group 5, demonstrating a trend of net carbon emission outflow. The carbon emission outflow from Sub-group 4 to Sub-group 5 is 10.64, and it receives a carbon emission inflow of 6.45 from Sub-group 5, showing a trend of net carbon emission outflow.

In conclusion, within the CECN, Sub-group 1, by virtue of its relatively high number of internal carbon emission relationships and the significant carbon emission inflows and outflows with various sub-groups, occupies a core-radiating position, functioning like a network hub. Its developed and diversified industrial structure enables it to serve as an industrial leader, influencing the carbon emission pattern through means such as industrial transfer. Sub-group 2, as an important connecting node, has close internal linkages and considerable carbon emission interactions with other groups. It acts as a participant in industrial complementarity and plays an active role in regional coordination. Sub-group 3 is likely to be a resource-based or specific-industry concentrated area. It functions as a carbon emission supplier in some correlations. Although it currently lies in a relatively marginal position, it holds the potential to transition towards the core. Sub-group 4, due to its low number of internal relationships and complex carbon emission relationships with other groups, is an area with industrial differentiation, carbon emission undertaking and balancing. It also possesses the potential to become a stabilizer of the network structure. Sub-group 5, with weak internal interactions and low degrees of association with other groups, is in a marginal position. These sub-groups are intertwined with each other, jointly constructing a carbon emission spatial correlation network pattern with different levels and functions.

4.2. Network Impact Factor Analysis

In a randomly selected set of 5000 permutations, the QAP correlation analysis results between the average values of the CECN from 2011 to 2021 and the geographical spatial differences, population differences, economic differences, and technological-level differences were obtained by calculating the correlation coefficients between each permutation. From

Table 2. QAP correlation analysis.

Var.	Obs. Value	Sig.	Ave.	Std. Dev.	Min.	Max.	Prop ≥ 0	Prop ≤ 0
D	−0.2437 ***	0.0002	0.0001	0.0165	−0.0583	0.0645	1.0000	0.0002
P	0.2271 ***	0.0002	−0.0002	0.0231	−0.0640	0.1037	0.0002	1.0000
R	0.2908 ***	0.0002	−0.0003	0.0159	−0.0539	0.0669	0.0002	1.0000
T	0.3146 ***	0.0002	0.0002	0.0256	−0.0703	0.1107	0.0002	1.0000

Note: D, P, R, T represent geographical spatial difference, population difference, affluence difference, and technical-level difference; *** significance at 1% level.

, it can be observed that factors such as geographical spatial differences ($D$), population disparities ($P$), economic differences ($R$), and technological level differences ($T$) pass the test at a 1% significance level. The results indicate a significant correlation between these four factors and the formation of spatial correlation in carbon emissions among Chinese cities. Specifically, the correlation coefficient of geographical spatial differences is negative, suggesting a negative correlation between geographical spatial distance relationships and the spatial correlation network of carbon emissions in Chinese cities. The correlation coefficients of population differences, economic differences, and technological-level differences are positive, indicating a positive correlation between population, economic, technological level, and the spatial correlation network of carbon emissions in Chinese cities.

QAP regression analysis is widely used to examine the relationships between multiple independent variables and a dependent variable. To compare correlations between two matrices, multivariate regression is performed by regressing the long vector of the dependent variable matrix against that of the independent variable matrix. A large number of random permutations are then applied to each variable, and the significance levels of the regression coefficients are used to evaluate the correlation results. In this study, 5000 random permutations were conducted, and the results are reported in

Table 3. QAP regression analysis.

Variable	Unstandardized Coefficient	Standardized Coefficient	Significance	p ≥ 0	p ≤ 0
D	−0.1488	−0.2520 ***	0.0002	1.0000	0.0002
P	0.0441	0.0663 ***	0.0002	0.0002	1.000
R	0.1321	0.2245 ***	0.0002	0.0002	1.000
T	0.1415	0.2010 ***	0.0002	0.0002	1.000
Interception	0.0568	0.0000

Note: D, P, R, T represent geographical spatial difference, population difference, affluence difference, and technical level difference; *** significance at 1% level.

.

The key findings are as follows. (1) The coefficient for the geographical spatial matrix is –0.252 and significant at the 1% level. This indicates that shorter geographical distances between cities promote spatial correlations in carbon emissions, as the efficient and cost-effective transfer of low-carbon resources is more evident between nearby cities. (2) The regression coefficient for the population difference matrix is 0.0663, positive and significant at the 1% level. This implies that larger population disparities increase the likelihood of spatial correlations in carbon emissions, as population mobility intensifies economic activities, transportation, and building energy consumption, thereby shaping carbon emission flows. (3) The regression coefficient for the economic difference matrix is 0.2245, positive and significant at the 1% level. This indicates that greater economic disparities increase the likelihood of spatial correlations in carbon emissions. Although more developed cities often exhibit lower direct emissions due to efficient public transportation and energy use, their higher consumption demand, concentration of headquarters and service industries, and supply chain linkages with less-developed cities can transfer part of their carbon emissions to production-oriented cities, thereby reinforcing intercity linkages. Larger economic gradients thus foster stronger carbon emission linkages through mechanisms such as production–consumption transfers, logistics and factor flows, and industrial complementarity and outsourcing. (4) The regression coefficient for the technological difference matrix is 0.201, positive and significant at the 1% level. This suggests that greater technological disparities increase the likelihood of spatial correlations in carbon emissions. Such disparities affect spatial correlations through several mechanisms: wider gaps promote technology exchange and cooperation, particularly when less advanced cities adopt technologies and personnel from advanced ones; they also stimulate production activities and drive spatial flows of carbon emissions. Moreover, technological disparities amplify diffusion effects, as advanced cities enhance the production capacity of surrounding regions through transfer or collaboration, further intensifying regional flows. Finally, they drive industrial restructuring, fostering low-carbon technologies and green industries that reshape spatial patterns of carbon emissions.

4.3. Discussion

This study constructed the CECN from 2011 to 2021 based on a modified gravity model, and revealed the spatiotemporal evolution of intercity carbon emission spatial correlations from the perspectives of overall network structure, individual network characteristics, and regional features. It also explored the influence of geographical distance, population differences, economic disparities, and technological level differences on intercity carbon emission linkages.

First, in terms of the overall network structure, the CECN pattern remained relatively stable during the study period, with a highly dense network structure. This is consistent with previous studies, indicating that a stable spatial dependence structure for carbon emissions has been formed in Chinese cities [27,28]. In addition, the dominant role of core cities has been continuously strengthened, and regional differentiation has intensified. Second, regarding individual network characteristics, cities such as Beijing, Shanghai, Shenzhen, and Guangzhou—located in the eastern coastal region and serving as political centers—maintained long-term advantages in degree centrality, out-degree centrality, and betweenness centrality. This is closely related to their large economic scale, high energy consumption, and high level of urbanization [27]. Resource-based cities such as Daqing, on the other hand, occupied key positions in carbon inflow relationships, as energy industry clusters played the role of receiving end in carbon transfer.

The regional feature analysis shows that the CECN exhibits a clear regional agglomeration effect: intra-subnetwork connections have strengthened, while interregional connections have relatively weakened. This regionalization characteristic is particularly evident in urban agglomerations such as the Yangtze River Delta, the Pearl River Delta, and the Beijing–Tianjin–Hebei region, which is consistent with existing research on the impact of regional coordinated development on energy and carbon flows [40,59]. Eastern coastal core cities, due to developed economies and concentrated high-energy-consuming industries, have become the primary sources and radiation centers of carbon emissions. Meanwhile, with industrial transfer and the implementation of environmental policies, some high-emission industries have shifted to resource-based cities in central and western regions, contributing to the growth of carbon inflows. At the same time, regional integration policies have promoted industrial synergy and resource sharing within city clusters, enhancing intra-regional carbon emission correlations and reducing interregional linkages [60].

Finally, the analysis of influencing factors revealed that geographical spatial differences were significantly negatively correlated with carbon emission spatial linkages, confirming the hypothesis that proximity facilitates the transmission of low-carbon resources and factors, thereby promoting carbon emission connections [61]. Differences in population, affluence, and technological level all showed significant positive correlations, suggesting that industrial complementarity, technological exchange, and factor flows among cities at different stages of development may promote intercity carbon emission linkages. This finding is consistent with the theory of regional economic gradients driving factor flows [62].

5. Conclusions and Policy Implications

5.1. Conclusions

This study investigates the structural characteristics and driving factors of CECN among Chinese cities. First, an improved gravity model was applied to construct the CECN. Second, the structural characteristics of the CECN were analyzed from three perspectives: overall, individual, and regional levels. Finally, QAP regression analysis was employed to examine the factors influencing the CECN.

Based on the network analysis, several findings emerge. The CECN, as a whole, demonstrates high connectivity, a strengthening hierarchical structure, and an increasing role of core cities. Cities with more carbon emission linkages are concentrated in eastern coastal areas and political centers, showing the pattern of “more in the east and less in the west, more along the coast and less inland,” with examples including Beijing, Shanghai, Shenzhen, Guangzhou, and Daqing. In contrast, cities with fewer linkages, such as Lijiang and Xining, are dominated by low-carbon industries such as tourism and agriculture. Beijing and Shanghai exhibit relatively high outflows of carbon emissions, while Daqing and Dongying show higher inflows. Shenzhen, Beijing, Guangzhou, Nanjing, and Shanghai serve as bridging nodes connecting other cities within the network. From 2011 to 2021, the total number of carbon emission linkages fluctuated but generally declined, largely due to emission control policies and economic restructuring. Over the same period, the modularity index increased, indicating stronger regional clustering and more distinct spatial patterns.

The CECN can be classified into five sub-groups. Sub-group 1 is centered on Dongying and Hangzhou, encompassing most cities in the Yangtze River Delta, Beijing–Tianjin–Hebei, and Shandong Peninsula clusters, functioning as a core hub with a radiating influence. Sub-group 2 centers on Shenzhen and Guangzhou, covering most cities in the Pearl River Delta and along the Yangtze River, acting as a key connector that contributes to industrial complementarity and regional coordination. Sub-group 3 is centered on Beijing and Chongqing, comprising mainly inland cities in central and western urban agglomerations; it currently occupies a marginal position but has the potential to move toward the core. Sub-group 4 includes cities in Northeast China and eastern Inner Mongolia, characterized by industrial differentiation and emission balancing, with potential to stabilize the network structure. Sub-group 5 consists of cities in the Poyang Lake Ecological Economic Zone, the West Coast of the Taiwan Strait, and eastern Hubei, but exhibits weak internal interactions and limited external connections, placing it in a marginal position.

Based on the analysis of factors influencing the formation of the CECN, the following conclusions are drawn. A negative correlation exists between geographical distance and the carbon emission spatial correlation network. Shorter geographical distances between cities facilitate the formation of carbon emission correlations, as the transfer of low-carbon resources between nearby cities is more efficient and economical, thereby strengthening carbon emission linkages. Larger differences in population size between cities increase the likelihood of carbon emission correlations. Population mobility intensifies economic activities, transportation, and building energy consumption, thereby influencing intercity carbon emission flows. Greater disparities in affluence between cities also increase the likelihood of carbon emission correlations. Affluent cities, through their advanced public transportation systems, policies, and industrial cluster relocations, tend to establish carbon emission linkages with less affluent cities. Wider technological gaps between cities are more likely to generate carbon emission correlations. Technical exchanges and personnel mobility between cities with substantial technological differences enhance production interactions, thereby intensifying carbon emission flows.

5.2. Policy Implications

The findings of this study offer valuable insights for China’s carbon emission management policies and may also provide a reference for other countries in addressing climate change and emission reduction.

First, since provinces and cities with strong carbon emission correlations are concentrated in the economically developed eastern region, the government should strengthen carbon emission policies in these areas to ensure the rational allocation of emissions. This will help safeguard the green and sustainable development of these regions [63].

Second, the carbon emission flow correlation coefficients among Chinese cities have consistently remained high. The government should actively promote low-carbon technological innovation and industrial development, accelerating the transformation and upgrading of traditional industries toward green and low-carbon pathways. Through policy guidance and market mechanisms, the growth of green industries such as clean energy, energy conservation, and environmental protection should be further cultivated and expanded [64].

Third, given China’s vast geography and the substantial differences in carbon emissions and economic development across provinces and cities, the government should strengthen interdepartmental cooperation mechanisms and emphasize the spatial interdependence of carbon emissions [65]. This requires shifting emission reduction policies from a localized perspective to a comprehensive, nationwide approach, thereby forming a collaborative force to implement carbon emission policies and jointly address related challenges [66].

Finally, in spatial clustering, efforts should actively promote the integration of large and small communities. When formulating and implementing emission reduction policies, larger communities should consider the conditions and needs of smaller ones, thereby ensuring policy specificity and effectiveness [67]. At the same time, by integrating into larger sub-groups, smaller communities can participate in broader policymaking and implementation processes, contributing to a stronger collaborative force for emission reduction.

The policy recommendations of this study have strong international applicability. Globally, carbon emissions across different countries and regions exhibit significant spatial heterogeneity, particularly the differences in emissions between developed and developing countries, as well as variations in technology, industrial structure, and economic development stages. These factors may generate similar spatial interaction effects in carbon emission flows and associations. Therefore, although the context of this study is China, its policy insights are broadly applicable to other countries and regions in promoting low-carbon economies, emission reduction targets, and green innovation. For instance, in Europe, North America, and some Asian countries, governments can draw from China’s experience, adapt it to their own contexts, and establish cross-regional cooperation mechanisms and carbon reduction networks. This would facilitate the sharing and transfer of low-carbon technologies, advancing the achievement of global climate goals.

5.3. Limitations and Future Prospects

Although this study provides a comprehensive analysis of the structural characteristics and driving factors of intercity carbon emission linkages in China, several limitations remain and warrant further exploration.

First, the analysis is based primarily on officially reported carbon emission data at the city level. While these data enable the construction of a nationwide carbon emission correlation network, they may not fully capture real-time emissions fluctuations or informal intercity exchanges of energy and resources that also influence carbon flow. Future research could integrate multiple data sources, such as satellite-derived emissions, real-time energy consumption records, or cross-sectoral trade flows, to obtain a more precise and dynamic representation of intercity carbon emission interactions.

Second, this study focuses on the city level as a unit of analysis and does not consider the heterogeneity of actors within each city, such as industrial enterprises, transportation sectors, and urban households. Such internal differences may influence how carbon emission linkages form and propagate. Future studies could adopt a multi-scale approach linking city-level networks with intra-city actor interactions to better understand the mechanisms through which local production, consumption, and technological activities shape broader spatial emission patterns.