Introduction

Chinese modernization is the modernization of harmonious coexistence between man and nature1. In recent years, metropolitan areas have increasingly become an important platform for promoting coordinated regional development. The report to the 20th National Congress of the Communist Party of China in 2022 clearly stated that we should build a coordinated development pattern among large, medium, and small cities based on urban agglomerations and metropolitan areas. Relying on the spatial network relationship between metropolitan areas to carry out collaborative carbon reduction is conducive to promoting the green and low-carbon development of China’s economy and society.

At present, the research on regional carbon emission includes the following aspects. From the research level, scholars mainly studied the spatial correlation characteristics and influencing factors of carbon emissions at the national and provincial levels, such as Shaanxi Province and Zhejiang Province2,3. In recent years, Yu et al. (2024), Qi et al. (2023) and other scholars have studied the Yellow River Basin, the Yangtze River Delta, the Beijing-Tianjin-Hebei region, and the western region4,5,6, Spatial differences and dynamic evolution of carbon emissions in urban agglomerations or river basins are discussed. Some scholars have conducted preliminary studies on the spatial correlation of carbon emissions in metropolitan areas7,8, but the research results are not abundant at present. From the perspective of research content, on the one hand, the spatial and temporal evolution or spatial correlation network of energy consumption and energy intensity carbon emissions of provinces and regions were analyzed9,10; on the other hand, regional carbon emission studies primarily focused on industries, and scholars mainly studied the spatial correlation characteristics and influencing factors of carbon emissions of some industries in provinces and regions, such as fishery, service industry, tourism, agriculture, etc11,12,13. Currently, scholars mostly utilize methods such as the gravity model to establish carbon emission correlation relationships. They employ approaches like geographical detectors and quadratic assignment procedures to explore the driving mechanisms behind the spatial correlation networks of carbon emissions. When analyzing the spatial correlation characteristics of carbon emissions, social network analysis is frequently applied in carbon emission research14,15. Compared with spatial statistical analysis and other methods16, SNA has advantages in in-depth study of the complexity and dynamics of carbon emission correlation networks, so it is widely used in the field of spatial correlation research of regional carbon emission networks17,18. This method is a powerful tool for scholars to intuitively reveal the spatial correlation network structure characteristics of carbon emissions among provinces and cities and urban agglomerations and the transmission mechanism of carbon emissions. The empirical results not only provide empirical analysis basis for policy makers to optimize carbon emission reduction policies, but also enrich the relevant research results of the spatial correlation of carbon emissions. Among them, QAP is mainly used to study the regression relationship between relational variables. Scholars mostly investigate the factors that influence the spatial correlation of carbon emissions, such as spatial distance, economic development level, environmental regulation, industrialization level, energy consumption, and industrial structure differences19,20,21.

The research of the Hefei metropolitan area is mainly based on the evaluation of industrial cooperation, rural revitalization, ecological quality, and territorial space quality, as well as research on the spatio-temporal evolution of various aspects such as the quality of urban economic development, urban land use, and the quality of urbanization in the Hefei metropolitan area22,23,24,25. Liang (2022) and Wu et al. (2022) evaluated and analyzed the ecological environment quality and spatial and temporal distribution characteristics of urban land expansion in the Hefei metropolitan area respectively26,27; Song (2021) and Liang (2022) explored and thought about the inter-governmental cooperation and urban development countermeasures of the Hefei metropolitan area28,29. In general, there is a lack of relevant research on carbon emissions of industrial industries in the Hefei metropolitan area.

In general, current studies on the spatial correlation of carbon emissions are primarily carried out from the perspectives of countries, urban agglomerations or provinces, and few specific areas within urban agglomerations are studied from a local perspective. However, as an important part of urban agglomerations, studying the characteristics and influencing factors of the carbon emission spatial correlation network of the metropolitan area is of great significance to regional sustainable development. The innovation of the paper is mainly reflected in its research perspective, object and application value. Therefore, from a local perspective, this paper selected the Hefei metropolitan area as the research object. Based on municipal data, the revised gravity model, social network analysis and QAP were introduced into the study of industrial carbon emissions in the Hefei metropolitan area, and the changes in the spatial correlation degree of each influencing factor on industrial carbon emissions in different years were analyzed. This study makes up for the shortcomings of the current research on the structural characteristics and driving factors of the industrial carbon emission correlation network in the Hefei metropolitan area. It enriches the research findings on the spatial correlation of carbon emissions in the industrial sector within metropolitan areas, and can also provide references for other metropolitan areas to formulate emission reduction policies, which is of great significance for the collaborative emission reduction and low-carbon development of urban agglomeration.

Materials and methods

The logic of this research is shown in Fig. 1.

Fig. 1
figure 1

Research logic diagram.

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Research area

As one of the significant metropolitan areas in China’s Yangtze River Delta (Fig. 2), The land area of the Hefei Metropolitan Area accounts for about 40.6% of the total area of the province, and its population accounts for about 43% of the province’s total population. In 2022, the GDP was 2,820.414 billion yuan, approximately 63% of Anhui Province’s GDP. The average urbanization rate was 66.38%, higher than Anhui Province’s 60.15%. Since its formal rise to the national development strategy in 2016, it has built a “1 + 6 + N” planning system for the metropolitan area, and promoted high-quality integrated development in infrastructure and other aspects.

Fig. 2
figure 2

Location map of the Hefei metropolitan area in China. For Fig. 2, all map data in this article are sourced from https://www.resdc.cn/Default.aspx, the ArcMap 10.8 download website for drawing maps is https://desktop.arcgis.com/zh-cn/desktop/index.html.

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The Hefei metropolitan area is not only the core growth pole of Anhui’s development, but also has an important strategic position in the overall national modernization and regional coordinated development. Considering the availability of data, seven prefecture-level cities in the Hefei metropolitan area, namely Hefei, Luan, Huainan, Chuzhou, Bengbu, Maanshan, and Wuhu, as the research objects.

Data sources

The energy data and indicators required for carbon emissions in this paper are sourced from the statistical yearbooks of the seven cities, including Hefei, and so on. As the statistical yearbooks of some cities are only published until 2023, in order to obtain the data, this paper chooses 2010–2022 as the research period. Find relevant data in the municipal Statistical yearbooks (2011–2023).

Carbon emission measurement

Using the carbon emission calculation method stipulated by IPCC. This paper mainly selects 7 kinds of energy sources to calculate industrial carbon emissions in the Hefei metropolitan area during 2010–2022. Table 1 shows the carbon emission coefficients of relevant energy sources.

Table 1 The carbon emission coefficients of main energy.
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Calculated by Eq. (1).

$$\:M=\sum\:{N}_{j}{m}_{j}$$
(1)

M is industrial carbon emissions (10,000 tons); \(\:{N}_{j}\)is the energy consumption after the reduction of standard coal; \(\:{m}_{j}\) is carbon emission coefficient (\({10}^{4}\text{t}/{10}^{4}\text{t}\)); \(\:j\) is the type of energy.

Gravity model

The gravity model is a method to describe the spatial correlation by considering population, economy, geography, and other factors. This paper aims to utilize the gravity model to calculate the attraction of carbon emissions between cities and establish the correlation of carbon emissions. Based on Pang’s relevant research30, this paper introduced the gross regional product G, per capita gross regional product g, population size p, total carbon emission C, and economic geographical distance D to revise the gravity model. Te calculation formula is Eq. (2).

$$\:L_{{ij}} = a_{{ij}} \frac{{\sqrt[3]{{P_{i} C_{i} G_{i} }}\sqrt[3]{{P_{j} C_{j} G_{j} }}}}{{D_{{ij}} ^{2} }},\:a_{{ij}} = \frac{{C_{i} }}{{C_{i} + C_{j} }},\:D_{{ij}} ^{2} = \left( {\frac{{d_{{ij}} }}{{g_{i} - g_{j} }}} \right)^{2}$$
(2)

Lij represents the attraction between cities i and j; aij represents the contribution rate between city i and city j, and D is the comprehensive economic and geographical distance between cities; d represents geographical distance31. The city centroid distance is obtained using the ArcGIS 10.8 software to obtain centroid coordinates and calculated using the point distance tool. Through the revised gravity model, the gravity values between cities in the 2010–2022 interval were calculated, and a spatial correlation matrix (gravity matrix), which needs to be transformed into a 0–1 matrix, and use the average of each row in the gravity matrix as a threshold: assign a value of 1 if above the threshold, and 0 if below32.

Social network analysis (SNA)

The social network analysis model distinguishes itself from traditional analytical models by placing greater emphasis on the overall network structure and the relationships among various action units33. This study, used it to analyze the structural characteristics of the carbon emission correlation network in the Hefei metropolitan area from both the overall and individual perspectives. The specific calculation steps are as follows23:

The four indexes of the overall network characteristics are calculated by Eqs. (3–6). ND, NC, NG, and NE respectively network density, network correlation degree, network hierarchy, and network efficiency.

$$\:ND=\frac{X}{Y(Y-1)/2}$$
(3)
$$\:NG=1-\frac{Q}{max\left(Q\right)}$$
(4)
$$\:NC=1-\left[\frac{O}{Y(Y-1)/2}\right]$$
(5)
$$\:NE=1-\frac{P}{max\left(P\right)}$$
(6)

Where: O and Y represent the number of unreachable points and cities; X represents the number of actual relationships that occur between cities; Q represents the logarithm of points that are symmetrically reachable; P is the number of extra lines8.

Centrality is calculated by Eqs. (7–9). CRD, CRC, and CRP respectively degree centrality, betweenness centrality, and closeness centrality.

$$\:{C}_{RD}\left(i\right)=\frac{z}{(Z-1)}$$
(7)
$$\:{C}_{RC}\left(i\right)=\frac{2\sum\:_{j}^{Z}\sum\:_{k}^{Z}{b}_{jk}\left(i\right)}{(Z-1)(Z-2)}$$
(8)
$$\:{C}_{RP}\left(i\right)=\frac{\sum\:_{i=1}^{Z}{e}_{ij}}{(Z-1)}$$
(9)

Where: z represents the number of cities that are directly connected to other cities, Z-1is the maximum number of cities that may be directly connected. bjk(i) is the probability that the third city i is on the shortcut between j and k; eij is the number of lines contained in the shortcut between points i and j8.

QAP regression analysis

In this paper, relational data is used to study the influencing factors, and considering the issue of multicollinearity, QAP (Quadratic Assignment Procedure) regression analysis is selected for the research32. QAP correlation analysis is generally used before QAP regression analysis to verify whether there is a significant correlation between matrix variables34. QAP regression analysis can explore the regression relationship between matrices, and its basic calculation principle is as follows:

In the first step, multiple regression is performed on the independent variable and dependent variable matrix; in the second step, the rows and columns of the dependent variable matrix are randomly replaced and the regression coefficient and r2 are recalculated. The above steps are repeated many times. It should be noted that all matrices in the regression must be N×N square matrices.

Combined with relevant studies, Yu et al.(2024) found that spatial geographic distance, level of opening up and economic development would have a certain impact on the development of spatial correlation network of carbon emissions in urban agglomerations4. The adjacency relationship between cities is conducive to the formation of spatial correlation of industrial carbon emissions. The increase of per capita GDP and urbanization rate is often accompanied by the growth of carbon emissions, but with the promotion of urbanization to optimize industrial structure and the implementation of carbon emission reduction policies, carbon emissions will be reduced. The level of opening up has a two-sided impact on carbon emissions. On the one hand, the use of foreign capital and new technologies to promote the upgrading of industrial structure in the region can reduce carbon emissions; on the other hand, transportation and other activities will also produce certain carbon emissions. Huo (2022), Dong (2022), Yang (2024), and Shi(2024) et al. believe that urbanization level, industrial structure, and technological innovation are essential factors in the spatial correlation of carbon emissions across provinces and city clusters31,35,37. The proportion of gross tertiary industry in GDP and gross secondary industry in GDP is an important indicator to measure the industrial structure. The higher the proportion of gross secondary industry in GDP, the higher the carbon emissions brought by high-energy industries such as mining, while the increase of gross tertiary industry in GDP can effectively reduce carbon emissions. R&D expenditure in GDP of industrial enterprises and scientific and technological level have a positive impact on carbon emissions, and both reduce carbon emissions by improving energy efficiency through technological innovation. Pang (2019), Chen(2018), and Meng(2024) et al. investigated the impact of scientific level, energy intensity, and industrialization level on carbon emissions in Chinese city clusters30,38,39. The influence of energy intensity and industrialization level on carbon emissions cannot be ignored. Energy consumption increases with the increase of energy intensity, thus promoting the increase of carbon emissions. The energy consumption structure changes with the improvement of industrialization level. In the early stage, the use of fossil energy and the development of resource-intensive industries lead to higher carbon emissions. In the later stage, the development of technology and the optimization of industrial structure may reduce carbon emissions.

Therefore, we hypothesized that economic development level, energy intensity, industrialization level, scientific and technological level, level of opening up, geographical adjacency relationship, urbanization level, industrial structure, and technological innovation level would affect the spatial correlation of industrial carbon emission in the Hefei metropolitan area. Ten influencing factors were used to construct the QAP model. The expression of the model is shown in Eq. (10).

$$N = f(X_{1} ,X_{2} ,X_{3} ,X_{4} ,X_{5} ,X_{6} ,X_{7} ,X_{8} ,X_{9} ,X_{{10}} )$$
(10)

In the formula, each variable is a relational matrix. N is the spatial correlation matrix of industrial carbon emissions, and X1-X10 is the difference matrix constructed by driving factors. The descriptions of the driving factors are shown in Table 2.

Table 2 The driving factors definitions.
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Results

Analysis of the spatio-temporal evolution of industrial carbon emissions in the Hefei urban agglomeration

The carbon emission calculation results of 7 cities in the Hefei metropolitan area during 2010–2022 are shown in Fig. 3.

Fig. 3
figure 3

Trend chart of industrial carbon emissions in the Hefei metropolitan area from 2010 to 2022.

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From the perspective of time, industrial carbon emissions in the study area showed a fluctuating and rising trend during 2010–2022, but the overall trend was flat. The industrial carbon emission of Huainan City from 2010 to 2022 showed a fluctuating upward trend, and its carbon emission was much higher than that of other 6 cities. The carbon emissions of Wuhu City and Hefei City showed a “up - down - up” trend, and the growth rate slowed down after 2012. The carbon emissions of Luan City, Chuzhou City and Bengbu City were all below 5 million tons during the study period, and the overall trend remains consistently stable.

At the same time, this paper drew the spatial distribution maps of carbon emissions for the years 2010, 2016, and 2022 (Fig. 4), conducting a visual analysis of the spatial distribution of carbon emissions in this region. From the perspective of space, the natural breakpoint method divides the carbon emissions of these 7 cities in 2010–2022 into five different ranges (A, B, C, D, E). Figure 4 only shows the spatial distribution of carbon emissions in 2010, 2016 and 2022. According to Fig. 4, during the study period, with Hefei City as the center, the carbon emission of the Hefei metropolitan area showed a spatial feature: the eastern part was larger than the western part and the northwest part was larger than the southeast part. Huainan City, Hefei City and Maanshan City increased their carbon emission range levels during 2010–2016, and the spatial distribution of carbon emissions in other cities was basically stable except for Luan City, which increased its level in 2022. In general, by 2022, the carbon emission range ranks Huainan City > Maanshan City > Hefei City, Wuhu City > Bengbu City, Luan City > Chuzhou City.

Fig. 4
figure 4

Spatial evolution of industrial carbon emissions. For this figure, all map data in this article are sourced from https://www.resdc.cn/Default.aspx, the ArcMap 10.8 download website for drawing maps is https://desktop.arcgis.com/zh-cn/desktop/index.html. The five ranges of carbon emissions are A (0–191.554), B (191.555–461.765), C (461.766–1073.369), D (1073.370–1849.285), E (1849.286–3023.310).

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Analysis of industrial carbon emission gravity between cities

According to the calculation results of the gravity model, the natural breakpoint method is used to divide the gravity value from low to high into five grades: A, B, C, D, and E. Moreover, we visualized the gravity of industrial carbon emissions in the Hefei metropolitan area in 2010, 2016, and 2022 by the ArcGIS 10.8.

As can be seen from Fig. 5, in 2010, there were 6 B-class gravity lines and 2 C-class gravity lines in the Hefei metropolitan area. There is a with medium gravitational connection between Bengbu City and Huainan City, as well as between Bengbu City and Chuzhou City. In 2016, the gravity intensity relationship among cities changed. As can be seen from Fig. 5(b), there is a relatively strong gravitational connection between Hefei City and Huainan City, and a medium gravitational connection between Hefei City and Luan City, respectively. In 2022, it can be seen that there are 7 C-class gravity lines, 2 E-class gravity lines and 1 D-class gravity line. There are medium gravitational connection among Hefei City, Chuzhou City, Luan City, and Wuhu City. Hefei City has relatively strong gravitational connection with Bengbu City and Luan City, and an strong gravitational connection with Huainan City. In conclusion, from 2010 to 2022, the Hefei metropolitan area has gradually formed a strong industrial carbon emission network spatial pattern with Hefei as the core node.

Fig. 5
figure 5

Interurban carbon emission gravity intensity map in 2010, 2016, and 2022. Note: The gravity value is divided into five grades: A (Weak gravitational connection), B (Relatively weak gravitational connection), C (Medium gravitational connection), D (Relatively strong gravitational connection), E (Strong gravitational connection).

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Analysis of structural characteristics of industrial carbon emission correlation network

The software Ucinet 6 was used to calculate the data of five relevant indicators from 2010 to 2022 (Table 3). It can be seen that from 2010 to 2022, the degree of NC remained at a high level of 1, which means that there is accessibility between nodes. Each city within the metropolitan area has direct or indirect connections with other cities.

Table 3 Analysis of overall spatial network structure index of industrial carbon emission in the Hefei metropolitan area.
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As shown in Fig. 6(a). Both the ND and the number of network relationships show a Tendency of “down - up - down - up”, and the changing trends of both are consistent. The network density fluctuates generally around the mean value of 0.238 during 2010–2022. It increased from 0.191 to 0.262 in 2021–2022, In the past two years, the spatial correlation of industrial carbon emissions in Hefei metropolitan area has gradually increased. Over a period of thirteen years, The number of network association relationships is far lower than the theoretical maximum of 42, with an average of 9.6923. the tightness of the spatial correlation relationship in carbon emissions among cities in the Hefei metropolitan area is not enough, and spatial correlation can be further improved.

Fig. 6
figure 6

Overall structural characteristics of carbon emission spatial correlation network in the Hefei metropolitan area from 2010 till 2022.

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As shown in Fig. 6(b). The NG first decreases and then increases, It fell from 0.929 in 2010 to 0.667 in 2012, and then showed an upward trend. Since 2015, the network level of carbon emission spatial correlation network in the Hefei metropolitan area has been stable at 0.909, which indicates that node cities have relatively stable relationship gradient in the carbon emission spatial correlation network, and individual cities have absolute “right to speak” on emission reduction. In terms of network efficiency, from 2010 to 2022, the spatial correlation network efficiency of industrial carbon emissions in the Hefei metropolitan area was all above 0.733, fluctuating around the mean value of 0.815. The network efficiency remained stable during 2013–2015 and 2017–2019, and decreased in 2022 compared with the previous year. It shows that the stability of the carbon emission spatial correlation network structure in the Hefei metropolitan area has improved.

The structure analysis of individual spatial network is also the centrality analysis of spatial network. The values of individual network characteristics in 2010, 2016, and 2022 are shown in Table 4.

Table 4 Individual centrality analysis of industrial carbon emission spatial network in the Hefei metropolitan area.
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The mean values of degree centrality in 2010, 2016, and 2022 are 2.86, 2.57 and 2.86, respectively. In 2010, Hefei City, Maanshan City, Bengbu City, and Huainan City exceeded the average value. In 2022, Chuzhou City, Hefei City, Bengbu City, and Huainan City were all higher than the mean value of 2.86, In the carbon emission network of Hefei metropolitan area, these four cities are closer to the center than other cities. Meanwhile, the CRD of Huainan City and Hefei City has always maintained a high level. Combined with Table 4, shows that Huainan City and Hefei City are in the center of the carbon emission network, and have relatively more connections with other cities, and have more significant impact on other cities. This may be because Hefei City, as a provincial capital, has advantages in geographical ___location, economy, transportation, technology, etc., which makes it have intense radiation and attraction.

The mean CRC of carbon emission spatial correlation network in the Hefei metropolitan area in 2010, 2016, and 2022 were 0.57, 0.29, and 0.57, respectively. In 2010, Wuhu City, Chuzhou City and Luan City had zero betweenness centrality and were at the edge of the network structure, while Huainan City and Bengbu City had higher than average CRC and were at the network’s core. During 2016–2022, Wuhu City, Chuzhou City and Luan City remained in marginal positions, with weak control over other cities. In 2022, the CRC of Hefei is much higher than the average. Hefei has become the core of the carbon emission network in the metropolitan area and holds a greater power of carbon emission. Huainan City and Bengbu City have the middle centrality degree of 1, ranking in second place, and are the critical nodes in the carbon emission network of the metropolitan area. At the same time, the total degree of network betweenness centrality in 2022 is 4, among which the top three cities account for 100%, indicating that the carbon emission network of the Hefei metropolitan area has a very obvious non-equilibrium.

As indicated in Table 4, the Closeness centrality average degree of carbon emission spatial correlation network of the Hefei metropolitan area in 2010, 2016, and 2022 is 63.03, 64.49, and 63.84, respectively. In 2022, Hefei City, Bengbu City, Chuzhou City, and Huainan City are the cities with higher Closeness centrality to the center than the average, indicating that they are more likely to have spatial correlation with the remaining cities in the carbon emission spatial network. At the same time, Hefei City, Bengbu City, and Huainan City, the three cities with the top degree of Closeness centrality to the center of the Hefei metropolitan area, have the proximity degree of 75, which is much higher than other cities in the metropolitan area, indicating that they are in the center of the network and play the role of “central actors”. However, Maanshan City, Luan City and Wuhu City are relatively close to the center, and far below the average, indicating that they have a long communication distance with other cities, are susceptible to the influence of other cities. The efficiency driven by other cities is low.

Analysis of influencing factors of spatial correlation of carbon emission in the Hefei metropolitan area

QAP method was used to explore the factors affecting the spatial correlation of carbon emissions in the industrial circle of the Hefei metropolitan area.

QAP correlation analysis

In this study, the difference matrix of 10 influential factors and the spatial association matrix of industrial carbon emission in 2022 were input into Ucinet 6 software for QAP correlation analysis, and 5,000 random substitutations were selected to finally obtain the correlation analysis between the spatial association matrix of industrial carbon emission in the Hefei metropolitan area and the driving factors shown in Table 5. As shown in Table 5, the correlation coefficients of X1 and X5 are significantly positive at the 1% level, the correlation coefficients of X7 and X9 are significantly positive at the 5% level, the correlation coefficients of X4, X8, and X10 are significantly positive at the 10% level, and the correlation coefficients of X2, X3, and X6 are not significant. Then, QAP correlation analysis was performed on the independent variables to observe whether there was a correlation between them.

Table 5 Results of QAP correlation analysis between spatial correlation matrix and influencing factors.
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We selected these 7 influencing factors for QAP correlation analysis. The results in Table 6 show a significant correlation between most of the influencing factors, indicating a multicollinearity problem between the variables. Therefore, the QAP method was chosen to conduct regression analysis of the influencing factors.

Table 6 QAP correlation analysis results of influencing factors.
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QAP regression analysis

5,000 random permutations were selected to finally obtain the QAP regression results of the spatial correlation matrix and influencing factor matrix of industrial carbon emissions in the Hefei metropolitan area. The QAP regression results of influencing factors in 2010, 2016, and 2022 are shown here. An analysis was conducted on how the influence degree of factors impacting carbon emission spatial correlation varied over time. As seen from Table 7, the adjusted R2 for 2010, 2016, and 2022 are 0.414, 0.680, and 0.678 respectively. These 7 independent variable matrices can explain 41.4%, 68%, and 67.8% of the spatial correlation of industrial carbon emissions in the Hefei metropolitan area in 2010, 2016, and 2022, indicating that the model has a strong overall explanatory ability.

Table 7 QAP regression results.
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From the perspective of time, it can be seen from Table 7 that in 2010, the regression coefficients of X1, X7, and X9 all passed the significance test of 5%, indicating that per capita GDP, urbanization rate and technological innovation in 2010 had an important impact on the establishment of carbon emission correlation among cities in the Hefei metropolitan area. The standardized regression coefficients of 0.382, -0.865, and − 0.658 indicate that the greater the difference in economic development level between cities, the smaller the difference in urbanization level and technological innovation level, and the easier it is to strengthen the correlation of industrial carbon emissions. X5, X4 and X10 are significant at the level of 1% and 10% respectively, indicating that the differences in the level of opening up, Scientific and technological level, and the proportion of the secondary industry in GDP among cities in the Hefei metropolitan area also have a certain impact on the spatial correlation of carbon emissions.

In 2016, the regression coefficients of other driving factors except X4 and X7 passed the significance test. X5 and X9 are significant at the 1% level, indicating that the differences in the level of opening up and technological innovation have more significant impacts on the correlation of carbon emissions. The regression coefficient of the proportion of R&D internal expenditure in GDP of industrial enterprises is negative, indicating that the reduction of technological innovation level difference between cities has a certain positive effect on the spatial correlation of carbon emissions.

In 2022, X1, X5, X7, X9 and X10 all passed the significance test. At the significance level of 1%, X7 has a negative impact on the spatial correlation of carbon emissions; at the significance level of 5%, the regression coefficients of X1 and X9 show a positive and negative significant impact, respectively; at the significance level of 10%, the regression coefficients of X5 and X10 are significant. Economic development level, opening-up level, urbanization level, technological innovation level and industrial structure are the main driving factors affecting the industrial carbon emission correlation in the Hefei metropolitan area.

From the perspective of variables, it can be seen from Table 7 that the regression results of per capita GDP in 2010, 2016 and 2022 are all significant and have a positive impact on the correlation of carbon emissions in 2022. Per capita GDP represents the level of economic development of a city. In the early stage, due to the demand of urbanization, production modes with high carbon emission were widely chosen, and per capita GDP played a role in strengthening the economic ties between cities. With the implementation of policies such as the Implementation Plan of Anhui Province for the Development Plan of Yangtze River Delta Urban Agglomeration, people are more in pursuit of high-quality low-carbon life. The difference in economic level among cities still affects the formation of carbon emission spatial correlation network in the Hefei metropolitan area, Economic differences promote carbon emission transfer and strengthen industrial carbon correlation.

The regression coefficient of Scientific and technological level changed from positive significant in 2010 to negative insignificant in 2022, indicating that with the passage of time, the higher the similarity of science and technology level among cities, the stronger the spatial correlation of industrial carbon emissions in the Hefei metropolitan area. At present, the difference of Scientific and technological level cannot have a significant impact on the spatial correlation of industrial carbon emissions in Hefei metropolitan area, which because since the ratio of science and technology investment expenditure to general budget expenditure of each city in the Hefei metropolitan area during the study period is relatively stable except for Hefei city and Wuhu city, and the difference of Scientific and technological level of cities in the Hefei metropolitan area has not significantly changed. As a comprehensive national science center and the central city of G60 Science and Innovation Corridor, Hefei’s science and technology investment in 2022 is 24567.08 million yuan, much higher than other cities, so the science and technology investment is unbalanced, and the degree of scientific and technological achievement transformation varies among cities. The technological gap hinders the development and construction of carbon emission network in the Hefei metropolitan area.

During 2010–2022, the proportion of internal R&D expenditure in GDP of industrial enterprises is always at a significant level of 5% or 1%, which has a significant impact on the spatial correlation of industrial carbon emissions. The regression coefficient is negative, indicating that the higher the similarity of urban technological innovation levels, the stronger the spatial correlation of industrial carbon emissions in the Hefei metropolitan area. This is because the narrowing of differences in technological innovation levels is conducive to the exchange of industrial technological innovation achievements among cities, thus promoting the formation of spatial correlation of carbon emissions.

The QAP regression results of opening up level showed a significant positive correlation in 2010, 2016 and 2022. As time goes by, it has always had an important impact on the spatial correlation of industrial carbon emissions in the Hefei metropolitan area. The greater the difference in the level of opening up among the seven cities, the stronger the spatial correlation of industrial carbon emissions between cities in the metropolitan area. Hefei’s foreign trade grew rapidly, and the proportion of total imports and exports in GDP increased from 24.25 to 32.75, while Huainan’s total imports and exports accounted for only 5.64 in 2022, and the opening up level of other cities increased.

The regression coefficient of urbanization level in 2010 and 2022 is significant at 5% and 1% respectively, which has become an important driving factor for the development of industrial carbon emission correlation network in the Hefei metropolitan area. A negative regression coefficient indicates that the smaller the difference in urbanization level among the seven cities, including Hefei, is conducive to the exchange and learning of industrial energy conservation and emission reduction technologies and policies among cities, and the easier it is to form the spatial correlation of industrial carbon emissions.

In 2022, the proportion of the total value of the tertiary industry in GDP had a positive but insignificant impact on the spatial correlation of industrial carbon emissions in the Hefei Metropolitan Area. The absolute value of the regression coefficient shows an overall upward trend, increasing from 0.029 in 2010 to 1.073 in 2022, indicating that although it is not an important factor affecting the spatial correlation of industrial carbon emissions, the degree of influence is gradually increasing, and it may still play a certain role in the future. In 2010, 2016 and 2022, X10 was always significant at the level of 5% or 1%, and the proportion of the secondary industry in GDP was always an important factor affecting the spatial correlation of industrial carbon emissions in the Hefei metropolitan area during the study period. It shows that the difference of industrial structure has a significant effect on the spatial correlation of industrial carbon emissions in the the Hefei metropolitan area. The industrial structure of Hefei is gradually optimized, mainly developing high-tech manufacturing industry, strategic emerging industry, and tertiary industry, which has certain similarities with the industrial structure of Chuzhou, Wuhu, and Bengbu, while the industrial structure of Maanshan and Huainan is more inclined to resource-based industry and heavy industry with high energy consumption due to different resource endowments. The industrial chain of each city is interwoven, the economic and trade exchanges increase, the carbon emission level of each city influences each other, and the greater the difference in the proportion of the secondary industry in industrial structure, the stronger the correlation of industrial carbon emission.

Discussion

  1. (1)

    In terms of the research object, the Hefei metropolitan area is selected as the research object in this paper. At present, relevant research on the Hefei metropolitan area is carried out, and most of the achievements are in ecological risk assessment, ecological security construction, etc40,41. There is a lack of research on the spatial correlation characteristics and driving factors of industrial carbon emissions. Therefore, in terms of research feasibility, This study has enriched the research results of industrial carbon emissions in the Hefei metropolitan area, and the research ideas and methods can also be applied to the analysis of spatial correlation characteristics of carbon emissions in other metropolitan areas.

  2. (2)

    In terms of the research content, according to the results of gravity model calculation and social network analysis, the gravitational linkage of carbon emissions among cities in the Hefei metropolitan area has been strengthened year by year, forming a spatial pattern of carbon emissions network with Hefei as the core. In terms of the overall network structure characteristics, the network correlation degree is 1, indicating that the spatial correlation network structure of carbon emissions in metropolitan areas has a general spatial overflow path, which verifies the research conclusion of Song et al.6; Network density fluctuates above and below the mean value of 0.2381, and network grade and network efficiency decrease first and then increase but are generally stable, this indicates that the spatial correlation network of carbon emission in the Hefei metropolitan area has more connections, and the stability of network structure has improved but the rank is obvious. Therefore, the Hefei metropolitan area should continue to increase network density in the future, so that more cities can play a role in the carbon emission network. Break the status quo of the obvious hierarchy of carbon emissions.

    Regarding individual network structure characteristics, the degree of point centrality and proximity centrality of Hefei City and Huainan City have always maintained a high level, indicating that they are located in the center of the whole network. The degree of intermediary centrality of Hefei is much higher than the average, which plays the role of a bridge and has a significant impact on the spatial network of carbon emission, which is consistent with the conclusion of scholars Xi20, Chuzhou and Bengbu are gradually approaching the center of the network, so the reduction of industrial carbon emission in Hefei metropolitan area can be started from these cities. The position of each city in the spatial correlation network of carbon emissions is obviously unbalanced. The formation of carbon emission reduction coordination mechanism in future metropolitan areas requires the government to formulate carbon emission reduction policies according to local conditions, and give play to the respective advantages of central cities and marginal cities.

    The QAP empirical analysis results indicate that in 2022, economic development level, urbanization level, technological innovation level, industrial structure, and Level of opening up had significant impacts on the carbon emission spatial network correlation within the Hefei metropolitan area. These findings are consistent with the research results of Dong and Liu et al.18,31. The smaller the difference in urbanization level in the Hefei metropolitan area, the greater the difference in industrial structure, and the tighter the spatial correlation of carbon emissions. The level of technological innovation has a negative impact on the spatial correlation of carbon emissions within the Hefei metropolitan area, which differs from the positive impact found by Dong et al.31. on the carbon emission correlation network of the Yangtze River Delta urban agglomeration. This may be due to the fact that the proportion of internal R&D expenditure in GDP of industrial enterprises is selected as the indicator to describe technological innovation in this paper. Hefei metropolitan area is a part of the Yangtze River Delta urban agglomeration, and the relevant status quo and data obtained in this region are not exactly the same as that in the Yangtze River Delta urban agglomeration. From 2010 to 2022, the narrowing trend of technological innovation level differences in the seven cities is conducive to the exchange of technological innovation achievements in the industry, thus affecting the spatial correlation of carbon emissions.

  3. (3)

    Overall, the research findings of this paper have significant practical implications for the development of green urbanization in the Hefei Metropolitan Area. This study takes a localized perspective by selecting the Hefei metropolitan area, one of the five metropolitan areas in the Yangtze River Delta urban agglomeration, as the research subject. Analyzing the characteristics and influencing factors of its industrial carbon emission spatial correlation network, aids governments in understanding the current status of industrial carbon emissions in the Hefei Metropolitan Area and grasping the role of each city within the spatial correlation network of carbon emissions. Furthermore, by identifying the influencing factors of the industrial carbon emission spatial correlation network, it provides a basis for municipal governments to formulate differentiated energy conservation and emission reduction policies as well as rational urban planning, thereby playing a positive role in promoting green and low-carbon urbanization in China’s metropolitan areas.

However, this study also has certain limitations and can be further improved in the future. Firstly, since the relevant research data in this paper have not been updated by official sources to 2023, extending the research period in the future is recommended for more comprehensive analysis. Secondly, in the gravity model, an attempt can be made to consider the ___location of urban industrial zones as carbon emission points for cities when calculating the distance d. Lastly, this paper focuses on the impact of external factors on the carbon emission spatial correlation network. In the future, the Exponential Random Graph Model (ERGM) can be employed to explore further the endogenous driving forces behind the development of this network.

Conclusions and recommendations

The ArcGIS 10.8 was used to conduct spatiotemporal analysis of industrial carbon emissions in the Hefei metropolitan area during 2010–2022. Based on the calculation of carbon emissions, the revised gravity model and SNA were adopted to explore the overall and individual characteristics of the spatial correlation network of carbon emissions in the Hefei metropolitan area. The driving factors of carbon emission correlation network formation in the Hefei metropolitan area were studied by QAP method. The conclusions are as follows:

  1. (1)

    During the study period, the industrial carbon emissions of the Hefei metropolitan area showed a fluctuating and rising trend, and the overall trend was flat, showing a spatial feature of greater east than west and northwest than southeast. By 2022, the Hefei metropolitan area has gradually formed a spatial pattern of industrial carbon emissions network with Hefei City as the core node.

  2. (2)

    From the overall network characteristics, the spatial correlation of industrial carbon emissions in the Hefei metropolitan area is gradually intensifying. There is a universal spatial correlation relationship, and the overall network structure is relatively stable. However, the tightness of the spatial correlation relationship in carbon emissions among cities is not enough, and the hierarchy is relatively obvious.

  3. (3)

    From the perspective of individual network characteristics, the carbon emission spatial correlation network of the Hefei metropolitan area with Hefei and Huainan as the center gradually formed during 2010–2022, and Chuzhou and Bengbu gradually approached the center of the network. The position of each city in the carbon emission spatial correlation network is obviously unbalanced.

  4. (4)

    The results of QAP analysis show that the formation and development of the spatial correlation network of industrial carbon emissions in the Hefei metropolitan area are significantly affected by urbanization level, economic development level, technological innovation, level of opening up and industrial structure.

Based on the above conclusions, carbon emission reduction cooperation and collaborative development among cities in the Hefei metropolitan area can be promoted from the following aspects:

  1. (1)

    Based on the structural characteristics of the spatial correlation network of industrial carbon emissions in the Hefei metropolitan area, to improve the density of carbon emission network in Hefei metropolitan area, it is necessary to practice the governance concept of linkage and coordination, and promote cross-city exchanges and cooperation in energy conservation and emission reduction within the metropolitan area. Maanshan and other cities should continue to enlarge their own advantages and undertake innovative industries in central cities, so as to achieve low-carbon development of the Hefei metropolitan area.

  2. (2)

    Giving play to the leadership role of Hefei as the central city, it is imperative to foster technical exchanges with industrial cities such as Bengbu, Maanshan, Huainan, while making use of Hefei’s industrial and technological advantages to promote the upgrading of industrial structure in surrounding industrial cities. At the same time, Maanshan and other industrial cities should also give play to their resource advantages, improve their energy utilization efficiency, and promote the formation of carbon emission reduction coordination mechanism among metropolitan areas.

  3. (3)

    It is crucial to improve the carbon emission correlation network of the Hefei metropolitan area, and considering the status of cities within the metropolitan area in the carbon emission network. On the one hand, Hefei, Bengbu, Huainan and other cities should play the role of Bridges, fostering the two-way spillover effect with Luan and other network edge cities. On the other hand, different carbon emission reduction policies should be implemented according to local conditions, ensuring that all cities should jointly promote the implementation of emission reduction policies.

  4. (4)

    Considering the impact of urbanization level, industrial structure and other factors on the spatial correlation network of carbon emission in the Hefei metropolitan area, the government should promote the integrated development of urban infrastructure in the Hefei metropolitan area, reduce the proportion of secondary industry and optimize resource allocation. By introducing green technologies, we can promote technological innovation to lead industrial innovation, thereby facilitating the achievement of green and low-carbon development goals.