Convergence Analysis of Inclusive Green Growth in China Based on the Spatial Correlation Network

: The purpose of the research is based on the spatial network correlation to explore the convergence path of inclusive green growth. Inclusive green growth is a sustainable development model that emphasizes the integration of economic, social, and ecological systems. Based on the three subsystems of economic growth, social inclusion, and green sustainability, this study structures the indicator system of China’s inclusive green growth and reveals the characteristics of China’s inclusive green growth network using the social network analysis (SNA) method. Then, from the perspective of system deconstruction, this work tests whether and how China’s inclusive green growth converges by constructing a spatial econometric model with different subsystems of spatial correlation networks as spatial weights. The results show that: (1) China’s inclusive green growth level is on the rise in general, showing a spatial distribution pattern of “high in East and West, low in the Central”. (2) China’s inclusive green growth network relationship is signiﬁcant, and the network system is stable, but there is still room for improvement in network relevance. The spatial correlation of economic growth is relatively closer than other subsystems. (3) China’s inclusive green growth has a remarkable convergence trend in the spatial correlation scenario, and the spatial correlation of social inclusion has the most signiﬁcant promoting effect on the convergence of the national inclusive green growth; there is a trend of club convergence in the East, Central, and West regions, and the speed of convergence is the fastest in the central region. The spatial correlation of economic growth has a strong promoting effect on the convergence of inclusive green growth in all regions.


Introduction
Currently, many countries and regions have faced serious environmental and social problems while experiencing economic growth. For example, excessive consumption of energy resources, pollution and destruction of the ecological environment, widening gap between rich and poor, and "Middle-income trap" [1]. The traditional mode of industrial growth makes it difficult to achieve sustainable development. In response to the global development challenges mentioned above, the 2012 United Nations Conference on Sustainable Development first proposed the concept of inclusive green growth. In the same year, the World Bank released a report entitled "Inclusive Green Growth: The Road to Sustainable Development", emphasizing the importance of achieving coordinated development among the economy, society, and environment. Since then, more and more countries have begun to focus on inclusive and green growth [2].
With the rapid growth of the economy, especially since the reform and opening up, China is also facing issues of social equity and environmental protection. Since the 11th Five-Year Plan, the Chinese government has actively promoted the construction of an environmentally friendly and resource-conserving society, and introduced the concepts of

Literature Review
There is currently no uniform definition in the academic community of inclusive green growth, but some studies have been conducted to define its connotation from different perspectives. Certain scholars and research institutions have elaborated on it from the perspective of development economics. For example, the World Bank [5] considers inclusive green growth as a development model that reduces environmental pollution, uses resources efficiently in a socially inclusive way, and is an important way to achieve sustainable development. At the same time, other scholars consider inclusive green growth from a welfare economics perspective. Slingerland and Kessler [6] emphasize that the goal of inclusive green growth is to increase the overall welfare of society and that growth should contribute to the well-being of current as well as future generations via a green, low-carbon, equitable, and inclusive approach. Jiang and Chen [7] and Li et al. [8] argue that inclusive green growth is an important approach and means to promote sustainable human development, which mediates the contradiction between economic growth and nature and society by changing the way of human production and life. Together, the above studies from various perspectives reflect the core connotation of inclusive green growth, which is to minimize environmental risks and ecological deficiencies while increasing human welfare and improving social equity [9,10].
As countries around the world paid more and more attention to inclusive green growth [11,12], relevant studies on the level measurement of inclusive green growth were carried out. Regarding the evaluation of inclusive green growth, existing studies have mainly adopted two approaches: index system construction and inclusive green growth performance measurement. Constrained by the scarcity of environmental data, Albagoury [13] constructed separate index systems for inclusive growth and green growth, which were measured separately and then jointly reflected the inclusive green growth in Ethiopia; Herrero [14] calculated an Inclusive Green Energy Index for 157 countries based on data on social inclusion, cleaner production and energy consumption to assess progress on key aspects of the United Nations Sustainable Development Goals; Isaac K. and Francesco [15] constructed a rather simplified index system to evaluate inclusive green growth in Africa starting from the concept of inclusive green growth; Lin and Zhou [16] constructed an index system from the inter-provincial and three major regional levels to measure the level of inclusive green growth in China using the entropy method. In addition, there are Sustainability 2023, 15,12344 3 of 21 also a number of studies that evaluate the efficiency of inclusive green growth in terms of inputs and outputs. For example, Sun et al. [17] portrayed the efficiency of inclusive green growth in China using the DDF-SBM model; Wang et al. [18] measured and analyzed the inclusive green total factor productivity of Chinese provinces from 1995 to 2017 using the Malmquist-Lemberg index; Guan et al. [19] assessed the inclusive green total factor productivity of 286 cities in China using the Super SBM.
At present, the research on inclusive green growth is more in-depth, and the research on factors affecting inclusive green growth is gradually rich. Existing studies have examined the impact of technological innovation [20], economic policies [21], institutional quality [22], resource allocation [23], FDI [24], industrial structure [25], and government governance [26] on inclusive green growth. For example, Qian [27] used the panel regression model and intermediary effect model to investigate the impact of energy-biased technological progress on inclusive green growth, and the study found that energy-biased technological progress can promote inclusive green growth using industrial structure advancing and cleaning. Li and Yin [28] found that its inconsistency and insufficiency are prominent when measuring the inter-provincial inclusive green growth index in China, and technological innovation and economic system changes have two effects on inclusive green growth. Ref. [29] found that there is a positive spatial spillover effect of inclusive green efficiency, and factors such as economic development level, industrial structure, and industrialization have significant effects on inclusive green efficiency. He and Du [23] found that land resource mismatches hinder the improvement in inclusive green growth in China, and inclusive green growth in China had a clear spatial correlation.
In addition, a lot of literature has studied the spatial-temporal pattern of inclusive green growth. After constructing inclusive green growth evaluation indicators from four sub-dimensions, Wang et al. [12] found that there were significant differences in the absolute level of inclusive green growth in the three regions of China and explored the sources of differences via the decomposition of the Dagum index. Liu et al. [30] also used nuclear density and the Dagum Gini coefficient to describe the distribution and spatial differences within and between urban agglomerations. Ref. [31] found that China's inclusive green growth has obvious spatial heterogeneity and time-series characteristics using Moran' I and LISA agglomeration maps. Although Li et al. [4] analyzed the structural characteristics and evolution of the spatial correlation network of inclusive green efficiency, but their convergence was not examined. The existing literature mainly focuses on its influencing factors and spatial and temporal distribution but ignores the discussion on the convergence of inclusive green growth.
The innovations of this paper include: (1) To reflect the practical requirements of synergistically promoting green growth and people's livelihood, this study constructs an index system from three subsystems of economic growth, social inclusion, and green sustainability, enriching the evaluation system of inclusive green growth. (2) From the perspective of spatial correlation, this article constructs an inter-provincial inclusive green growth network and uses social network analysis (SNA) to reveal its network structural characteristics. (3) This study will make up for the lack of convergence testing for inclusive green growth in existing studies and introduce a spatial econometric model considering spatial factors to test the convergence of inclusive green growth in China based on spatial correlation networks. (4) From a multidimensional perspective, this study explores the impact of different subsystems on the convergence of inclusive green growth in China by using the spatial correlation network of subsystems as spatial weights.
The structure of this paper is as follows: Section 2 provides an overview of the research methods and objects of the article. Section 3 defines the connotation of inclusive green growth and proposes research hypotheses. Section 4 constructs an inclusive green growth indicator system and measures it. Section 5 examines the spatial correlation network characteristics of inclusive green growth. Section 6 tests the convergence of inclusive green growth under different spatial network weights. A discussion of the research results is found in Section 7. Additionally, Section 8 summarizes and proposes relevant policy recommendations.

Inclusive Green Growth Level Measure: Entropy Method
The entropy method is an objective assignment method that could comprehensively consider the information values provided by each index, effectively handle the internal contradictions of multi-attribute decision-making, and make the relative weights of each index more objective, precise, and reasonable [31]. Compared with the subjective assignment method, the entropy method has the advantages of being free from the interference of subjective factors and high calculation accuracy. The main idea of this method is that the entropy value is used to measure the size of the information contained in the indexes to determine the weights. The smaller the entropy of information indicates that the greater the degree of dispersion within a certain index, the stronger the importance of the evaluation, and the higher the weight, and vice versa. The specific steps were described in the literature [32,33].

Identification of Inclusive Green Growth Correlation Relationships: Modified Gravity Model
"Relational data" is the basis of social network analysis, and before examining the spatial correlation characteristics of inclusive green growth, it is necessary to identify the correlation relationships [34]. Currently, there are two main methods to establish spatial correlation relationships: VAR Granger Causality and modified gravity model. Since the VAR Granger Causality test is too sensitive to the selection of the lag order and cannot integrate economic factors with geographical distance factors [35]. Therefore, in this paper, based on numerous existing studies [36,37], the gravity model was used to identify the spatial correlation relationships of inclusive green growth in China. The modified model equation is: is the contribution ratio of province i in the inclusive green growth correlation between provinces i and j. Additionally, in Equation (1) R ij denotes the gravitational force between the inclusive green growth of province i and province j; M i(j) , P i(j) and G i(j) denote the inclusive green growth index (total index or subsystem index), population and real GDP of province i(j), respectively; D ij is the spherical geographic distance between province i and province j. Based on Equation (1), this paper calculates the matrix of inclusive green growth gravitational values between provinces, and takes the mean value of each column as the threshold value. If the gravitational value between two provinces is higher than the threshold value, it is recorded as 1, indicating that there is a spillover relationship between the province in that row to the inclusive green growth of the province in that column; otherwise, it is recorded as 0 [38]. This results in a spatial binary matrix, which is used as the base data for network structure analysis.

Characterization of Correlation Networks for Inclusive Green Growth: Social Networks Analysis (SNA)
Provinces are the "points" in China's inclusive green growth spatial correlation network, and the inclusive green growth correlation relationships among provinces are the "lines". The collection of these points and lines constitutes an intricate inclusive green growth spatial correlation network. After constructing the spatial correlation network, the characteristics of the network structure can be examined using social network analysis, which usually uses indexes such as network density, network hierarchy, network connectedness, and network efficiency to reflect the overall structural characteristics of the network. The calculation formula of specific network characteristics indexes is referred to in the literature [39][40][41].

Model Setting
β convergence is derived from the growth theory of neoclassical economics school, which includes absolute convergence and conditional convergence. Absolute β convergence means that under the assumption of the same initial endowment, the regions with lower development levels have higher growth rates, and with the passage of time, the inclusive green growth of each region tends to the same steady-state level; conditional β convergence refers to the convergence of inclusive green growth in each region to their respective steadystate levels after accounting for the different effects of other initial endowments. Given the possible extensive spatial correlation of inclusive green growth in China, this paper needs to introduce a spatial econometric model that considers spatial correlation in its convergence test. Common spatial econometric models include the spatial lag model (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), whose corresponding spatial convergence models for inclusive green growth are as follows: where W is a spatial weight matrix, i represents provinces (i = 1, 2, 3,. . ., N), and t represents time (t = 1, 2, 3,. . ., T − 1). IGG i,t indicates the inclusive green growth level of province i in period t, and ln (IGG i,t+1 /IGG i,t ) indicates the annual growth rate of inclusive green growth in province i in period t~t + 1. β is the convergence coefficient. If β < 0 and passes the significance test, then it indicates that China's inclusive green growth has a convergence trend, and the convergence rate is −ln (1 + β)/T; If β > 0 and passes the significance test, then it indicates that China's inclusive green growth diverges. µ i and η t are individual and time-fixed effects, respectively. ε it is a random perturbation term. ρ denotes the spatial lag coefficient, λ denotes the spatial error coefficient, and δ denotes the coefficient of the IGG spatial lag term affecting the interpreted variable.
Referring to [42], the specific selections for models (2)-(4) were determined in this paper based on the results of the LM test, LR test, and Wald test. Similarly, after adding a series of control variables X that affect inclusive green growth, the corresponding conditional convergence models can be constructed (specific formulas are not listed), thus making the β convergence test more accurate.

Spatial Network Weights Setting
A reasonable setting of spatial weight is the key to a spatial econometric model. In order to ensure the stability and reliability of spatial weight, this paper comprehensively examined the spatial correlation of overall inclusive green growth and its constituent subsystems (economic growth, social inclusion, green sustainability) and set spatial weights with them, represented by W I , W E , W S , and W G , respectively. Specifically, the weight matrix of spatial network correlation was constructed by the modified gravity model introduced earlier. The matrix formed using the gravitational values between the two regions is called the gravity matrix. Take the mean of each column of the gravity matrix as the threshold. If the gravity value between two provinces is higher than the threshold, it is recorded as 1; otherwise, it is 0. The 0-1 matrix formed from this is the spatial network weight matrix. At the same time, in order to compare with the convergence test based on the traditional weights, this paper also uses the geographical distance weight to test. The factor of the geographical distance weight is set based on the square of the reciprocal distance between i and j, i.e., w i,j = 1/d 2 . The above matrices are all subjected to row normalization.

Research Object and Data Source
Due to the data availability, the research objective of this paper is 30 provincial-level administrative regions in China (excluding Tibet, Hong Kong, Macao, and Taiwan) from 2006 to 2019. The sample data were sourced from the National Bureau of Statistics, China Statistical Yearbook, China Household Survey Statistical Yearbook, China Energy Statistical Yearbook, China Third Industry Statistical Yearbook, China Urban-Rural Construction Statistical Yearbook, China Environmental Statistical Yearbook, and various regional statistical yearbooks, and carbon dioxide data comes from the CEADs database. In order to eliminate the impact of price fluctuations, the regional gross domestic product, disposable income of urban residents, net income of rural residents, and disposable income of all residents were deflated by the price level of the year 2006.

Definition of Inclusive Green Growth
Inclusive green growth was first proposed at the United Nations Conference on Sustainable Development in 2012, and its idea is derived from inclusive growth and green growth, which is an integration of the core concepts of both. Ali and Zhuang (2007) advocate that inclusive growth is a kind of development with equal opportunities, where all people can enjoy the opportunities and fruits of economic development fairly [43]. Green growth, on the other hand, encompasses a low-carbon economy and resource conservation, emphasizing sustainable economic development under the premise of improving the ecological environment and increasing the efficiency of resource use. It can be seen that both inclusive growth and green growth emphasize the sustainability of economic growth, but at the same time, each has its own focus. Inclusive growth focuses on the harmonization of economic and social systems, while green growth focuses on the organic integration of economic and environmental systems. Based on their different focus characteristics, it can be found that green growth is not necessarily socially inclusive. The fruits of green growth can either benefit the poor or expose them to greater inequality. Likewise, inclusive growth is not necessarily green. Pursuing green and inclusive growth without pursuing development is tantamount to "seeking fish from a log"; pursuing development without green and inclusive growth is "drain the pond to get all the fish". Inclusive green growth emphasizes that "inclusion", "green", and "growth" are coordinated and inseparable, and its core lies in "to be green and inclusive, but also to grow" [44]. Therefore, this paper defines inclusive green growth as an approach to growth that simultaneously promotes economic, ecological, and social improvements.

Research Hypothesis
According to the first law of geography [45], there are generally strong or weak spatial correlations among spatial data. With the coordinated development of regions and the construction of a new development pattern, economic growth, social safeguard, and ecological and environmental governance have extensive connections among different parts of China. This is reflected in the following: First, economic growth between regions has a universal spatial correlation. With the rapid development of China's reform and opening up, the regional economies are becoming more and more closely connected to each other. The resulting external markets are also more attractive, and the spatial correlation effect emerges in China's regional economic development [46]. For example, Ying (2000) was the first to find that there is a strong spatial spillover effect from the "inner regions to the periphery" in China [47]. Second, in the new era, "Common Prosperity" has been given a new connotation. China's livelihood safeguard system has been gradually improved, and inter-regional and inter-industry social and livelihood correlations have been strengthened. With the interaction of government regulation and market mechanisms, China's people's livelihood development has formed a diverse hierarchy and wide geographical correlation. Third, there is also a general correlation relationship in terms of green sustainability. Due to the natural properties of pollutants (e.g., wastewater and exhaust gas), pollutants move between regions with the cycle of ecosystems. This leads to the fact that pollution prevention and control efforts in one region must cooperate with other regions. Besides, according to the theory of new institutional economics, the implementation of a unified tax system and ecological compensation strategy can correct the problem of negative externality within a region so as to promote a synergistic improvement in ecological welfare [48,49]. Economic growth, social inclusion, and ecological environment are the three important aspects of inclusive green growth, and based on the above content, hypothesis H1 is proposed in this paper.

H1: China's Inclusive Green Growth Has a Wide Spatial Correlation Relationship.
The market potential theory proposed by Krugman (1993) suggests that the higher the degree of economic development of a region, the larger its economy will be, and the greater the external market potential of the surrounding areas affected by it [50]. This suggests that regions with higher levels of development can pull the economies of neighboring regions and reduce disparities among them. It also implies that in the case of spatial correlation of economic growth, regional economic growth levels have a synergistic tendency to converge. For inclusive green growth, higher-level regions might also drive the growth of neighboring regions. At the same time, the idea of a steady state in economic growth theories, such as the Solow model, also indicates that economic growth has a trend of convergence towards a steady state. Inclusive green growth is also an economic growth model, in essence. Therefore, we hypothesize the following.

H2: China's inclusive green growth has a convergence trend.
In essence, the correlation relationships of inclusive green growth are the interactions among three systems of economic, social, and ecological in the regions. Its spatial correlation network is a collection of inter-regional correlation relationships that facilitate the flow of "fluid factor resources" such as capital, technology, and management methods for inclusive green growth. However, different regions have different economic development, resource endowment, ecological environment, and location status. These conditions will definitely affect the level of inclusive green growth, resulting in uncoordinated and insufficient inclusive green growth and generating "potential energy differences" among provinces. Under the joint action of market regulation mechanism and governmental macroeconomic regulation and control, the fluid factor resources for inclusive green growth, such as people, information, materials, technology, and capital, can be aggregated and spread across provinces using spatial correlation networks. Thus, the differences in inclusive green growth between regions can be reduced, and inclusive green growth can gradually converge. Based on the above content, hypothesis H3 is proposed in this paper.
H3: Spatial Correlation Relationships Can Effectively Promote Spatial Convergence of China's Inclusive Green Growth.

Index System Construction
Taking full reference to existing research literature, this work starts from the scientific connotation of inclusive green growth and selects 26 specific indexes (see Table 1) from three subsystems of economic growth, social inclusion, and green sustainability to measure the level of inclusive green growth in China.
This paper examines economic growth in terms of both the quality of economic growth and the level of economic growth. Achieving economic growth is the core essence of inclusive green growth and a prerequisite for improving people's livelihoods. Economic growth must focus on both the quality and quantity of development [51], so this paper selects five indexes, including capital productivity, labor productivity, GDP per capita, and disposable income of all residents, to measure economic growth. The social inclusion dimension constructs the index system from two aspects: social equity and public services. Social inclusion is the value orientation of inclusive green growth, which emphasizes that economic growth should be accompanied by attention to guaranteeing social livelihood, equity, justice, and fruit sharing [21]. Therefore, this dimension contains nine specific indexes, including the urban registered unemployment rate, basic pension insurance coverage rate, urban-rural income ratio, fiscal expenditure per capita, and public transport vehicles per ten thousand people, etc.
The green sustainability dimension is portrayed in three aspects: resource endowment, green production, and environmental governance. As an essential requirement for inclusive green growth, green sustainability focuses on the mutual promotion of economic development and environmental protection and requires green economic development within the constraints of ecological environment and resource-carrying capacity. Among them, resource endowment corresponds to "green expansion", green production represents "carbon reduction", and environmental management measures "pollution reduction". This paper, based on the existing studies [5,12], selected 12 indexes, including the proportion of green space per capita, water resources per capita, electricity consumption per unit of GDP, household waste harmless disposal rate, etc., to measure green sustainability.

Measurement of Inclusive Green Growth Level
Based on the above evaluation indexes, this paper calculated the total index and each subsystem index (due to space constraints, detailed results are not listed in the article, and readers can obtain them from the authors if necessary) of inclusive green growth of 30 provinces in China from 2006 to 2019. Then, based on the calculated indexes, the situation diagram of inclusive green growth of 30 provinces in 2006 and 2019 were plotted by ArcGIS10.2 (see Figure 1) to preliminarily examine the spatial differences of inclusive green growth in China.
per capita, and public transport vehicles per ten thousand people, etc.
The green sustainability dimension is portrayed in three aspects: resource endowment, green production, and environmental governance. As an essential requirement for inclusive green growth, green sustainability focuses on the mutual promotion of economic development and environmental protection and requires green economic development within the constraints of ecological environment and resource-carrying capacity. Among them, resource endowment corresponds to "green expansion", green production represents "carbon reduction", and environmental management measures "pollution reduction". This paper, based on the existing studies [5,12], selected 12 indexes, including the proportion of green space per capita, water resources per capita, electricity consumption per unit of GDP, household waste harmless disposal rate, etc., to measure green sustainability.

Measurement of Inclusive Green Growth Level
Based on the above evaluation indexes, this paper calculated the total index and each subsystem index (due to space constraints, detailed results are not listed in the article, and readers can obtain them from the authors if necessary) of inclusive green growth of 30 provinces in China from 2006 to 2019. Then, based on the calculated indexes, the situation diagram of inclusive green growth of 30 provinces in 2006 and 2019 were plotted by ArcGIS10.2 (see Figure 1) to preliminarily examine the spatial differences of inclusive green growth in China.  Figure 1 adopts equal intervals to divide the inclusive green growth level of 30 provinces from low to high into five levels: "light gray", "relatively light", "grey", "relatively deep", and "dark gray". Consistent cross-period classification criteria ensure comparability between samples in the longitudinal direction. From the national level, the level of inclusive green growth in China is showing a clear upward trend. From 2006 to 2019, the national overall inclusive green growth index increased from 10.65 to 15.21, with an average annual growth rate of 2.78%. As can be seen directly from Figure 1, from 2006 to 2019, the color level in most parts of China has obviously deepened. This shows that with the promotion of sustainable development and comprehensive green transformation of the economy and society, the level of inclusive green growth in China has increased significantly. From the regional level, there are obvious differences in inclusive green growth among provinces. The level of inclusive green growth presents a distribution pattern of "high in East and West, low in the central". In Figure 1, the provinces with deep color are mainly distributed in the Eastern and Western regions, while the central provinces inland are generally lighter in color.

The Spatial Correlation Network Characteristics of Inclusive Green Growth
Based on the data of average gravity values between 30 provinces calculated using the modified gravity model, 207 inter-provincial correlation relationships were determined, and the spatial correlation network of China's inclusive green growth was visualized using the software UCINET 6 (see Figure 2). It can be seen from Figure that each province is more or less associated with other provinces, indicating that inclusive green growth is "universally correlation" in space, and the spatial correlation network is characterized by complexity and multi-threading.

The Spatial Correlation Network Characteristics of Inclusive Green Growth
Based on the data of average gravity values between 30 provinces calculated using the modified gravity model, 207 inter-provincial correlation relationships were determined, and the spatial correlation network of China's inclusive green growth was visualized using the software UCINET 6 (see Figure 2). It can be seen from Figure that each province is more or less associated with other provinces, indicating that inclusive green growth is "universally correlation" in space, and the spatial correlation network is characterized by complexity and multi-threading.

Overall Network Characteristics
To comprehensively grasp the correlation of inclusive green growth, this paper starts with three dimensions of inclusive green growth and adopts the modified gravity model to identify the spatial correlation of economic growth, social inclusion, and green sustainability. The number of correlation relationships for the three dimensions is 220, 206, and 200, respectively. Table 2 reports on the overall characteristics of an inclusive green growth network and its dimensions' networks.

Overall Network Characteristics
To comprehensively grasp the correlation of inclusive green growth, this paper starts with three dimensions of inclusive green growth and adopts the modified gravity model to identify the spatial correlation of economic growth, social inclusion, and green sustainability. The number of correlation relationships for the three dimensions is 220, 206, and 200, respectively. Table 2 reports on the overall characteristics of an inclusive green growth network and its dimensions' networks. Network density represents the strength of correlations between provinces. The greater the network density, the closer the correlations between provinces for inclusive green growth. For the inclusive green growth network, the correlation number is 207, and the network density is 0.2379. Compared with the maximum possible correlation number 870, the spillover and correlation effects of inclusive green growth are looser, and there is still much room for the network density to rise. The degree of correlation of the inclusive green growth network is 1, indicating that there is a direct or indirect correlation between any provinces, and no province is excluded from the spatial network. The hierarchical degree of the network represents the degree to which the spatial network is asymmetrically accessible. The hierarchical degree of the inclusive green growth network is 0.2407. Finally, network efficiency reflects the degree of stability of the inclusive green growth spatial network. The lower the network efficiency, indicating the spillover relationship in the network appears the redundancy, the network is more stable. The overall network efficiency of inclusive green growth is 0.7118, which indicates there are more related channels among provinces, and the spatial-related network is relatively stable.
In terms of the network characteristics of the three subsystems, firstly, the economic growth dimension has the largest number of network correlations, up to 220, with a density of 0.2529. The network density of the green sustainable dimension is the lowest at 0.2299. This indicates that there are more interactions between regions in terms of economic growth, while there are relatively fewer in terms of green sustainability. Secondly, for the network correlation degree, the network correlation degrees of the three dimensions are all the same as 1. This indicates that no matter in which dimension interaction mode, all provinces are included in the spatial network, and the spillover and correlation effects are obvious. Thirdly, for the network hierarchical degree, the network hierarchical degrees of the three dimensions are all the same as 0.2407. It shows that each province is relatively equal in each dimension network and the whole network, and the spatial correlation network has no significant class character. High-level provinces can play a leading role in synergistically promoting inclusive green growth. Finally, the efficiency values of the three dimensions exceed 0.65, among which the green sustainable dimension is the highest, reaching 0.7266. Economic growth was the lowest at 0.6601. This indicates that the spatial correlations of different dimensions overlap and have diversified spatial interactions.

Convergence Test in Spatial Network Correlation Scenario
This section first tested whether inclusive green growth in China has converged, then examined how inclusive green growth in China converges under different spatial correlations, and finally conducted heterogeneity analysis on the three major segments of East, Central and West regions (The eastern region includes 11 provinces, autonomous regions and municipalities, namely Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan; The central region covers eight provinces and autonomous regions: Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan; The western region consists of 12 provincial-level administrative regions: Sichuan, Chongqing, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Guangxi, Inner Mongolia).

β Convergence
Combined with previous related studies [11,[53][54][55], the following indexes are selected as control variables for the conditional β convergence test in this paper: (1) Urbanization level (URB). Urbanization is an important means and goal to promote economic and social development, and the proportion of the urban population is used as an index of urbanization level in this paper. (2) Industrialization level (lnIND). The industrialization level reflects the degree of development of a region, and different stages of development have different growth rates. In this paper, the value added of secondary industry per capita is used as a measure index, and logarithmic treatment is taken. (3) Educational attainment (EDU): education is the basic guarantee to promote scientific and technological progress and is an important foundation to improve production efficiency and enhance the concept of green development. In this paper, the proportion of the total number of students in high schools, secondary vocational schools, and colleges in the total population is used to measure the educational level. (4) Opening-up degree (OPE), which reflects the change in the regional economic system. An open and competitive market is an important means to improve the efficiency of resource allocation and promote economic and social inclusion. In this paper, the proportion of total import and export trade to GDP is used to indicate the degree of opening-up.
Regarding the model selection, based on the reference to existing studies [41,53], this paper first performs OLS regression followed by the LM test. The results of the OLS regression and LM test (Table 3) show that the Lagrange multiplier (LM) of spatial error and spatial lag is very significant under the geographical distance weight and inclusive green growth spatial association weight (WI), indicating that spatial factors should be included in the convergence test. The Spatial Durbin Model (SDM) can not only include the spatial lag terms of both the dependent and explanatory variables but also analyze the spatial spillover effects of variables simultaneously. It is a more general form of the Spatial Autoregressive Model (SAR) and Spatial Error Model (SEM). Therefore, this article selects the spatial Durbin model as the basic model for empirical analysis. Later, the LR Test and Ward Test results in Table 4 significantly show that the SDM model cannot be degraded into SAR or SEM models, which shows the rationality and optimality of SDM Model selection.    (2) and (4) are absolute and conditional convergence regression results under the W I (inclusive green growth spatial network weights), respectively.
Firstly, the coefficient β of convergence of inclusive green growth in China is less than 0 under both absolute and relative convergence regression tests and passes the 1% significance level test. This indicates that China's inclusive green growth shows a robust global convergence phenomenon during the full sample survey period. Secondly, comparing columns (3) and (4) with columns (1) and (2), the absolute value of β coefficient under conditional convergence is significantly larger than that of β coefficient under absolute convergence. This indicates that the convergence rate of inclusive green growth in China has significantly improved after taking into account socio-economic factors such as urbanization level, industrialization level, and education level. In addition, comparing columns (2) and (4) with columns (1) and (3), it can be seen that the absolute convergence rate (2.356%) and relative convergence rate (2.957%) under the inclusive green growth spatial network weight (W I ) are higher than that under the traditional geographical weight (2.248% and 2.818%). This shows that errors in spatial weight selection will lead to errors in the results. Further, hypothesis H3 confirms that inclusive green growth converges faster in the case of spatial correlation.

How Does China's Inclusive Green Growth Converge?
Given that the spatial interactions of each dimension of inclusive green growth are different, the spatial networks of different dimensions have different effects on the convergence. Therefore, it is necessary to further test the β convergence of inclusive green growth. Table 5 reports the convergence test results of China's inclusive green growth under the spatial correlation of different dimensions. Among them, columns (1)-(3) are the absolute convergence test results under W E (economic growth spatial network weight), W S (social inclusion spatial network weight), and W G (green sustainable spatial network weight), and columns (4)-(6) are the conditional convergence test results under W E , W S , and W G , respectively.
According to Table 5, it is easy to find that the convergence regression coefficient of China's inclusive green growth under the spatial network weight of each dimension is significantly negative, and China's inclusive green growth also shows an obvious convergence trend under the spatial correlation of each dimension. Similar to the results in Table 3, the absolute value of β coefficient of conditional convergence is obviously larger than that of absolute convergence under the spatial weight of each dimension, and the convergence rate of β conditional convergence is relatively higher. Specifically, in the absolute β convergence test, the convergence rate of inclusive green growth under the spatial network weight of economic growth (W E ) is the fastest, which is 2.366%. Under the green sustainability (W G ) dimension, inclusive green growth has the slowest convergence rate of 2.287%. In the conditional β convergence test, the convergence rate of inclusive green growth under the social inclusion spatial network weight (W S ) is the fastest (2.968%), and the convergence speed under the economic growth spatial network weight (W E ) is the slowest (2.871%). This suggests that the spatial network of economic growth is not the best channel for inclusive green growth to converge under the control of other factors. Strengthening the spatial correlation of social inclusion is more conducive to promoting the level of inclusive green growth in less-developed areas.     Note: Standard errors are reported in parentheses. ***, ** and * represent significance at the levels of 1%, 5% and 10%, respectively. Stata 14.0 is used for calculation.

Convergence Test of Inclusive Green Growth in Different Regions
Further, based on the set of spatial incidence matrices of inclusive green growth in the eastern, central, and western regions, this work investigates the characteristics of club convergence. As shown in Table 6, the coefficient of conditional convergence is negative in all three regions, indicating that inclusive green growth in three regions of the east, central, and west all have a significant convergence trend. Additionally, the absolute value of β coefficient is central > western > eastern, meaning the convergence speed in the central region is faster than eastern and western regions. This is mainly due to the lower level of inclusive green growth in the central and western regions, with continuous promotion of ecological civilization construction and high-quality development, the capacity of inclusive green growth in the central and western regions is rapidly improving, and inclusive green growth has shown higher marginal effect. Meanwhile, there are still significant regional differences in inclusive green growth between the eastern, central, and western regions. In the context of spatial correlation, the eastern region continuously provides growth momentum to the central and western regions via spillover effects, which may promote the rapid convergence of the central and western regions towards an equilibrium level.  Table 7 further reports the convergence test results of the east, central, and west regions under W E (economic growth spatial network weight), W S (social inclusion spatial network weight), and W G (green sustainable spatial network weight). From the perspective of convergence speed between regions, the basic characteristics of central > west > east regions are still maintained under the spatial correlation weights of various dimensions, further verifying the existence of "club" convergence characteristics in regions. From the perspective of different spatial network weights, the eastern, central, and western regions have the fastest convergence rate of inclusive green growth under the spatial network weight of economic growth, and the convergence rate of central regions is the same under the spatial correlation dimension of economic growth and social inclusion. Unlike the overall convergence situation across the country, the spatial correlation of economic growth has a more significant promoting effect on the convergence of inclusive green growth in the eastern, central, and western regions, while the spatial correlation of social inclusion has the most significant promoting effect on inclusive green growth at the national level.

Subregional
East Central West

Discussion
China has been committed to achieving social equity and ecological protection while growing its economy. Most of the existing research focuses on the measurement, spatiotemporal distribution, and influencing factors of inclusive green growth. Unlike existing research, this study focuses on the correlation network and convergence of inclusive green growth in China after examining its level and spatial pattern. Additionally, this article innovatively uses spatial network weights to explore the impact mechanism of spatial correlation of inclusive green growth on its convergence. This study is of great practical significance to provide empirical lessons for exploring the convergence path of inclusive green growth in China, and thereby promote the coordinated improvement in inclusive green growth in various regions.
(1) The measurement of inclusive green growth level shows that China's inclusive green growth level shows a distribution pattern of "high in the east and west, low in the central region", which is generally consistent with Sun et al.'s conclusion, 2020, that inclusive green growth in the eastern coastal areas is higher than that in the central and western regions [17]. Over time, by 2019, the vast majority of provinces had achieved an increase in the level of inclusive green growth, with more provinces having intermediate levels of inclusive green growth, showing a preliminary convergence trend. Further investigation reveals that Beijing and Shanghai have always been at the forefront of inclusive green growth in China. After 2013, Beijing surpassed Shanghai to become the region with the highest level of inclusive green growth. This may be related to the Chinese government's commitment to alleviating air pollution, especially addressing the haze problem in the northern region after 2012.
(2) Using a modified gravity model and social network analysis (SNA), 207 interprovincial inclusive green growth associations were identified, which confirmed hypothesis H1, that inclusive green growth in China is widely spatially correlated. Previous research has, to some extent, proven that inclusive green growth has spatial spillover effects. For example, Zhao et al. [56] used the spatial Durbin model to study the spatial spillover effects of inclusive green growth. However, traditional measurement methods can only reveal the spatial clustering characteristics of inclusive green growth and focus on spillover effects between neighborhoods [53]. It is difficult to quantify the relationship between any two regions, especially cross-regional relationships. Therefore, this article uses the modified gravity model and social network analysis (SNA) to characterize and reveal the relationships and features between each province and finds that the proposed network structure is complex and multi-threading. Li et al. [4] provided similar findings in their study on the efficiency of inclusive green growth.
(3) Both the results of σ convergence test and β convergence test show that China's inclusive green growth has a clear convergence trend (see Table 8). Thus, hypothesis H2 is confirmed. Beyond that, traditional convergence tests often lack the examination of spatial factors. Due to the widespread spatial correlation of inclusive green growth, the convergence test of traditional models may have significant errors. Therefore, this article introduces a spatial econometric model to test the convergence of inclusive green growth on the basis of spatial correlation networks. In Table 8, the convergence rate of inclusive green growth under the IGG spatial correlation weight is faster than that under the traditional geographic weight, which indicates that hypothesis H3 is confirmed; that is, spatial correlation can promote the convergence of inclusive green growth. In addition, heterogeneity analysis shows that the spatial correlation of economic growth has a stronger promoting effect on the convergence of inclusive green growth in the eastern, central, and western regions, while at the national level, the spatial correlation of social inclusion has a more significant promoting effect on inclusive green growth. The possible reason for this is that, on the one hand, the formulation of livelihood policies and systems such as social security and public services is coordinated and planned by the central government, and social inclusion has a strong correlation across the country. On the other hand, in the eastern, central, and western regions, economic growth remains the most closely connected channel among provinces, and the improvement in inclusive green growth in one province first interacts with other provinces via the spillover of economic growth. Therefore, under the weight of economic growth correlation, the eastern, central, and western regions have the fastest convergence rate of inclusive green growth. (4) This article also investigates the factors that affect the speed of inclusive green growth. From the regression coefficient of the control variable, the estimated coefficient of urbanization level (URB) has passed the significance test by at least 10% level under geographical distance weight, W E , and W G weight, and its coefficient sign is positive. This indicates that the improvement in urbanization level in one region is not conducive to the reduction in regional differences in inclusive green growth. The estimated coefficient of industrialization level (lnIND) is significantly negative under all spatial weights, indicating that the improvement in industrialization level not only helps to improve the level of inclusive green growth but also promotes the narrowing of the gap in inclusive green growth between regions, which is consistent with the result of Ref. [57]. At the same time, the spatial lag coefficient of the industrialization level (W × lnIND) is significantly positive, indicating that the improvement in the industrialization level in other regions will contribute to the steady convergence of inclusive green growth towards a higher level.
Due to the availability of research data, this article still has certain limitations in terms of research scope and topic. In the future, we will further strengthen research on the development level, regional differences, and development shortcomings of inclusive green growth globally and deeply explore the spillover relationships of inclusive green growth between different countries and regions.

Conclusions and Policy Implications
This study measures the inclusive green growth index of 30 provinces in China from 2006 to 2019. On this basis, the modified gravity model and social network analysis method are used to construct and analyze the spatial correlation network of China's inclusive green growth, and the convergence trend of inclusive green growth in the spatial network correlation scenario is tested at the national and sub-regional levels by using the spatial econometric model. The main conclusions are as follows.

Conclusions
Firstly, from the perspective of level measurement results, the level of inclusive green growth in China showed a significant upward trend during the sample review period, but there was a significant gap between provinces. The spatial distribution pattern of inclusive green growth level is roughly "high in east and west, low in the central". Secondly, in terms of spatial correlation networks, China's inclusive green growth has significant spatial correlation and spillover effects between provinces. The spatial correlation network presents a complex network structure with multiple threads, differentiation, and globality. The spatial correlation network of each dimension has similar structural characteristics to the overall network of inclusive green growth, and the spatial correlation of economic growth is relatively closer than other dimensions. Finally, the convergence test results of inclusive green growth show that inclusive green growth in China has significant β convergence characteristics under different spatial network weights, and after controlling other factors that may affect the convergence of inclusive green growth, the convergence rate of inclusive green growth has increased. Nationwide, inclusive green growth converges faster under the network weight of the social inclusion dimension. The results of regional studies show that China's inclusive green growth presents obvious club convergence characteristics. The convergence rate of the three major segments is central > west > east. Additionally, compared with other dimensions, under the spatial network weight of economic growth, the convergence rate of three major regions is the fastest.

Policy Implications
According to the above conclusions, this paper draws the following policy implications. First, we shall understand the rich connotation of inclusive green growth and promote the continuous improvement in inclusive green growth levels. It is necessary to improve the factor price formation mechanism, in which the market plays a decisive role, so as to prevent the distortion of factor prices from reducing the inclusiveness and greenness of economic and social development. On the one hand, information asymmetry, transaction cost, and other factors can lead to price distortion; on the other hand, improper incentives based on rent-seeking for enterprises and tax funds for the government can also lead to the deviation of factor prices. Therefore, in China's market-oriented reform, we shall perfect the factor pricing mechanism and the government supervision system to prevent resource mismatch and innovation inhibition caused by factor price distortion.
Second, we shall play the role of spatial correlation network of inclusive green growth and promote the spatial synergy of inclusive green growth. It is necessary to smooth the domestic circulation to promote the cross-regional flow and efficient agglomeration of various "fluid factor resources" such as capital, knowledge, technology, and management methods. Further, we should enhance the spillover driving effect in the East region and optimize the development environment of the central and western regions. For example, promoting the construction of transportation and information network infrastructure, as well as improving the ecological compensation mechanism and financial transfer payment system, can establish a good relationship-receiving platform for the central and western regions and accelerate inclusive green growth in the central and western regions.
Third, we should accurately grasp the convergence characteristics of the whole country and each region, implement classified strategies, and explore the effective path for the convergence of inclusive green growth. From the national level, the spatial correlations of social inclusion contribute more significantly to the convergence of inclusive green growth. Therefore, we should optimize the cross-provincial medical records, the mutual recognition of pension insurance, and the sharing of educational resources and employment information to promote the coordination of people's livelihood safeguards. From the regional level, the spatial correlation of economic growth dimensions is still the most effective dimension to promote the convergence of inclusive green growth in the three major regions. Therefore, it is necessary to break down institutional barriers, such as administrative division and market division, and promote intra-regional knowledge and technology spillover. At the same time, we should ensure the logical and orderly flow of production factors and innovation resources to realize the synchronous improvement in resource allocation efficiency, social security capacity, and green technology level.