Analysis of Spatial Correlation and Influencing Factors of Building a Carbon Emission Reduction Potential Network Based on the Coordination of Equity and Efficiency

Abstract

Collaborative promotion of carbon emission reduction has become one of the most significant strategies for China to realize the dual-carbon goal. The purpose of this study is to utilize “relational data” to investigate overall and regional building carbon emission reduction networks based on the coordination of equity and efficiency. Specifically, the difference in importance between equity and efficiency principles is measured by an improved Markov chain. The spatial correlation network is constructed under the principle of coordinating equity and efficiency, and the network is analyzed using the modified gravity model and social network analysis. The results indicate that (1) the long-term “low-efficiency” problem of building carbon emissions is more serious than the long-term “low-equity” problem, and (2) the efficiency principle should be given greater weight in calculating carbon emission reduction potential. (3) The strength of network spatial association is increasing, and the spillover effect is significant, but the network form remains unstable. (4) The network is significantly impacted by geographic proximity, environmental regulations, energy consumption intensity, and the development level of the construction industry. The main achievement will assist developing countries in promoting sustainable development and collaborative carbon emission reduction in the construction sector.

1. Introduction

Global warming induced by the substantial emission of carbon dioxide has profoundly influenced the environment and posed a serious threat to the survival of humanity. Consequently, mitigating carbon dioxide emissions has emerged as a shared objective among nations worldwide. The Paris Agreement, which aims to keep temperature rises to 1.5–2 °C, was adopted by almost 200 nations during the Paris Climate Change Conference in 2015 [1]. China, as the largest developing nation globally, has demonstrated its commitment to global environmental protection. During the Paris Climate Conference, China pledged to reduce CO₂ emissions per unit of GDP by 60–65% by 2030, compared to 2005 levels [2]. Furthermore, at the 75th UN General Debate, President Xi Jinping proposed a “dual carbon” target, aiming to peak CO₂ emissions by 2030 and achieve carbon neutrality by 2060 [3].

As a significant contributor to carbon emissions and pollution, the construction industry plays a crucial role in achieving carbon emission reduction targets. According to the Research Report on Energy Consumption and Carbon Emissions in China’s Construction, China’s construction industry has produced an astounding 5.08 billion tons of CO₂ and will account for 50.9% of the nation’s overall carbon emissions by 2020 [4]. These findings highlight the criticality of reducing carbon emissions in the construction industry to meet China’s “dual carbon” target. In the 14th Five-Year Plan for national economic and social development, the Party Central Committee has emphasized the collective effort required to promote pollution and carbon reduction. Given China’s vast size, regional disparities exist in the level of development within the construction industry, leading to variations in construction-related carbon emissions. Moreover, the production of building materials in specific regions contributes to carbon emissions, while the consumption of these materials occurs in different regions, resulting in a transfer of construction carbon emissions across locations. Neglecting the transfer of construction carbon emissions between regions can hinder the full realization of government-enacted emission reduction policies, potentially leading to isolated reductions in carbon emissions in certain areas but an overall increase [5]. Consequently, achieving effective carbon emission reduction in the construction industry necessitates comprehensive consideration from the perspective of regional collaborative governance.

In this context, a comprehensive assessment and clarification of the relationship between the carbon reduction potential of buildings across provinces and regions assume particular significance. Given the disparities in economic development, the level of advancement within the construction industry, and the energy structure across provinces and regions, it becomes imperative to consider comprehensively the principles of equity and efficiency when evaluating the carbon reduction potential of buildings. From the point of view of the principle of equity, it is necessary to consider the differences in the development of the construction industry between regions and appropriately measure the regional emission reduction capacity. From the viewpoint of the principle of efficiency, it is necessary to take into account the strength of the regional construction industry’s ability to reduce emissions and reasonably assess the regional emission reduction capacity. Consequently, this study employs a formula proposed by Wei et al. [6], which incorporates both equity and efficiency factors, to assess the carbon reduction potential. Based on this, the correlation of regional carbon emission reduction potential is examined from a global viewpoint, taking into account that the regional carbon emission reduction potential of buildings is unequal and that the correlation between regions is continuously strengthening. This research holds significant implications for achieving the “dual carbon” target and is vital for promoting synergistic actions toward mitigating carbon emissions in the building sector.

This study makes several significant contributions. Firstly, it clarifies the coordination and importance of efficiency and equity in evaluating the carbon reduction potential of buildings, providing a clearer understanding of the relationship between them. On this basis, we calculate the carbon reduction potential of buildings in each province and construct a building carbon reduction network. Secondly, this study investigates the building of carbon emission reduction networks in both global and regional dimensions by using “relational data” and a combination of the modified gravity model and social network analysis. In the context of the expanding trend of networking in the construction sector, relational data is better suited for collecting more conclusions when compared to attribute data. Additionally, the multidimensional analysis allows for a more accurate interpretation of the interactions between the provinces in terms of carbon emissions reduction. Finally, a quadratic assignment procedure is utilized to analyze the variables influencing the network of building carbon reduction potential. These findings can provide a reference for China as well as other developing countries to promote sustainable development and the coordinated management of carbon emissions in the construction industry.

2. Literature Review

2.1. Principles for Measuring Carbon Reduction Potential

The issue of environmental climate change caused by massive carbon dioxide emissions has attracted widespread attention, and numerous scholars in China and abroad have conducted studies on carbon emission reduction. Currently, the principles of equity and efficiency are widely accepted in studies on carbon emission reduction research.

In terms of equity, a region with a higher level of economic development or greater carbon emissions should bear a bigger portion of the burden of carbon emissions reduction [7]. In other words, it is legitimate and equitable to evaluate a region’s capacity to reduce carbon emissions in light of regional differences in economic development or carbon emissions. According to previous studies, disparities in economic development, energy intensity, industrial structure, and population size are the primary causes of variances in regional capacity to reduce carbon [8,9,10,11]. Gan et al. [12] chose carbon emissions per unit of floor area and carbon emissions per capita as indicators in their study of carbon inequity in the construction industry, and the results showed that carbon emissions per unit of floor area were an important factor in exacerbating inequity. The findings demonstrate that carbon emissions per unit of floor area are a significant contributor to the escalation of inequality.

In terms of efficiency, the stronger the emission reduction capacity of a region, the heavier the responsibility for carbon emission reduction it should bear [13]. Specifically, when different locations have the same inputs, the regions with more desired outputs and lower carbon emissions are regarded as having a better carbon emission reduction capacity. Data envelopment analysis (DEA) models [14] and their evolution models [15,16] now make up the majority of models used to determine carbon emission efficiency. Among them, models with a maximum efficiency value exceeding one are called “super-efficiency models” [17,18]. These models allow for a more thorough study of units when there are several units with efficiency values of 1, as opposed to data envelopment analysis models with a maximum efficiency value of 1.

Only a few researchers have combined the principles of equality and efficiency [18] in their studies, and the majority of researchers have done studies on carbon emissions based on either one of the principles of equity [12] or efficiency [15]. There are almost no studies that combine the two principles on the carbon reduction potential of buildings.

2.2. Methods of Spatial Network Analysis

Currently, spatial network analysis has two primary facets. One is to evaluate the relevance of spatial networks, and the other is to analyze the structure of spatial networks.

The Moran index, Granger causality test, and gravity model are the three basic correlation measurements of spatial networks in previous research [19]. The gravity model, which can assess both the overall spatial correlation and the spatial correlation between individuals, performs better than the previous two techniques [8]. However, since the traditional gravity model has the flaw of neglecting the bi-directionality and asymmetry of spatial correlation between nodes [20], the model needs to be modified when analyzing the potential of carbon emission reduction. Social network analysis (SNA), as an important method for spatial network structure analysis, can fully explore and analyze relational data. Many academics have used the gravity model and SNA as crucial techniques for spatial network analysis in their actual research. Liu and Xiao [21] used a modified gravity model and SNA to analyze the spatial network of China’s industrial carbon emissions after obtaining the data for the study from several statistics yearbooks. Wang et al. [22] obtained CO₂ emissions, population, and GDP data for each state through the U.S. Energy Information Administration, the U.S. Census Bureau, and the Bureau of Economic Analysis. Using SNA and an improved gravity model, spatial correlation networks of carbon emissions in the fifty states of the United States were examined based on these data.

2.3. Analysis of Factors Affecting Carbon Emission Reduction

To better achieve carbon emission reduction, many scholars have analyzed the factors affecting carbon emission reduction. Most of the existing studies use attribute data to analyze and research, and most of them are about a specific region or industry. Jiang et al. [23] used remote sensing night-lighting technology to obtain the carbon emission data of 358 cities in China. On this basis, they analyzed the factors influencing the reduction of carbon emissions, and the results showed that the development of clean energy can effectively reduce carbon emissions. Li et al. [24] took the eleven cities in Guangdong, Hong Kong, Macao, and the Greater Bay Area as the research object and obtained relevant data through carbon emission accounts and data sets (CEADs) and statistical yearbooks to analyze the factors influencing the reduction of carbon emissions. Zeng and He [25] analyzed the inter-provincial carbon emission data of the transport industry, and the results showed that strengthening regulation can effectively achieve carbon emission reduction in the transport industry. Li et al. [26] measured and analyzed the carbon emissions of the iron and steel industry using relevant statistical yearbooks, and the results showed that capacity and energy efficiency are significant drivers of carbon emission reduction.

2.4. Summary of Literature Review

Existing studies can offer a solid foundation for our research, but there are still certain limitations. Firstly, most academics have conducted research on carbon reduction potential only under one principle of equity or efficiency, and few scholars have performed investigations based on the coordination of equity and efficiency. Secondly, in their study on carbon emission reduction, most researchers employ “attribute data”, and just a few use “relational data”. Thirdly, most academics exclusively examined carbon emission reduction networks in a single location, and just a few investigated them from multiple dimensions. To compensate for the above shortcomings, under the principle of coordinating efficiency and equity, this study analyzes the network of building carbon emission reduction potential from the overall and regional dimensions by using “relational data”. The quadratic assignment procedure (QAP) is employed to analyze the influencing elements of the network and provide an effective path to promote the collaborative management of carbon emissions in the construction industry.

3. Methodology

Figure 1 depicts the methodological flow chart for this study. We use the super-efficiency slack-based model to measure carbon emission efficiency and express carbon emission equity in terms of carbon emissions per unit of floor area. Based on this, a modified Markov chain model is utilized to measure the club convergence coefficients of efficiency and equity, and the weights of both are determined accordingly. The building carbon reduction potential is derived by standardizing the data on equity and efficiency of carbon emissions from buildings and combining it with the previously chosen weights. Based on the data on labor, carbon reduction potential, construction output, and the distance between nodes, a modified gravity model is employed in this study to depict the degree of spatial correlation strength of nodes in the network. Social network analysis is used to analyze the overall characteristics, individual characteristics, and cohesive subgroups of the network. Simultaneously, the quadratic assignment procedure in social network analysis is used to analyze the influencing factors of the network.

3.1. Super-Efficiency Slacks-Based Measure

It is crucial to evaluate the carbon emission efficiency of the construction industry in a scientifically sound way. Since it is essential to increase carbon emission efficiency in this industry as a way to minimize carbon emissions, this study evaluates the carbon emission efficiency of the construction sector using the Super-efficiency Slacks-Based Measure (Super SBM) [27] model. The outputs of this model, in contrast to conventional DEA models [28,29], may be separated into desired and undesirable outputs. Therefore, it is more logical to incorporate carbon emissions as undesirable outcomes in actual industrial operations. Additionally, the model may prevent a scenario in which many locations simultaneously have an efficiency of 1, which is more advantageous for the examination of carbon emission efficiency that follows. Equation (1) is the mathematical expression of the super-efficiency SBM.

Table 1. Building carbon emission efficiency index.

Index Type	First-Order Index	Second-Order Index
Input index	Labor	Number of employees in the construction industry
	Capital	Total construction assets
	Energy consumption	Construction uses energy converted into coal scalars
	Machine	Total power of self-owned construction machinery and equipment at year-end
Output index	Economic	Gross construction product
	Carbon emission (Undesirable)	Building process carbon emissions

shows the parameters used to measure the carbon emission efficiency of buildings.

$$\begin{array}{l}{\tau }^{*}=\min \frac{\frac{1}{m}{\displaystyle \sum _{i=1}^m\frac{{\overline{x}}_i}{x_{i0}}}}{\frac{1}{s_1+s_2}({\displaystyle \sum _{r=1}^{s_1}\frac{{\overline{y}}_r^g}{y_{r0}^g}}+{\displaystyle \sum _{r=1}^{s_2}\frac{{\overline{y}}_r^b}{y_{r0}^b}})}\\ s.t.\left\{\begin{array}{l}\overline{x}\ge {\displaystyle \sum _{j=1,\ne 0}^n{\lambda }_j{x}_j}\\ {\overline{y}}^g\le {\displaystyle \sum _{j=1,\ne 0}^n{\lambda }_j{y}_j^g}\\ {\overline{y}}^b\ge {\displaystyle \sum _{j=1,\ne 0}^n{\lambda }_j{y}_j^b}\\ \overline{x}\ge x_0,{\overline{y}}^g\le y_0^g,{\overline{y}}^b\ge y_0^b,\lambda \ge 0\end{array}\right.\end{array}$$

(1)

where ${\tau }^{*}$ is the building carbon emission efficiency; $m$, $s_1$ and $s_2$ are the input variables, desired and undesired outputs, respectively; ${\overline{x}}_i$, ${\overline{y}}_r^g$ and ${\overline{y}}_r^b$ are their relaxation vectors; $\lambda$ is the weight vector, and $n$ is the number of decision units.

3.2. Improved Markov Chain

Considering the need to assign corresponding weights to carbon emission equity and efficiency when calculating the carbon reduction potential index, the degree of solidification of both is used to measure the weights in this study. Specifically, the degree of consolidation is the club convergence index as constructed in the paper. The transfer matrix of the improved Markov chain model [30] can visually reflect the degree of solidification of the index, so this model is used to measure the club convergence index of carbon emission equity and efficiency in this paper to analyze the significance of the principles of equity and efficiency in examining the carbon reduction potential of buildings and the focus of policy formulation. The formula for calculating the carbon reduction potential is shown in Equation (2).

$$A=C{E}_{ef}\times EF+C{E}_{eq}\times EQ$$

(2)

where $C{E}_{ef}$ and $C{E}_{eq}$ are the weights of carbon emission efficiency and equity in the calculation of carbon reduction potential, $EF$ and $EQ$ are the normalized values of carbon emission efficiency and equity, respectively.

In this study, the equity and efficiency of carbon emissions are discretized into four categories: low, medium-low, medium-high, and high. The transfer probabilities of equity and efficiency are then determined using an improved Markov chain model. The improved model can create transfer matrices over a multi-year period, which allows it to discover more information about the degree of consolidation than the conventional Markov chain model. Equations (3)–(5) illustrate the precise formula for computing the transfer matrix. Equation (6) is the formula for the club convergence index.

$$P_{ij}^{t,t+d}=\left\{X_{t+d}=j|X_t=i\right\}$$

(3)

where $P_{ij}^{t,t+d}$ is the probability value of the Markov transfer probability matrix for a time duration of $d$ years.

$$P_{ij}^d={\displaystyle \sum _{t=t_0}^{t_n-d}{n}_{ij}^{t,t+d}}/{\displaystyle \sum _{t=t_0}^{t_n-d}{n}_i^t}$$

(4)

where $P_{ij}^d$ is the probability that an area with a level in type $i$ in year $t$ will be in type $j$ after $d$ years, $n_{ij}^{t,t+d}$ is the sum of all areas that are in type $i$ in year $t$ and shift to type $j$ in year $t+d$, $n_i^t$ is the total number of areas with carbon efficiency or carbon equity in type $i$ in year $t$.

$$\left[\begin{array}{l}\frac{n_{11}^d}{n_1^d}\cdots \frac{n_{1j}^d}{n_1^d}\cdots \frac{n_{1k}^d}{n_1^d}\\ \frac{n_{21}^d}{n_2^d}\cdots \frac{n_{2j}^d}{n_2^d}\cdots \frac{n_{2k}^d}{n_2^d}\\ \cdots \cdots \cdots \cdots \cdots \\ \frac{n_{k1}^d}{n_k^d}\cdots \frac{n_{kj}^d}{n_k^d}\cdots \frac{n_{kk}^d}{n_k^d} \end{array}\right]=\left[\begin{array}{l}{p}_{11}^d\cdots p_{1j}^d\cdots p_{1k}^d\\ p_{21}^d\cdots p_{2j}^d\cdots p_{2k}^d\\ \cdots \cdots \cdots \cdots \cdots \\ p_{k1}^d\cdots p_{kj}^d\cdots p_{kk}^d\end{array}\right]$$

(5)

Equation (5) is the Markov transfer probability matrix. Where $n_i^d$ is the size of the type $i$ area, $p_{ii}^d$ is the transfer probability that an area of type $i$ will still be of type $i$ after $d$ years. A larger value of this transfer probability represents a deeper consolidation degree of carbon efficiency or equity, which means that there is club convergence.

$$CC{I}^d=p_{11}^d\times \frac{n_1^d}{{\displaystyle \sum n_i^d}}+p_{22}^d\times \frac{n_2^d}{{\displaystyle \sum n_i^d}}+\cdots +p_{kk}^d\times \frac{n_k^d}{{\displaystyle \sum n_i^d}}$$

(6)

Equation (6) is the club convergence index. Where $p_{kk}^d$ is the diagonal element in Equation (4), and $\frac{n_k^d}{{\displaystyle \sum n_i^d}}$ is the size share of clubs in the category $k$.

3.3. Modified Gravity Model

In the area of energy research, the gravity model has become more prevalent as one of the key techniques for examining urban spatial relationships. To provide a thorough and informative analysis of the geographical connection among nodes in the building carbon reduction network, we employ the gravity model in this study. As shown by Equations (7) and (8), we have modified the classic gravity model to improve its applicability because it neglects the bi-directionality and asymmetry of spatial correlations among nodes [26]. These adjustments fix the previously noted problem and provide us with a more complex understanding of the spatial dynamics in the network.

$$y_{ij}={\alpha }_{ij}\frac{\sqrt[3]{L_i{A}_i{G}_i}\sqrt[3]{L_j{A}_j{G}_j}}{d_{ij}^2}$$

(7)

$${\alpha }_{ij}=\frac{A_i}{A_i+A_j}$$

(8)

where $y_{ij}$ is the spatial correlation strength of carbon reduction potential from region $i$ to region $j$, $L_i$ and $L_j$ are the construction labor in region $i$ and region $j$ respectively, $A_i$ and $A_j$ are the building carbon reduction potential in region $i$ and $j$ respectively, $G_i$ and $G_j$ are the construction output in region $i$ and $j$ respectively.

3.4. Social Network Analysis

One of the primary techniques for analyzing relational data is social network analysis (SNA), which explores the relational paradigm and how it impacts the network as a whole as well as the network’s members individually. In this study, SNA is used to investigate the spatially linked network of building carbon reduction potential, which is based on the carbon reduction potential relationships between provinces and cities, with 30 Chinese provinces and cities as network nodes and their interconnections as the edges of the network. UCINET is one of the main tools for social network analysis and is used in this study to conduct a comprehensive analysis of the network’s carbon reduction potential. which includes the overall characteristics, individual characteristics, and cohesive subgroups of the network. Equations (9)–(12) describe the overall characteristics of the network, and Equations (13)–(15) describe the individual characteristics of the network. By continually computing the correlation coefficients for each row of the network matrix produced from Equation (7), converging to a coefficient matrix with a value of 1 or −1, and splitting it into two slabs in accordance, the cohesive subgroup analysis of the network is carried out. Since there are four clustering panels in this research, the computation of Equation (7) needs to be done twice. In actuality, the overall characteristics of the network, the individual characteristics, and the analysis of cohesive subgroups are implemented by the UNINET software.

$$D=\frac{2E}{n(n-1)}$$

(9)

where $D$ is the overall density of the network; $E$ is the number of network edges that are associated; $n$ is the number of nodes.

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

(10)

where $C$ is the correlation of the network; $V$ is the number of unreachable pairs of nodes in the network; $n$ is the number of nodes.

$$H=1-\frac{K}{\max \left(K\right)}$$

(11)

where $H$ is the rank of the network; $K$ is the actual number of symmetrically accessible pairs of nodes in the network; $\max \left(K\right)$ is the maximum possible number of symmetrically accessible pairs of nodes in the network.

$$E=1-\frac{S}{\max \left(S\right)}$$

(12)

where $E$ is the network efficiency; $S$ is the number of redundant node pairs in the network.

$$DC=\frac{D{C}_{in}+D{C}_{out}}{2n-2}$$

(13)

where $DC$ is the degree of centrality, $D{C}_{in}$ is the point-in degree, $D{C}_{out}$ is the point-out degree, and $n$ is the number of network nodes.

$$CC=\frac{{\displaystyle {\sum }_{j=1}^n{d}_{ij}}}{n-1}$$

(14)

where $CC$ is the closeness centrality, $d_{ij}$ is the distance between nodes, and $n$ is the number of network nodes.

$$BC=\frac{2{\displaystyle {\sum }_j^n{\displaystyle {\sum }_k^n\raisebox{1ex}{$g_{jk}\left(i\right)$}\!\left/ \!\raisebox{-1ex}{$g_{jk}$}\right.}}}{3n^2-3n+2}$$

(15)

where $BC$ is the between centrality, $g_{jk}\left(i\right)$ is the number of shortest association paths of the origin and destination nodes through the $i$ node, $g_{jk}$ is the number of all associations between the origin and destination nodes, and $n$ is the number of network nodes.

3.5. Quadratic Assignment Procedure

Regression analysis and correlation analysis are included in the quadratic assignment procedure, which is a non-parametric test for random permutations and may be used to successfully analyze the relationships between several matrices. A problem of autocorrelation and multicollinearity in econometric models may be successfully resolved by the technique, which does not need the assumption of variable independence [31]. Equation (16) is the basic model setting for QAP. QAP correlation analysis is similar in principle to QAP regression analysis and consists of two basic steps:

Step 1. The square matrixes $\beta$, $I$, and $R$ are transformed into vectors of dimensional length $n\left(n-1\right)$, and ordinary least squares regression is performed to obtain the goodness of fit and the set of regression coefficients. Since the QAP model, being a relational analysis model, is inherently autocorrelated, the results of the ordinary least squares regression are not reliable. Therefore, a second step is required.

Step 2. The residual matrix is obtained using random permutations, and the reference value of the test statistic is estimated afterwards.

$$\begin{array}{l}\beta ={\alpha }_0+{\alpha }_{1}I+{\alpha }_{2}R+V\\ \end{array}$$

(16)

where ${\alpha }_0$, ${\alpha }_1$ and ${\alpha }_2$ are the coefficients of the variables, and $\beta$, $I$, $R$ and $V$ are the explanatory variables, control variables, and residuals. All variables in the model are square matrices, with elements ${\beta }_{ij}$, $I_{ij}$ and $R_{ij}$ of the square matrices representing the difference between two regions in the explained, explanatory, and control variables, respectively. When $i=j$, the elements of the main diagonal of the square matrixes are all zero.

QAP is chosen to investigate the factors influencing the spatial correlation network of the building carbon reduction potential since the variables are presented in the form of matrices and are relational data, meaning that they are already connected. The QAP correlation analysis and QAP regression analysis in this study are implemented through UCINET.

3.6. Data Source

This study analyzes the building carbon reduction potential based on data from 30 provinces in China for the period 2006–2020. Among them, the Tibetan region is not included in the study due to the unavailability of its data. The input and output indicators of the Super-SBM model, which is used to calculate carbon efficiency, are displayed in Table 1. In particular, labor data is obtained from the China Statistical Yearbook, and capital, economic, and machine data are obtained from the China Statistical Yearbook of the Construction Industry. Energy consumption and carbon emission calculation base data are from the China Energy Statistical Yearbook, and the carbon emission calculation formula is shown in Equation (17). In this article, carbon emissions per unit of floor area are used to reflect carbon equity, and the floor area data is obtained from the China Construction Statistical Yearbook. The rest of the data used in the model and analysis in this article are from the aforementioned data, and the data sources are also consistent with those sources.

$$CE=E\times f=\frac{44}{12}\times E\times J\times C\times O$$

(17)

where $CE$ is carbon emission, $f$ is the carbon emission factor, the data for which is taken from the appendix section of the China Energy Statistics Yearbook, $J$ is the average low-level heat content, $C$ is the carbon content per unit calorific value, and $O$ is the carbon oxidation rate.

4. Results and Discussion

4.1. Coordination Analysis of Equity and Efficiency

In this study, the Super-SBM model is employed to quantify the efficiency of building carbon emissions, while the carbon emissions per unit of floor area are utilized as a measure of building carbon emission equity. The average values of building carbon emission equity and efficiency in each province and city in China are depicted in Figure 2.

Based on the above calculations of efficiency and equity in building carbon emissions, an improved Markov chain model is applied to capture the curing of these two variables over different time horizons.

Table 2. State transfer matrix for carbon emission efficiency of construction.

Time Span /Year	Category	n	Low	Medium-Low	Medium-High	High
1	Low	105	0.7905	0.1524	0.0476	0.0095
	Medium-low	107	0.1776	0.6168	0.2056	0.0000
	Medium-high	103	0.0583	0.1845	0.6408	0.1165
	High	105	0.0095	0.0095	0.1238	0.8571
2	Low	96	0.7500	0.1667	0.0625	0.0208
	Medium-low	99	0.2222	0.5253	0.2424	0.0101
	Medium-high	96	0.0938	0.2500	0.5000	0.1563
	High	99	0.0101	0.0303	0.1919	0.7677
3	Low	83	0.7590	0.1807	0.0602	0.0000
	Medium-low	91	0.2088	0.4945	0.2637	0.0330
	Medium-high	94	0.1383	0.2340	0.4149	0.2128
	High	92	0.0217	0.0652	0.2283	0.6848
4	Low	73	0.7397	0.2055	0.0411	0.0137
	Medium-low	85	0.2118	0.4471	0.3059	0.0353
	Medium-high	87	0.1609	0.2184	0.4138	0.2069
	High	85	0.0588	0.0824	0.2000	0.6588
5	Low	68	0.6765	0.2647	0.0441	0.0147
	Medium-low	75	0.2133	0.4133	0.3600	0.0133
	Medium-high	78	0.1538	0.2308	0.3718	0.2436
	High	79	0.1013	0.0759	0.1899	0.6329

and

Table 3. State transfer matrix for carbon emission equity of construction.

Time Span /Year	Category	n	Low	Medium-Low	Medium-High	High
1	Low	100	0.7200	0.2000	0.0700	0.0100
	Medium-low	107	0.2430	0.5047	0.1869	0.0654
	Medium-high	106	0.0283	0.2075	0.5189	0.2453
	High	107	0.0374	0.1028	0.2150	0.6449
2	Low	89	0.6404	0.2247	0.1011	0.0337
	Medium-low	103	0.2718	0.4466	0.2136	0.0680
	Medium-high	102	0.0490	0.2647	0.3824	0.3039
	High	96	0.0521	0.1042	0.2396	0.6042
3	Low	81	0.6667	0.1728	0.1358	0.0247
	Medium-low	96	0.2500	0.4167	0.2292	0.1042
	Medium-high	93	0.0860	0.3118	0.3226	0.2796
	High	90	0.0444	0.1444	0.2222	0.5889
4	Low	73	0.6712	0.1781	0.0959	0.0548
	Medium-low	85	0.2471	0.3882	0.2000	0.1647
	Medium-high	85	0.0941	0.3647	0.2824	0.2588
	High	87	0.0805	0.1494	0.2759	0.4943
5	Low	63	0.6032	0.2540	0.0635	0.0794
	Medium-low	76	0.3158	0.3553	0.1974	0.1316
	Medium-high	79	0.1266	0.3418	0.2785	0.2532
	High	82	0.0976	0.1463	0.2927	0.4634

show the transfer probabilities for efficiency and equity under different time horizons, respectively. It is worth noting that the main diagonal element of each transfer probability matrix in Table 2 and Table 3 represents the probability that each state remains unchanged over the specified period. The value of this probability can reflect the degree of efficiency and equity in curing carbon emissions.

Overall, the main diagonal elements of each transfer probability matrix are mostly greater than the values of the elements in the other positions. This suggests that the various types of regions remain relatively stable with little probability of change. Among them, the high-level and low-level regions are more prominent, and there is a more obvious club convergence phenomenon. And as the time span lengthens, the degree of solidification is still the highest for high and low levels. Moreover, in comparing the transfer probability matrices of carbon emission efficiency and equity horizontally, it is not difficult to find that, under any time span, the main diagonal elements of the transfer probability matrix of carbon emission efficiency are larger than the main diagonal elements of the transfer probability matrix of carbon emission equity. To sum up, there is a problem of “high and low-level curing” in the carbon emission efficiency and equity of China’s buildings, but the problem of carbon emission efficiency is more serious.

To more accurately reflect the degree of curing of building carbon emission efficiency and equity, the overall degree of curing of the two under different time horizons is quantified in this study using Equation (6), and the results are shown in

Table 4. Club convergence index.

Time Span	1	2	3	4	5
Carbon emission efficiency club convergence index	0.7262	0.6359	0.5833	0.5576	0.5200
Carbon emission equity club convergence index	0.5953	0.5128	0.4917	0.4515	0.4167

. It is worth noting that the club convergence index of building carbon emission efficiency is consistently higher than the club convergence index of carbon emission equity over any time horizon. This suggests that there is a more pronounced dissonance between the two and a greater degree of solidification of carbon emission efficiency.

Combining the results of the transfer probability matrix analysis and the club convergence index analysis, it is easy to find that there exists a solidification phenomenon of “the higher is always higher, the lower is always lower” in the carbon emission efficiency and equity of the construction industry, and the former is more significant. This suggests that the “long-term inefficiency” curing problem in China’s construction industry is more serious than the “long-term unfairness” curing problem. Therefore, when assessing the potential for carbon emission reduction under the principle of coordinating carbon emission efficiency and equity, efficiency indicators should be given a higher weight.

Based on the conclusions drawn from the above analysis, this study determines the weights of efficiency and equity in building carbon emissions using the club convergence coefficients in Table 4. The calculated weights are 0.5505 and 0.4495, respectively. By substituting these weights into Equation (2), the carbon emission reduction potential of buildings under the principle of harmonization of equity and efficiency is calculated. Figure 3 shows the average annual carbon reduction potential coefficients for each province. It is worth noting that the central and eastern regions have higher building carbon emission reduction potentials compared to the western region.

4.2. Spatial Network Analysis of Carbon Reduction Potential of Buildings

4.2.1. Spatial Correlation Strength Analysis

In this study, the improved gravity model was used to construct the gravity matrix of building carbon emission reduction for each province in China from 2006 to 2020, and the spatial correlation strength was demonstrated using ArcGIS. Considering that the research period selected for the study includes the 11th Five-Year Plan to the 13th Five-Year Plan, the period is relatively long. However, due to the limited space of the article and to more effectively reflect the policy changes, the potential for carbon emission reduction in buildings In this paper, we only show the correlation intensity of the building carbon emission reduction potential of each province in 2006, 2010, 2015, and 2020, as shown in Figure 4a–d. As can be seen in Figure 4, there were no isolated nodes in the network during the study period. This indicates that the communication of building carbon emission reduction among nodes in the network has broken the limitation of geographic location. In addition, the figure also intuitively reflects that the building carbon emission reduction exchanges between nodes have become closer, the spatial correlation strength of the network has been enhanced, and the spatial network relationship has become more complex. Based on the different colors of the nodes in the figure, it can also be seen that Beijing, Tianjin, Hebei, Jiangsu, Zhejiang, and Shanghai have been the most closely connected regions in the network. These regions have outstanding performance in the collaborative development of the construction industry and collaborative emission reduction.

4.2.2. Overall Network Characterization

We use UCINET software to measure the density, relevance, number of relationships, rank, and efficiency of the network of building carbon reduction potentials over the period 2006–2020, and Figure 5 shows the trend of the overall network characteristics. Since the network relevance is always 1, it is not shown in the figure. However, this indicator can intuitively reflect that the network has strong stability and there are no isolated nodes in it. The overall network density demonstrates an initial decrease followed by an increase, while remaining at a relatively low level. This suggests that the spatial correlation degree of the carbon emission reduction potential network has plenty of room for improvement. The network’s rank exhibits fluctuating dynamics, with a rise from 0.2442 in 2006 to 0.4715 in 2020. This indicates an enhanced structural composition of the construction carbon emission reduction potential network, with certain provinces assuming increasingly dominant positions in the core. The network efficiency experiences slight fluctuations, showcasing a marginal overall decrease, thereby signifying increased network stability. The number of connections in the network follows a fluctuating pattern, with a general increase in the overall number of connections. However, the existing number of connections remains relatively small compared to the maximum possible connections in the network, suggesting the need for further improvement in the spatial connections of carbon emission reduction potential.

4.2.3. Individual Network Characterization

In this study, the degree centrality, closeness centrality, and betweenness centrality of the nodes in the network are measured using the UCINET software, and these metrics are used to clarify the position and role of each node in the network. Since the overall change of each indicator in different years is not significant, the average value of each indicator is selected to reflect the results.

Figure 6a and Figure 6b depict the point-out and point-in degrees of point-degree centrality, respectively. It is evident that the provinces with high points are predominantly located in the central and western regions. Conversely, provinces with high point-in degrees are primarily located in the central and eastern regions. This observation highlights the considerable imbalance in the distribution of carbon emission reduction potential among regions. Additionally, it corroborates the information presented in Figure 4, highlighting the central and eastern provinces as key contributors to the network’s association strength. This disparity can be attributed to the relatively lagging development of the construction industry in the western region compared to the Eastern region. The western provinces exhibit lower development quality in the construction industry, resulting in lower carbon emission reduction investment and effectiveness. Consequently, these provinces have persistently occupied the low-value range of carbon emission reduction potential. Conversely, the eastern region prioritizes the development quality of the construction industry and allocates greater resources and innovation toward carbon emission reduction. As a result, these provinces demonstrate higher carbon emission reduction potential, which radiates to the surrounding provinces.

Figure 7a and Figure 7b present the out-closeness centrality and in-closeness centrality, respectively. In general, the in-closeness centrality surpasses the out-closeness centrality, indicating that each node province in the network tends to absorb superior resources to bolster its own carbon reduction potential. Notably, the eastern region predominantly receives external resources, while the western and northeastern regions primarily benefit from spillover effects, exhibiting significant regional disparities. This pattern primarily stems from the favorable locations, economic prowess, and technological advantages enjoyed by most eastern provinces, enabling them to effectively leverage the resource advantages of external nodes to enhance their carbon emission reduction potential. In contrast, provinces in the western and northeastern regions encounter challenges in harnessing the advantages offered by other nodes due to their geographical and economic limitations. Consequently, these regions exhibit an overall spillover effect in terms of carbon emission reduction potential.

Figure 8 illustrates the centrality of the network nodes. In general, the provinces with high centrality are predominantly situated in the central and eastern regions, assuming crucial communication roles within the network of construction carbon emission reduction potential and functioning as key nodes. These provinces hold strategic positions due to their favorable transportation locations and advanced levels of development in the construction industry. As bridge nodes in the network, they wield significant influence and exert a high degree of control over the overall network dynamics.

4.2.4. Condensed Subgroup Analysis

Due to space limitations, this study takes the specific years of 2006, 2010, 2015, and 2020 in the five-year plan as the research object. The CONCOR tool in UCINET software is used to analyze the cohesive subgroups of the network of carbon emission reduction potential in China’s construction industry, and the results are displayed in

Table 5. Correlation between spatial plates of building a carbon emission reduction potential network.

Year	Plate	Number of Members	Overflow Relation Number	Reception Relation Number	Expected Internal Relationship Ratio	Actual Relation Ratio
2006	1	9	21	23	27.59%	66.13%
	2	3	3	54	6.90%	66.67%
	3	6	26	21	17.24%	38.10%
	4	12	63	15	37.93%	49.60%
2010	1	9	22	21	27.59%	67.65%
	2	4	11	72	10.34%	47.62%
	3	5	19	15	13.79%	38.71%
	4	12	65	9	37.93%	41.44%
2015	1	9	28	11	27.59%	58.21%
	2	6	41	13	17.24%	8.89%
	3	7	9	82	20.69%	78.57%
	4	8	44	16	24.14%	40.54%
2020	1	5	21	33	13.79%	44.74%
	2	7	50	14	20.69%	16.67%
	3	7	17	100	20.69%	66.67%
	4	11	72	13	34.48%	33.95%

. The division of different subgroups is mainly based on the proximity of the linkages between provinces and cities in terms of collaborative management of carbon emission reduction in construction. It is worth noting that regional co-management of carbon emission reduction in China’s construction industry is still in its infancy, and a complete and stable co-management network has not yet been formed between regions. Except for 2006, the number of out-of-board relationships is greater than the number of in-board relationships in the remaining years, as shown in Table 5, and the gap between the two is gradually increasing. This indicates that the spillover effect of the building carbon emission reduction network is gradually becoming significant and that the spatial correlation is increasing.

Figure 9a–d corresponds to the cohesive subgroup clustering in 2006, 2010, 2015, and 2020, respectively. It is easy to find that the composition and number of provinces in different clusters show some differences in different years, indicating that the network of China’s building carbon emission reduction potential is still under continuous development and has not yet formed a stable network form. In addition, due to rapid economic growth and improved transport, the communication of building carbon emission reduction among provinces has broken the influence of geographical distance. Provinces that are not geographically close to each other also belong to the same cohesive subgroup, which creates a strong linkage in terms of building carbon emission reduction.

4.3. Analysis of Influencing Factors for Building a Carbon Emission Reduction Network

4.3.1. Variable Selection and Definition

After carefully reviewing the relevant literature on carbon emission studies [22,32,33,34], this paper has identified five key impact variables for in-depth analysis using QAP. The specific selection and definition of these variables are presented in

Table 6. Variable selection and definition.

Symbol	Variable	Definition
D	Geographical proximity	Geographical distance between nodes
R	Environmental regulations	Difference in pollution investment as a percentage of total investment
G	Development level of the construction industry	Difference in construction output
S	Energy structure of the construction industry	Difference in the coal consumption ratio
I	Energy consumption intensity in the construction industry	Difference in energy consumption per unit of GDP

.

4.3.2. QAP Correlation and Regression Analysis

In this study, QAP is employed to assess the relationship between each influencing factor and the spatial correlation structure of the construction industry’s carbon emission reduction potential network. The results presented in

Table 7. QAP correlation and regression analysis.

Variable	QAP Correlation Analysis		QAP Regression Analysis
	Correlation Coefficient	p Value	Regression Coefficient	p Value
D	−0.440	0.000 ***	−0.368	0.000 ***
R	−0.125	0.044 **	−0.053	0.053 **
G	0.313	0.000 ***	0.220	0.000 ***
S	−0.073	0.176	−0.0301	0.477
I	−0.094	0.021 **	−0.008	0.032 **
			R2: 0.272 adjusted R2: 0.268 p value: 0.000 ***

** and *** represent significance at the level of 0.01 and 0.05, respectively.

demonstrate that the correlation coefficients of the four variables D, R, G, and I all exhibit statistical significance at the 5% level. This indicates that these factors exert a significant influence on the network of carbon emission reduction potential in the construction industry. Specifically, the correlation coefficients of variables D, R, and I are all negative, implying a negative association with the spatial structure of the network. Conversely, the correlation coefficient of variable G is positive, indicating a positive association with the spatial structure of the network. On the other hand, variable S did not exhibit statistical significance at the 10% level, suggesting a lack of significant correlation with the network structure.

To mitigate the potential influence of multiple covariates among the independent variables on the regression outcomes, QAP is employed in this study to perform a regression analysis of the factors impacting the spatial correlation structure of the carbon emission reduction potential network in China’s construction industry. The findings are presented in Table 7. The p-value of the QAP regression analysis results is 0.000, indicating that the regression relationship between the independent and dependent variables is statistically significant at a significance level of 1%. The adjusted R-squared value is 0.268, suggesting that the five variables, namely D, R, G, S, and I, account for 26.8% of the variation in the spatial correlation structure of the building carbon emission potential network. It is important to note that the spatial correlation structure of the building carbon emission potential network is influenced by numerous factors, and the variables selected in this study can only explain a certain extent of the variation. Further analysis and research are required to explore additional factors and their effects in more depth.

The regression analysis reveals several key findings. Firstly, the regression coefficient of variable D is negative and passed the 1% significance level test, indicating that geographic proximity between provinces contributes to the formation of the spatial correlation structure in the building carbon emission potential network. This is because shorter distances facilitate the transfer of superior resources for carbon emission reduction, while increased geographical distance hinders inter-regional collaborative management, resulting in higher costs and difficulties. Consequently, it affects the spatial correlation between provinces in the carbon emission reduction potential network.

Secondly, both variables R and I exhibit negative regression coefficients, passing the 5% significance level test. This suggests that similar levels of environmental investment shares and energy consumption intensities contribute to enhancing synergistic management of building carbon reduction between provinces. Similar environmental investment and energy consumption intensities imply that provinces are at a similar stage of carbon reduction, sharing common needs for factors and resources required in the building sector. This fosters increased correlation between nodes in the network.

Thirdly, the regression coefficient of variable G is positive and passed the 1% significance level test, indicating that differences in the level of construction industry development among provinces enhance inter-node correlation. Variations in construction industry development promote the circulation of superior resources between nodes, with high-level nodes radiating to surrounding low-level nodes. Consequently, they provide emission reduction technologies and resources, assisting in the reduction of carbon emissions in the construction sector and strengthening inter-node correlation.

Lastly, the regression coefficient of variable S is negative but does not pass the 10% significance level test. This implies that inter-provincial differences in the share of coal consumption in the construction industry do not significantly affect the spatial correlation structure of the construction carbon emission potential network. This may be attributed to the relatively stable energy structure within the construction industry.

4.4. Discussion

Along with the open development of society and the deepening trend of networking, the flow of factors related to carbon emissions has become a medium for frequent inter-regional connections. China is in a critical period of ecological civilization construction, and collaborative promotion of pollution reduction and carbon reduction has become an important means to cope with the dual-carbon target. As the construction industry is one of the main sources of carbon emissions, collaborative promotion of carbon emission reduction in construction has become one of the hot research issues nowadays. Clarifying the mechanism of synergistic management of building carbon emissions is not only beneficial to regional environmental governance but also promotes regional sustainable development.

This study analyzes and researches the potential network for building carbon emission reduction in China under the principle of equity and efficiency coordination using an improved Markov chain, an improved gravity model, and social network analysis. Firstly, the improved Markov chain model is used to analyze the coordination between equity and efficiency in building carbon emissions and determine the difference in their importance. Secondly, the strength and structure of spatial associations in the building carbon emission reduction network were analyzed using a combination of the improved gravity model and social network analysis. Finally, the main factors influencing the building carbon emission reduction network were analyzed using a quadratic distribution procedure.

However, this study still has certain shortcomings. First, this study analyzes the potential network of building carbon emission reduction mainly from the national and provincial levels but fails to analyze it from an urban perspective, so the practical value of the research results is not enough. Secondly, as a complex network, the network of building carbon emission reduction is influenced by many factors, and some of the main influencing factors selected in this study can only partially explain the network but fail to clarify the mechanism of the network. Thirdly, the improved Markov chain can be a good model for assessing the changing state of carbon efficiency and equity in future years based on the current state. However, the model is only capable of assessing state transfer changes in the short term.

Given this, in future research, we will utilize geographic remote sensing tools to obtain urban nighttime lighting data. The corresponding energy carbon emission statistics will be utilized for fitting to obtain urban carbon emission data. Conducting a spatial analysis of building carbon emission reduction networks at a finer urban level will further improve the analysis from different research perspectives to obtain more references with more practical value. In addition, in the subsequent research, we will further expand the influencing factors affecting the network of carbon emission reduction in buildings to ensure that the operation mechanism of the network is more comprehensively clarified and to provide more bases for the collaborative promotion of carbon emission reduction in buildings.

5. Conclusions

In this study, the Super-SBM model is used to measure the building carbon emission efficiency of 30 provinces in China, and the building carbon emission equity of each province is measured by the building carbon emission per unit area. On this basis, the improved Markov chain model is used to determine the difference in importance of efficiency and equity principles in calculating China’s building carbon emission reduction potential in each province. Finally, the paper also analyzes the spatial network of China’s construction carbon emission reduction potential by integrating the modified gravity model and the social network analysis model. At the same time, the quadratic assignment procedure is also used to analyze the influencing factors in this network. The main conclusions drawn are as follows:

First, the long-standing problem of “low efficiency” in China’s construction industry is more serious than the problem of “low equity”, and there is an uncoordinated relationship between equity and efficiency in construction carbon emissions. Therefore, efficiency should be given a higher weight in the measurement of carbon emission reduction in construction. In other words, efficiency should be given more importance in the formulation of carbon emission reduction policies.

Second, from the viewpoint of network association strength, the communication between nodes in the network of building carbon emission reduction potential is getting closer and closer, the association strength is increasing, and the network relationship is getting more and more complex. From the viewpoint of network structure: (1) node participation and network efficiency are high, but the number and density of network relations are low. (2) Nodes occupying the dominant position in the network have stronger control and influence over the resources required for carbon emission reduction, while the edge nodes of the network have difficulties accessing key resources. (3) The network spillover effect is significant, and the network shape is not yet stable.

Third, geographic proximity, environmental regulations, and energy consumption intensity have a significant negative impact on network structure. On the contrary, the development level of the construction industry has a significant positive effect on the network structure. However, the energy structure has no significant effect on the network structure.