Research on the Spatial Network Characteristics, Synergistic Emission Reduction Effects and Mechanisms of Carbon Emission in Beijing–Tianjin–Hebei Urban Agglomeration

Abstract

With the in-depth advancement of the Beijing–Tianjin–Hebei coordinated development strategy, establishing a new mechanism for coordinated development in regional coordinated development is an important measure to realize the green, low-carbon and sustainable development of the Beijing–Tianjin–Hebei urban agglomeration. At present, there are significant differences in carbon emission intensity among different cities in the Beijing–Tianjin–Hebei urban agglomeration, which poses a significant obstacle to the synergistic development goals of the Beijing–Tianjin–Hebei region. Therefore, studying the carbon emissions of the Beijing–Tianjin–Hebei urban agglomeration is of great significance for achieving synergistic development in the Beijing–Tianjin–Hebei region and achieving China’s dual carbon goals. Based on the above practical background, this study focuses on the carbon emissions of the Beijing–Tianjin–Hebei urban agglomeration, using the gravity model, the social network analysis method, and the synergistic effects of carbon emission reductions model to analyze the general characteristics of the carbon emission spatial network, individual characteristics of the carbon emission spatial network, and synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration. The study found that the carbon emission spatial network of the Beijing–Tianjin–Hebei urban agglomeration presents a typical core–periphery structure. From the perspective of the general characteristics of the spatial network, the ranking structure of carbon emissions among cities in Beijing–Tianjin–Hebei is strict, and the network stability is good; from the perspective of individual characteristics of the spatial network, Beijing and Tianjin are the centers of the carbon emission spatial network of the Beijing–Tianjin–Hebei urban agglomeration, playing an important role of “betweenness” and “bridge”, while cities in Hebei Province are in a weak position in this regard. From the perspective of the measurement result of synergistic effects of carbon emission reduction, there is significant room for improvement in the synergistic effects of carbon emission reductions in the Beijing–Tianjin–Hebei urban agglomeration, and there are significant differences in the synergistic effects of carbon emission reduction among various cities. In general, at this stage, the core–periphery structure of the spatial network of carbon emissions in the Beijing–Tianjin–Hebei urban agglomeration is still solid, and the synergistic effects of carbon emission reduction between cities are weak. Establishing a sound synergistic mechanism of regional carbon emission reduction is the key to solving the carbon emission problem of the Beijing–Tianjin–Hebei urban agglomeration. Therefore, this study proposes countermeasures and suggestions to improve the synergistic mechanism of the reduction in carbon emissions in the Beijing–Tianjin–Hebei urban agglomeration from three levels—the formation layer, the implementation layer, and the guarantee layer—in order to promote synergistic emission reduction, ecological and environmental governance, and sustainable development of Beijing–Tianjin–Hebei urban agglomeration.

1. Introduction

Along with the in-depth advancement of major national development strategies such as the coordinated development of Beijing–Tianjin–Hebei and the construction of the Yangtze River Economic Belt, establishing a new mechanism for coordinated regional development with urban agglomeration as the main body is an important measure for China to adhere to the path of green and low-carbon development. As pivotal components of the advancement of numerous production and lifestyle components, urban agglomerations are essential nodes in the execution of strategies such as the “dual-cycle” new development model and coordinated regional growth. This agglomeration will thereby assume major responsibility and prominence in reducing carbon emissions [1]. China’s “13th Five Year Plan” and “14th Five Year Plan” have laid out 19 national-level urban agglomerations, forming a strategic pattern of urbanization of “two horizontal and three vertical”. According to 2020 statistical data, 19 urban agglomerations in China contain more than 75% of the urban population and contribute more than 80% of the gross domestic product. However, it is undeniable that China is still one of the countries with the largest carbon emissions in the world, and urban agglomerations are the areas with concentrated carbon emissions in China [2]. In view of this, under the concept of new development, the development of urban agglomeration cannot only consider the economic benefits of scale but also must place ecological functions in a more prominent position.

The Beijing–Tianjin–Hebei region is geographically interconnected, with high complementarity in industrial structure, development foundation, and resource endowment. Due to its vast population, robust technological innovation capacity and densely packed industrial and urban clusters, this area boasts exceptional political, resource-driven, and technological strengths. It stands as China’s third-largest economic growth pole, following only the Pearl River Delta and Yangtze River Delta. However, due to the significant differences in development levels within the Beijing–Tianjin–Hebei urban agglomeration and the lack of healthy cooperative relationships between cities, problems such as poor industrial correlation, unreasonable spatial layout, resource overload and environmental pollution have arisen in the Beijing–Tianjin–Hebei region [3]. In terms of environmental pollution, on the one hand, the Beijing–Tianjin–Hebei region is facing severe carbon emission growth pressure. The “Beijing–Tianjin–Hebei region Development Report (2022)” mentioned that the carbon emissions of the Beijing–Tianjin–Hebei urban agglomeration are on the rise and unevenly distributed. In 2020, the carbon emissions of the Beijing–Tianjin–Hebei urban agglomeration were 601 million tons, an increase of 335 million tons compared with 2009 (for which there were 266 million tons of carbon emissions). In the Beijing–Tianjin–Hebei region, carbon emissions in Hebei Province accounted for over 66% of the Beijing–Tianjin–Hebei region, while its GDP accounts for less than 50% of the regional economic total. On the other hand, the carbon emission intensity of the Beijing–Tianjin–Hebei region is still the highest among the three major urban agglomerations in China. In 2019, the carbon emission intensity of the Beijing–Tianjin–Hebei urban agglomeration was 14,800 tons/100 million yuan, while those of the Yangtze River Delta and Pearl River Delta regions were 9200 tons/100 million yuan and 8500 tons/100 million yuan, respectively. On this basis, ecological environment protection should be an important foundation and key task for deepening the coordinated development of the Beijing–Tianjin–Hebei region, especially in promoting carbon emission control, providing a reasonable layout of the spatial pattern of low-carbon development, establishing and improving the green and low-carbon development mechanisms, and taking the lead in forming a new pattern of green, low-carbon, and sustainable development of the regional economy.

It is of great significance to carry out carbon emission reduction work based on urban agglomeration. Firstly, the core position of urban agglomeration in various national strategic plans is constantly being consolidated and enhanced, and as an important form of carrying space for development elements, its core position will not change in the next 10–15 years; secondly, the urban agglomeration has large carbon emission, and there is a significant spatial effect on energy demand and carbon emission between adjacent cities. The general and structural regulation of carbon emission reduction in urban agglomeration is urgently needed; thirdly, the development of urban agglomeration is consistent with the dual-carbon goal, and building a spatial organizational form of urban agglomeration that matches the ecological environment pattern has become a current focus of attention. At present, the carbon-emission-reduction work in urban agglomeration still faces enormous challenges. Firstly, there is a trade-off between achieving economic growth and carbon emission reduction and achieving maximum comprehensive benefits. Secondly, there are differences in carbon emission efficiency and emission-reduction potential among different cities within urban agglomeration, and in how to achieve carbon emission reduction synergy and improve the synergy effect under this current situation. Thirdly, an understanding is needed of how to apply the concept of collaborative governance to the carbon-emission-reduction process of urban agglomeration in order to construct a set of synergistic control mechanisms for carbon emission reduction. In view of this, based on the improved gravity model, this study uses the social network analysis method and the synergistic effects model of carbon emission reduction to analyze the spatial network characteristics and synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration. At the same time, based on the theory of collaborative governance, a synergistic emission-reduction mechanism for the Beijing–Tianjin–Hebei urban agglomeration is constructed from three levels: the formation layer, the execution layer, and the guarantee layer.

2. Literature Review

Presently, research on carbon emission centers upon diverse aspects, including carbon and responsibility accounting, scenario prediction and simulation, carbon emission efficiency, influential factors, spatial characteristics, and correlations. I hope this revised version is helpful to you. The accounting research on carbon emission is mostly conducted at the regional or industrial level [4]. The research methods mostly use the carbon dioxide emission estimation method based on the calculation of apparent energy consumption in the “IPCC 2006 National Greenhouse Gas Inventory Guidelines” published by the IPCC, and it can also serve to predict future carbon emission trends [5]. Research on carbon emission responsibility accounting mainly focuses on three perspectives: producers, consumers, and income earners. From an economic perspective, carbon emission efficiency can be divided into two types: single-factor carbon emission and total-factor carbon emission. For example, the carbon dioxide emission per unit of energy consumption is used as a single factor indicator of carbon emission efficiency [6]; a comprehensive indicator of carbon emission efficiency is composed of multiple frameworks such as energy consumption, economic development and carbon emission [7]. The carbon emission rate is influenced by various factors, such as market-oriented reform [8], population economic effects [9], capital effects and resource endowment [10]. Moreover, there is spatial heterogeneity and spatial correlation between regions in carbon emission. Spatial heterogeneity is mainly manifested in regional differences in carbon emission across the country and provinces [11], and spatial correlation is mainly manifested in spatial agglomeration characteristics and spatial spillover effects [12].

Relevant scholars have conducted in-depth research on carbon emission from a multidimensional perspective, with the aim of finding entry points and path methods for carbon emission reduction. The “Kyoto Protocol” proposes four carbon emission reduction methods: emission trading, calculating greenhouse gas emissions based on net emission, the green development mechanism, and the group approach for emission reduction. Based on the above ideas, current research on carbon emission reduction mostly focuses on carbon emission trading, carbon taxes, carbon sinks, and other aspects [13]. The research object is generally a certain industry in economic and social development, such as electricity, steel, construction, transportation [14], or a certain development field, such as land use, air pollution prevention and control [15,16,17,18]. The research dimensions are divided into macro-level carbon-emission-reduction mechanisms and policies [19], meso-level standards and norms [20], micro-level performance and evaluation [21], etc. The proposal of the dual carbon strategy has put forward higher requirements for carbon-emission reduction. Under the dual carbon goal, synergistic emission reduction has become a necessary means to achieve this goal. There are two primary implications of synergistic emission reduction. Firstly, research emphasizes the synergistic benefits of various elements, such as Mao’s investigation into the combined advantages of reduction in greenhouse gases and local pollutants, while also highlighting the significance of “collaborative control” [22]; the second aspect is regional collaboration based on regional cooperation. For example, Liu explored the differences in the characteristics and potential of carbon emission reduction among different provinces in China from the perspective of provincial-level administrative units [23].

Existing research has to some extent revealed the spatial correlation and differences in carbon emission, laying the foundation for studying regional synergistic emission reduction. Urban agglomeration is a high-level phenomenon of regional spatial form that has emerged in the process of industrialization and urbanization. It is one of the symbols of the rapid development of the national economy and the continuous improvement in the modernization level [24]. Exploring carbon emission reduction synergy from the perspective of urban agglomeration can closely align with national strategic requirements. For example, Yang explored the spatiotemporal interaction relationship and driving factors between urban compactness and carbon emission intensity using the Changzhutan urban agglomeration as an example [25]; Li analyzed the spatial correlation between network structure characteristics and influencing factors of carbon emission using three major urban agglomerations in China as an example; Wang analyzed the basic characteristics and influencing factors of low-carbon layout in an urban agglomeration in China [26]. On the basis of existing research, there are still some research issues and spaces worth further exploration. Firstly, current research focuses more on the correlation between the spatial layout of urban agglomeration and carbon emission reduction, with less attention paid to issues such as the synergistic effects of carbon emission reduction in urban agglomeration; secondly, in terms of methodology, more emphasis is placed on the use of spatial econometric analysis, which only empirically examines the “attribute data” of carbon emission and does not reveal the linkage and synergistic structure between different regions from the perspective of “relational data”.

3. Analysis of the Current Situation of Carbon Emission and the Necessity of Synergistic Emission Reduction in the Beijing–Tianjin–Hebei Urban Agglomeration

3.1. Analysis of the Current Situation of Carbon Emission in the Beijing–Tianjin–Hebei Urban Agglomeration

According to reports released by the International Energy Agency and the World Bank, over 70% of global carbon dioxide emission come from urban energy consumption. The “IPCC 2006 National Greenhouse Gas Inventory Guidelines” also point out that the increase in carbon emission in the atmosphere is mainly due to the consumption of fossil fuels in human production activities and propose a method for calculating carbon dioxide emission based on apparent energy consumption. The carbon dioxide emission mentioned in this study refers to the carbon emission related to urban energy consumption. Urban carbon emission includes carbon emission generated by direct energy consumption, such as natural gas and liquefied petroleum gas, as well as carbon emission generated by indirect means such as electricity and thermal energy. The carbon emissions from direct energy consumption can be calculated using the relevant conversion factors provided in the “IPCC 2006 National Greenhouse Gas Inventory Guidelines”. The carbon emissions generated by electricity consumption are relatively complex. According to the methods of Glaeser and Kahn [27], each regional power grid has only one emission factor. The Beijing–Tianjin–Hebei urban agglomeration belongs to the category of the North China Power Grid. Based on the emission factors of the North China Power Grid baseline over the years and the electricity consumption of each city in the Beijing–Tianjin–Hebei urban agglomeration, the carbon emission generated by the electricity consumption of each city is calculated. Urban thermal energy mainly includes boiler room heating and thermal power plant heating, with raw coal being the main raw material. The “China Urban Construction Statistical Yearbook” provides statistical data on centralized heating in various cities over the years. The minimum standard for thermal efficiency of coal-fired industrial boilers specified in “GB/T 15317-2009 Energy Conservation Monitoring of Coal-fired Industrial Boilers” is between 65–78%. Considering that China’s central heating boilers are mainly small and medium-sized coal-fired boilers, a 70% thermal efficiency value is used for calculation. The average low calorific value of raw coal is 20,908 kj/kg. The necessary quantity of raw coal can be determined by considering several factors, including heat supply, thermal efficiency, and the calorific value of the raw coal. Then, the standard coal coefficient (0.7143 kgce/kg) can be used to calculate the energy consumption of centralized heating. According to the “IPCC 2006 National Greenhouse Gas Inventory Guidelines”, the carbon emission coefficient per kilogram of raw coal is 2.53 kgCO₂/kg, and the carbon emission generated by central heating can be calculated using the amount of raw coal consumed by thermal energy. In order to consider the availability of reliable energy consumption data and prevent the potential issue of double counting, this study aims to aggregate the carbon emission from various sources, including natural gas, liquefied petroleum gas, electricity, and thermal energy consumption. Ultimately, this will enable us to determine the carbon emission of each city within the Beijing–Tianjin–Hebei urban agglomeration [28]. The original data come from statistical data such as the “China Statistical Yearbook”, “China Urban Statistical Yearbook”, “China Urban Construction Statistical Yearbook”, and “China Regional Statistical Yearbook” over the years.

This study intends to compare the carbon emission intensity of each city. Carbon emission intensity generally refers to the carbon dioxide generated per unit of GDP in a country or region. The lower the carbon emission intensity, the lower the carbon emission generated per unit of GDP. From the results in

Table 1. Carbon emission intensity of each city in Beijing–Tianjin–Hebei urban agglomeration (2016–2019) Unit: ton/10,000 yuan.

City	2016	2017	2018	2019
Beijing	0.5245	0.4605	0.4510	0.3904
Tianjin	0.4216	0.4147	0.4418	0.6066
Shijiazhuang	0.7297	0.7423	0.7178	0.7627
Tangshan	0.8116	0.7758	0.6918	0.6499
Qinhuangdao	1.0029	1.0262	1.0231	1.4049
Handan	1.1220	1.2645	1.3532	1.4111
Xingtai	2.0026	1.8771	2.0946	2.2770
Baoding	0.7301	0.6945	0.7560	0.7273
Zhangjiakou	1.1240	1.1013	1.2131	1.2195
Chengde	1.3459	1.1326	1.2076	1.2166
Cangzhou	0.9504	0.8612	0.8499	0.8869
Langfang	0.5704	0.5802	0.4990	0.6873
Hengshui	1.1285	1.0068	1.1254	1.3090

, it can be seen that from 2016 to 2019, the carbon emission intensity of various cities in the Beijing–Tianjin–Hebei urban agglomeration increased and decreased, while Beijing, Tangshan, Baoding, Chengde, and Cangzhou showed a general downward trend; the carbon emission intensity in Tianjin, Shijiazhuang, Qinhuangdao, Handan, Xingtai, Zhangjiakou, Langfang, and Hengshui showed a general upward trend. In terms of the average of four years, all cities with high carbon emission intensity are concentrated in Hebei Province, including Qinhuangdao, Handan, and Zhangjiakou, while Beijing and Tianjin have lower carbon emission intensity. This is also in line with the development characteristics of the Beijing–Tianjin–Hebei urban agglomeration. Each city in Hebei Province lags far behind Beijing and Tianjin in terms of economic development level. At the same time, compared with Beijing and Tianjin, the economic development of Hebei Province is more driven by the secondary industry with higher carbon emissions, so the carbon emission intensity of each city in Hebei Province is relatively high. From the perspective of individual cities’ development, cities with increased carbon emission intensity are gradually slowing down their growth rate, while cities with reduced carbon emission intensity are increasing their reduction rate. This to some extent indicates that since the implementation of the Beijing–Tianjin–Hebei coordinated development strategy, various cities have achieved certain results in industrial structure adjustment, ecological environment protection, and other aspects. However, it is undeniable that there is still a significant difference in carbon emission intensity between the Beijing–Tianjin–Hebei urban agglomeration, and collaborative emission reduction will become the top priority of carbon emission reduction work in the Beijing–Tianjin–Hebei urban agglomeration.

3.2. Analysis of the Necessity of Synergistic Emission Reduction in Beijing–Tianjin–Hebei Urban Agglomeration

3.2.1. Synergistic Emission Reduction Helps Improve the General Emission Reduction Effects of Urban Agglomeration

The imbalance in the internal development of the Beijing–Tianjin–Hebei urban agglomeration determines that carbon reduction work must be in line with the actual development of each city, and the “one-size-fits-all” emission reduction strategy is clearly not reasonable. For cities that have made significant progress in carbon reduction work, due to their limited space for emission reduction, their intention to reduce emissions is relatively weak; for cities that have not made significant progress in carbon reduction work, although their willingness to reduce emission is high, the reduction effect is not significant due to the needs of economic development. From the perspective of emission reduction potential, cities that have made great progress have low carbon-emission intensity and high shadow price of carbon emission, which means that their emission reduction costs are large. Compared with cities that have not made great progress in carbon emission reduction, their economic costs for reducing the same carbon emission are large. As the main body of urban agglomeration, cities are not only the actual bearers of carbon emission reduction tasks but also important drivers of regional economic development [29,30,31]. Therefore, the development of Beijing–Tianjin–Hebei urban agglomeration needs to comprehensively balance economic growth and carbon emission reduction in order to achieve maximum comprehensive benefits. At the same time, considering the public goods attribute of carbon emission, synergistic emission reduction can effectively prevent free riding behavior between cities. Notably, many cities in Hebei Province have a notable economic disparity with Beijing and Tianjin, resulting in inadequate governance capabilities and efforts toward carbon emission reduction when compared with the aforementioned cities. This requires adopting a synergistic approach to reduce carbon emission and treating the Beijing–Tianjin–Hebei urban agglomeration as a unified whole.

3.2.2. Synergistic Emission Reduction Is More Conducive to Optimizing Resource Allocation within Urban Agglomeration

In comparison to independent emission reduction efforts, collaborative emission reduction strategies within the Beijing–Tianjin–Hebei urban agglomeration can facilitate the optimization of resource utilization and the reduction in negative externalities associated with carbon emission through intercity cooperation. The total population, industrial structure, energy intensity, and other factors of the Beijing–Tianjin–Hebei urban agglomeration have a significant positive correlation with the total carbon emission, while the economic development and urbanization level, respectively, exhibit an inverted U-shaped and positive U-shaped curve relationship with the total carbon emissions [32]. From the current development stage of the Beijing–Tianjin–Hebei urban agglomeration, it can be seen that Beijing has entered a stage of high urbanization and post-industrialization development. Its total urban population is close to saturation, and there is little space to further reduce the proportion of the secondary industry and energy intensity. Cities in Hebei Province are still in the stage of rapid urbanization and industrialization, and there is a large amount of space for improvement in economic development, urbanization level, industrial structure, energy intensity, and other aspects. Due to the marginal diminishing effect of output, the cost of reducing emissions increases as economic development accelerates. Therefore, if the same investment is used for cities in Beijing, Tianjin and Hebei, the emission reduction effects will inevitably be completely different. If, in the context of synergistic emission reduction, due to differences in resource endowments, cities achieve resource complementarity through collaborative cooperation, it will inevitably enhance the potential for carbon emission reduction and the effective utilization of resources. For example, the three governments have transferred part of the tertiary industry in Beijing to Hebei cities through cooperation and evacuated part of the population to Hebei cities, while providing economic compensation for environmental protection. On the one hand, this can not only directly drive the improvement in the industrial structure of the Beijing–Tianjin–Hebei urban agglomeration, solve problems such as uneven distribution of population density and large gaps in economic development within the urban agglomeration, and achieve optimal allocation of resources. On the other hand, it can directly drive the transformation of traditional high energy-consuming industries in various cities in Hebei Province, promote innovative development of green and low-carbon technologies, and directly reduce the general carbon emission of urban agglomeration.

4. Analysis of Spatial Correlation Characteristics of Carbon Emission and Synergistic Effects of Carbon Emission Reductions in Beijing–Tianjin–Hebei Urban Agglomeration

The large differences in carbon emissions between regions inevitably lead to conflicts of interest between regions when formulating carbon emission reduction policies and allocating carbon-emission-reduction tasks. The achievement of a region’s emission reduction goal depends not only on its own factors but also on the influence of other regions. The effective control of carbon emissions increasingly depends on regional coordination and cooperation. There are significant differences among the cities in the Beijing–Tianjin–Hebei urban agglomeration in terms of economic development level, industrial structure, energy intensity, total carbon emission, and other factors. It is difficult to achieve the general regional emission reduction goal by only relying on the individual reduction in emissions in each city. This problem can be fundamentally solved only through synergistic emission reduction among cities. Therefore, it is necessary to comprehensively understand the carbon emission correlation between cities in the Beijing–Tianjin–Hebei urban agglomeration and analyze the synergistic effects of carbon emission reductions in the Beijing–Tianjin–Hebei urban agglomeration. This study takes the Beijing–Tianjin–Hebei urban agglomeration as the research object and, based on the exploration of the spatial network correlation of carbon emission, measures the synergistic effect of carbon emission reduction, in order to provide a quantitative basis for the subsequent construction of urban agglomeration collaborative emission reduction mechanisms and the improvement in collaborative emission reduction policies [25,26,27,28,29].

4.1. Research Method and Data Sources

Social network analysis is a quantitative analysis method for “relationship data”. The determination of “relationship” is the key to social network analysis. At present, there are two main methods: the vector autoregression model and the gravity model. The gravity model is not only applicable to aggregate data, but can also comprehensively consider economic and geographical factors. Therefore, this study uses an improved gravity model to describe the spatial correlation of carbon emission of cities in the urban agglomeration. The basic formula is

$$G_{ij}=\frac{C_i}{C_i+C_j}\times \frac{\sqrt[3]{P_i{C}_i{E}_i}\times \sqrt[3]{P_j{C}_j{E}_j}}{{{\displaystyle [D_{ij}/(e_i-e_j)]}}^2}$$

(1)

In Formula (1), i and j represent cities i and cities j; G, C, D, P, E, and e, respectively, represent carbon emission gravity, carbon emission, space distance, total population, Gross Regional Product, Per Capita Gross Regional Product; and D_ij/(e_i−e_j) means the “economic distance” between cities.

The gravity matrix of carbon emission for urban agglomeration can be obtained from Formula (1), and the average value of each row in the matrix is selected as the critical value. If the value exceeds the critical value, it is set to “1”, which indicates that there is a carbon emission correlation between the two cities in the corresponding row and column; otherwise, it is set to “0”, indicating no correlation. In this way, the spatial correlation matrix of carbon emission for urban agglomeration can be constructed.

Using social network analysis, network density, network degree centrality, and network efficiency are used to reflect the general network structural characteristics of spatial correlation of carbon emission. Network density reflects the closeness of spatial correlation, with higher network density indicating closer carbon emission relationships between cities. Network degree centrality reflects the degree to which nodes are asymmetrically reachable, with a higher degree indicating a stricter hierarchical structure between cities. Network efficiency reflects the degree of redundant connections in the network, with lower network efficiency indicating more connections between cities, tighter carbon emission relationships, and more spatial overflow channels. The basic formulas are

$$ND=m/[n(n-1)/2]$$

(2)

$$NH=1-S/max(S)$$

(3)

$$NE=1-V/max(V)$$

(4)

In Formulas (2)–(4), ND, NH, NE represent network density, network degree, and network efficiency, respectively; m represents the actual number of relationships in the spatial relationship matrix; n represents the number of network nodes; S represents the number of symmetrically reachable pairs in the spatial relationship matrix; max(S) represents the number of pairs where i is reachable to j or j is reachable to i; V represents the number of extra lines; and max(V) represents the maximum possible number of extra lines.

Centrality is another one of the focal points in social network analysis, which utilizes degree centrality, betweenness centrality, and closeness centrality to reflect the structural characteristics of individual networks in spatial carbon emission correlations. Degree centrality measures the degree to which an individual city occupies a central position in the spatial network; betweenness centrality reflects the degree to which a city controls the relationships among other cities; and closeness centrality characterizes the degree to which it is not controlled by other nodes. In short, the higher the centrality of a city, the greater its control over the connections between carbon emission of other cities in the urban agglomeration. The basic formulas are

$$C_{RD}(i)=C_{AD}(i)/(n-1)$$

(5)

$$C_{RB}(i)=\frac{2{\displaystyle \sum _{j<k}{r}_{jk}(i)/r_{jk}}}{(n-1)(n-2)}$$

(6)

$$C_{Rp}(i)=(n-1)/{\displaystyle \sum _{j=1}^n{d}_{ij}}$$

(7)

In Formulas (5)–(7), CRD(i) represents degree centrality; CRB(i) represents betweenness centrality; CRP(i) represents closeness centrality; CAD(i) represents the number of other points connected to point i; rjk represents the number of relationship paths between city j and city k; rjk(i) represents the number of paths that pass through city i; dij represents the shortest distance between city i and city j in terms of government.

Due to the existence of externalities, carbon emission reduction in urban agglomeration requires collaborative governance among regions to achieve fundamental effectiveness. In the collaborative governance process of carbon emission reduction, regions with high economic development and low pollution levels are regarded as “benchmarks” for learning. The occurrence of consistent and similar changes in pollutant emission between the benchmark regions and other regions in the urban agglomeration is considered to have produced a “benchmark synergy” emission reduction effect between regions [33]. Therefore, this study draws on the method of Cerqueira P A and Martins R to construct a model of a carbon-emission-reduction synergy effect in urban agglomeration [34]. The basic formula is

$${Corr}_{bi,t}=1-\frac{1}{2}{{\displaystyle \left[\frac{\left(C_{b,t}-\overline{C_b}\right)}{\sqrt{\frac{1}{t}{\displaystyle \sum _1^t{{\displaystyle (C_{b,t}-\overline{C_b})}}^2}}}-\frac{\left(C_{i,t}-\overline{C_i}\right)}{\sqrt{\frac{1}{t}{\displaystyle \sum _1^t{{\displaystyle (C_{i,t}-\overline{C_i})}}^2}}}\right]}}^2$$

(8)

In Formula (8), Corrbi,t represents the synergistic effect of carbon emission reduction between city i and the “benchmark” city in urban agglomeration t. The closer its value is to 1, the higher the degree of synergy. Cb,t represents the total carbon emission of the “benchmark” city.

For this study, a spatial relationship matrix was established using thirteen cities in the Beijing–Tianjin–Hebei urban agglomeration as network nodes. The carbon emission calculation method employed for each city was based on Wu’s methodology [28]. The original carbon emission data were obtained from various statistical materials such as the China Statistical Yearbook, the China City Statistical Yearbook, the China Urban Construction Statistical Yearbook, and the China Regional Statistical Yearbook. The data sources of electricity, gas, liquefied petroleum gas, transportation, and thermal energy consumption required for calculating carbon emission are relatively complex, and specific references can be made to Wu’s literature [28]. Population, GDP, and per capita GDP data also came from the China City Statistical Yearbook of previous years. The geographical distance was calculated from the central longitude and latitude of each city.

4.2. Result Analysis

4.2.1. The General Characteristics of Carbon Emission Space Network

Using the improved gravity model in Formula (1), this study first calculates the carbon emission gravity matrix of the Beijing–Tianjin–Hebei urban agglomeration and converts it into a spatial correlation matrix. In order to demonstrate the spatial structure of the carbon emission network in the Beijing–Tianjin–Hebei urban agglomeration more effectively, this study uses the visualization tool Netdraw in Ucinet 6.0 software to draw the carbon emission spatial correlation network from 2016 to 2019. The specific results are shown in Figure 1.

As shown in Figure 1, there are almost universal spatial correlation relationships for carbon emissions among cities in the Beijing–Tianjin–Hebei urban agglomeration, and the spatial network structure of carbon emissions has been relatively stable over the years. In addition, with Beijing and Tianjin as the core cities, the carbon emission spatial correlation network in the Beijing–Tianjin–Hebei urban agglomeration presents a typical “central-peripheral” structural pattern. In order to better understand the network structure of carbon emission spatial correlations within the Beijing–Tianjin–Hebei urban agglomeration, this study aims to analyze the characteristics of the carbon emission spatial network from two perspectives: global network features and individual level features. Regarding network global features, the network density, network hierarchy, and network efficiency of the carbon emission spatial correlation network in the Beijing–Tianjin–Hebei urban agglomeration from 2016 to 2019 were calculated based on Formulas (2)–(4). The results are shown in

Table 2. The global features of the carbon emission spatial correlation network of Beijing–Tianjin–Hebei urban agglomeration (2016–2019).

	2016	2017	2018	2019
Density	0.1603	0.1603	0.1538	0.1538
Hierarchy	0.8571	0.8444	0.8511	0.8444
Efficiency	0.8636	0.8636	0.8788	0.8444

.

According to Table 2, the network density of the carbon emission spatial network in the Beijing–Tianjin–Hebei urban agglomeration showed a continuous downward trend from 0.1603 in 2016 to 0.1538 in 2019, indicating a sustained reduction in the spatial correlation of carbon emission among cities in the region. From this perspective, cities need to strengthen their carbon reduction cooperation with each other. The network hierarchy exhibited a fluctuating pattern of first decreasing, then increasing, and then decreasing again, with a fluctuation range around 0.8400–0.8600. The mean network hierarchy over the four years was 0.8493, indicating a strict hierarchical structure among cities in the Beijing–Tianjin–Hebei urban agglomeration, where a few cities occupy the central positions of the carbon emission spatial network. The network efficiency continued to increase from 2016 to 2018, with a slight decrease in 2019 but still at a relatively high level. This indicates that the current connections within the carbon emission spatial network are able to maintain network stability. However, it also showed the existence of unnecessary links and overlapping issues in carbon emission spatial overflow. The global features of the carbon emission spatial correlation network of the Beijing–Tianjin–Hebei urban agglomeration demonstrate the stability and inefficiency of the carbon emission network in the Beijing–Tianjin–Hebei region. Only by complementing and through mutually beneficial cooperation among cities, as well as establishing a collaborative emission reduction mechanism, can this problem be solved.

4.2.2. Individual Characteristics of Carbon Emission Space Network

In terms of the individual characteristics of the carbon emission spatial network in the 2019 Beijing–Tianjin–Hebei urban agglomeration, this study calculates the three indicators of the degree, betweenness, and closeness of the Beijing–Tianjin–Hebei urban agglomeration according to Formulas (5)–(7), as shown in

Table 3. The individual features of the carbon emission spatial correlation network of the Beijing–Tianjin—Hebei urban agglomeration (2019).

City	Degree	Betweenness	Closeness
Beijing	100.000	75.758	100.000
Tianjin	58.333	11.364	70.588
Shijiazhuang	16.667	0.000	54.545
Tangshan	25.000	0.758	57.143
Qinhuangdao	16.667	0.000	54.545
Handan	16.667	0.000	54.545
Xingtai	16.667	0.000	54.545
Baoding	16.667	0.000	54.545
Zhangjiakou	8.333	0.000	52.174
Chengde	16.667	0.000	54.545
Cangzhou	16.667	0.000	54.545
Langfang	8.333	0.000	52.174
Hengshui	16.667	0.000	54.545

.

According to Table 3, among the 13 cities in the Beijing–Tianjin–Hebei urban agglomeration, the degree of Beijing and Tianjin is significantly greater than other cities, indicating that Beijing and Tianjin are in the central position in the carbon emission network of Beijing–Tianjin–Hebei urban agglomeration. As far as betweenness is concerned, Beijing occupies an absolute core position. Tianjin is the second, and the other cities are far lower than Beijing and Tianjin. It can be seen that Beijing and Tianjin, which are located in the center of the carbon emission space of the Beijing–Tianjin–Hebei urban agglomeration, also play an important “betweenness” and “bridge” role in the carbon emission space network, and other cities are in a weak position in the network. This shows that Beijing and Tianjin, as the core cities of the Beijing–Tianjin–Hebei urban agglomeration, have absolute advantages in terms of economic development, industrial structure, and energy consumption in various cities in Hebei Province. The closeness of Beijing and Tianjin is as high as 100.000 and 70.588, respectively, indicating that the network distance between Beijing and Tianjin and other cities has a small distance. There are fewer direct connections between the cities of Hebei Province and other cities. In summary, the collaborative promotion of carbon emission reduction among cities will be a key task in the future coordinated development of Beijing–Tianjin–Hebei urban agglomeration. At the same time, it is urgent and necessary to analyze the synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration based on the clear characteristics of the Beijing–Tianjin–Hebei carbon emission spatial network.

4.2.3. The Synergistic Effects of Carbon Emission Reduction in the Beijing–Tianjin–Hebei Urban Agglomeration

According to Formula (8), this study selected Beijing as an example of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration, using carbon emission data in various cities in the Beijing–Tianjin–Hebei urban agglomeration; for Beijing, from 2016 to 2019, the synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration are calculated (

Table 4. The synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration (2016–2019).

City	2016	2017	2018	2019	Mean
Tianjin	−0.032	0.958	0.983	0.947	0.714
Shijiazhuang	0.926	0.459	0.598	0.368	0.588
Tangshan	0.930	0.535	0.536	0.187	0.547
Qinhuangdao	0.934	0.460	0.617	0.332	0.586
Handan	0.926	0.462	0.633	0.385	0.602
Xingtai	0.936	0.462	0.618	0.351	0.592
Baoding	0.933	0.462	0.615	0.348	0.589
Zhangjiakou	0.937	0.466	0.618	0.344	0.591
Chengde	0.938	0.461	0.606	0.324	0.582
Cangzhou	0.934	0.466	0.614	0.341	0.589
Langfang	0.940	0.465	0.611	0.318	0.584
Hengshui	0.934	0.461	0.617	0.343	0.589
Mean	0.853	0.510	0.639	0.382	0.596

).

According to Table 4, the synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration showed a decreasing, slightly increasing, and decreasing trend from 2016 to 2019. The average synergistic emission reduction effect decreased from 0.853 in 2016 to 0.510 in 2017, then slightly increased to 0.639 in 2018, and finally fell back to 0.382 in 2019. The main reason for this trend is the imbalanced development among various cities in the Beijing–Tianjin–Hebei urban agglomeration. As a national political, economic, technological, and cultural center, Beijing has great potential for carbon emission reduction, and its carbon emissions have been able to be controlled at a reasonable level for a long time. Other cities in the Beijing–Tianjin–Hebei urban agglomeration are vigorously promoting industrialization and urbanization, and the carbon emission levels of each city are showing a sustained growth trend. In the process of relieving Beijing’s noncapital functions, many cities in Hebei Province have played the role of undertaking Beijing’s high pollution enterprises, resulting in high carbon emission levels in most cities of Hebei Province in a short period of time. In general, the average synergistic effect of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration from 2016 to 2019 was 0.596, and there is still significant room for improvement in the level of synergistic emission reduction. From the perspective of various cities, there are also significant differences in carbon emission reduction synergies. Tianjin, Handan, Xingtai, Zhangjiakou, and Beijing have relatively high carbon-emission-reduction synergies, while other cities in Hebei Province have relatively low carbon-emission-reduction synergies with Beijing, with Tangshan having the lowest. Due to the division of administrative divisions, the contradiction between ecological protection and economic development, and other objective reasons, Beijing has an absolute advantage over other cities in terms of economic development, industrial structure, energy consumption, etc.; understanding how to promote the green and healthy transformation of industries in carbon emission reduction vulnerable cities; changing their economic development model of high investment, high consumption and high emissions; and building an effective coordinated emission reduction mechanism. Therefore, coordinating with the learning benchmark of carbon reduction work in Beijing will be an important task in the future.

5. Conclusions and Discussion

Based on the spatial network characteristics of carbon emission in the Beijing–Tianjin–Hebei urban agglomeration, it can be seen that the carbon emission spatial network exhibits a typical core–periphery structure. Looking at the general spatial network characteristics, the carbon emission levels between cities within the Beijing–Tianjin–Hebei region display a strong and stable network structure. From the perspective of individual spatial network characteristics, Beijing and Tianjin are the centers of the carbon emission spatial network in the Beijing–Tianjin–Hebei region, playing an important role as “intermediaries” and “bridges”, while cities in Hebei Province are in a weaker position in this regard. From the perspective of measuring the carbon emission reduction synergy, there is still a large space for improvement in the carbon emission reduction synergy in the Beijing–Tianjin–Hebei urban agglomeration, and the differences in synergistic effects of carbon emission reduction are significant. In general, the core–periphery structure of the carbon emission spatial network in the Beijing–Tianjin–Hebei urban agglomeration is still relatively stable at present, but the synergistic effect of carbon emission reduction is weak. According to the theory of collaborative governance, an important prerequisite for collaborative development between systems or behavioral entities is to establish a collaborative governance mechanism with multiple subjects. In view of this, with the introduction of new development concepts and dual-carbon strategic goals, establishing a synergistic emission reduction mechanism is an inevitable choice for China’s future. Therefore, this study proposes policy recommendations to improve the synergistic emission reduction mechanism in the Beijing–Tianjin–Hebei urban agglomeration at three levels: formation, implementation, and guarantee.

The formation layer of the carbon emission reduction synergy mechanism in the Beijing–Tianjin–Hebei urban agglomeration includes a conceptual consensus and a goal-driven dual mechanism. Among them, the conceptual consensus is the ideological foundation and starting logic of the formation layer. As for the Beijing–Tianjin–Hebei urban agglomeration, in recent years, Beijing has continuously optimized its industrial structure, alleviated noncapital functions, and achieved significant carbon reduction effects. At the same time, the steel and power industries in Hebei Province have a large scale and high carbon emission intensity and have not yet reached their carbon peak. The objective differences in industrial structure layout make the emission reduction work of the Beijing–Tianjin–Hebei urban agglomeration face multiple objective contradictions between regions, industries, economic development, and carbon reduction. Therefore, the issue of carbon emission reduction in the Beijing–Tianjin–Hebei region has become a regional cross-border environmental public issue. Only by coordinating and cooperating with different regional entities based on their functional advantages, action preferences, and resource conditions can we strengthen functional integration, action coordination, and resource complementarity among different entities, thereby achieving coordinated emission reduction in the Beijing–Tianjin–Hebei urban agglomeration [35]. This constitutes the conceptual consensus foundation of the collaborative mechanism of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration. The meaning of goal-driven is the goal set by the action subject to coordinate the conflicts of interest between regions and maximize the realization of regional public interests. As early as 2013, the State Council issued the “Action Plan for Air Pollution Prevention and Control”, which stipulated the goals for air pollution prevention and control in the Beijing–Tianjin–Hebei urban agglomeration and required the establishment of a collaborative mechanism for air pollution prevention and control in the Beijing–Tianjin–Hebei urban agglomeration. Practice has proven that the air quality in the Beijing–Tianjin–Hebei urban agglomeration has significantly improved after years of governance. As of 2021, the air quality in Beijing has fully reached the national second-level standard for the first time; the concentration of PM2.5 in Tianjin decreased by 62.3% compared with 2013; in 2022, all cities in Hebei Province will withdraw from the “bottom ten” list of national key cities in terms of air quality. In terms of carbon reduction, the report of the 20th National Congress of the Communist Party of China has made a top-level design for carbon reduction in the Beijing–Tianjin–Hebei urban agglomeration at a high level. The report proposes to deeply implement the regional coordinated development strategy and major regional strategies and to promote regional coordinated development as one of the important aspects of accelerating the construction of a new development patterns and promoting high-quality development. On this basis, the Beijing–Tianjin–Hebei urban agglomeration should introduce more policies to strictly control the total coal consumption and coordinate and deploy various aspects such as energy facility construction, energy governance, green energy development, and energy policies.

The implementation level of the synergistic emission reduction mechanisms in the Beijing–Tianjin–Hebei urban agglomeration includes three mechanisms: organizational integration, subject integration, and element integration. Organizational integration refers to the establishment of specific organizations to handle coordination matters between different city governments in order to optimize the carbon-emission-reduction workflow among cities and achieve established goals. The experience of the Beijing–Tianjin–Hebei Free Trade Zone has provided effective paths for three types of organizational integration: joint conference mechanisms, think tank alliance forums, and cooperative coordination working groups. These paths can provide valuable lessons for cross-regional collaboration in carbon-emission-reduction efforts. The competent finance, energy, transportation, and industrial departments of Beijing, Tianjin, and Hebei provinces can establish a joint conference mechanism to construct a communication and coordination platform for different regional government departments at a high level, taking into account the actual development of each region in the process of formulating carbon-emission-reduction plans while reducing the “free-rider” phenomenon during the cooperative carbon emission reduction process [36]. Subject integration refers to fully mobilizing enterprises, social organizations, and individual citizens to participate in the carbon emission reduction work of the Beijing–Tianjin–Hebei urban agglomeration through multiple means such as policy support and market mechanisms. Subject integration requires the establishment of a clear and coordinated carbon-emission-reduction execution system with well-defined responsibilities for government departments at different levels, in different regions, and in different fields. Meanwhile, the government should support social capital to enter the carbon emission reduction work through policy tools such as fiscal and taxation policies, creating a healthy and sustainable “PPP” relationship. The Opinions on Financial Support for Carbon Peak carbon neutrality issued by the Ministry of Finance includes measures such as setting up a national low-carbon transformation fund, encouraging social capital to set up a green low-carbon industry investment fund in a market-oriented manner, and including eligible green low-carbon development projects in the scope of government bond support. The Beijing–Tianjin–Hebei urban agglomeration can introduce new policies based on these policies, in order to better meet the synergistic emission reduction needs of the Beijing–Tianjin–Hebei urban agglomeration. Element integration refers to the effective integration and allocation of a series of elements, including talent, technology, information, material, and financial resources. The supporting policies for element integration come from the policy transformation of both top-down and bottom-up integration and internal and external integration. Top-down integration refers to integrating innovative practices and experiences from local and grassroots levels from the perspective of the overall Beijing–Tianjin–Hebei urban agglomeration. Internal and external integration refers to integrating more mature policy solutions and institutional texts from other fields from outside to inside. The specific types of element integration generally include exploratory pilots, demonstration pilots, experimental zones, and so on.

The role of the guarantee layer of the synergistic emission reduction mechanism in the Beijing–Tianjin–Hebei urban agglomeration is to provide supporting institutional guarantees for coordinated carbon emission reduction work, ensuring orderly and efficient operation through a dual mechanism of legal and regulatory guarantees. Legal guarantees refer to the application of laws and regulations to constrain the behavior of the main actors involved in coordinated carbon emission reduction in the Beijing–Tianjin–Hebei region, avoiding behaviors that violate the legitimate rights of other actors and ensuring and regulating the performance of PPP projects by local governments. The focus is on establishing a cross-regional legislative coordination mechanism for the Beijing–Tianjin–Hebei region based on principles of complementary advantages, mutual benefit, and regional integration, and enacting local regulations applicable to all three regions regarding carbon emission reduction work. Meanwhile, existing local regulations or government rules that do not meet the requirements of coordinated governance should be revised or repealed. Regulatory guarantees refer to the establishment of a supporting mechanism at the level of standardized norms by unifying production emission standards and project requirements in the Beijing–Tianjin–Hebei urban agglomeration [35]. The Beijing–Tianjin–Hebei urban agglomeration has already achieved uniformity in motor vehicle emission standards, which can be further expanded to include unified standards covering carbon trading rules, pollutant recognition standards, greenhouse gas emission measurement systems, and other aspects to promote coordinated carbon control work.

There are some limitations to this study. Considering the availability of carbon emission calculation data, the study period was set between 2016 and 2019. This time period is before the introduction of China’s dual-carbon strategy and therefore cannot measure the synergistic effects of carbon emission reduction in the Beijing–Tianjin–Hebei urban agglomeration after the implementation of the dual carbon strategy. The introduction of the dual-carbon strategy will elevate China’s path to green development to a new level and become one of the main themes of economic and social development in China for decades to come. Therefore, this study will continue to deepen, focusing on the goals of the dual-carbon strategy in future research, with the aim of providing references for the implementation of national strategies in urban agglomeration.