Temporal and spatial evolution of embodied carbon transfer network in the context of the domestic economic cycle

Abstract Under accelerated domestic economic cycle, it is significant to predict the embodied carbon transfer network (ECTNs) to identify key emission regions to improve emission reduction efficiency. Based on the existing China Multi-regional Input-Output Table (CMRIOs) for 2002, 2007, 2010, 2012, 2015 and 2017, the CMRIOs for 2002-2017 were updated, then the ECTNs were predicted and constructed from 2018 to 2025 through Particle Swarm Optimization- Support Vector Model. Finally, the spatial and temporal evolution trends of the ECTNs’ features were explored through complex networks analysis. The results showed that carbon leakage between provinces has been becoming increasingly serious. The small-world features of the ECTNs were becoming increasingly obvious. The distribution of provinces with great influence on carbon transfer was transferred from north to south, and then to the central region. Hebei, Jiangsu, Henan, Zhejiang, Inner Mongolia, and other resource-intensive and manufacturing provinces played an important "bridge" role in the trade between economic developed and developing provinces. Trade ties between non neighboring provinces have become increasingly close, which means the development of China’s integration has strengthened. This study provides a theoretical reference for the formulation of China’s overall carbon emission reduction policy. Graphical Abstract


Introduction
Over the past 30 years, China actively integrated into the globalization process, and achieved remarkable development worldwide.However, its sloppy development model has also taken a serious environmental cost [1,2].In the early days, China mostly participated in resource-intensive and low value-added production activities due to the backward development of China's industry, leading it being at the middle and low end of the global value chain, which resulted it once was a "pollution haven" and the largest emitter of carbon dioxide (CO 2 ) emissions [3].In the face of global warming, extreme weather and other climate problems caused by CO 2 , more and more countries are proposing carbon neutrality to support the goal of net zero carbon emissions in the second half of this century set by the Paris Agreement [4].China has also actively undertaken the responsibility of global CO 2 emissions reduction, and put forward the 2030 carbon peak and 2060 carbon neutral targets, demonstrating its commitment to CO 2 reduction.
Carbon emission reduction targets are divided into regional targets based on geographical location, and then emission reduction tasks are formulated according to the development and CO 2 emission status of each region.The research on CO 2 emissions caused by energy consumption has been relatively mature, and has become the main basis for policymakers to formulate CO 2 emission policies [5].However, China is a vast country with significant imbalances in provincial economic development and CO 2 emissions.In particular, in recent years, the eastern coastal regions and Beijing and Tianjin, where the industrial economy developed earlier, have actively sought industrial transformation, shifting polluting industries out to the central and western regions, which further widened the gap between regional economic development and environmental conditions [6].Along with increasingly convenient transportation, the domestic economic cycle has led to the separation of production and consumption between regions.The products in resources-oriented provinces, such as Inner Mongolia, Shanxi, represented the characteristics of low economic efficiency and high carbon emissions.While developed provinces, such as Beijing and Shanghai, transfer CO 2 emissions by purchasing polluting products from other regions, which leads to that consumption-side carbon emissions (CE) are significantly higher than production-side carbon emissions (PE) [7].Therefore, using only CO 2 emissions due to energy consumption as a reference for setting provincial carbon emission reduction tasks may be unfair to some provinces, which would even weaken the effectiveness of the policy [8].It would be more beneficial to comprehensively consider inter-provincial CO 2 transfer network when formulating CO 2 reduction tasks, which is relative fair for some provinces with unbalanced PE and CE [9].
As China's multi-regional input-output table (CMRIO) has been well developed, it is increasingly common to apply to explore embodied carbon emissions (EC) caused due to consumption demand between regions or sectors [10,11].Interprovincial trade leads to CO 2 transfer, so it is significant to build an embodied carbon transfer network (ECTN) through CMRIO to analyze key provinces of carbon emissions for in-depth analysis [12].However, the MRIO is heavily engineered and is usually prepared only once every 3-5 years, resulting in less available data, and the latest CMRIO is still 2017.The existing CMRIO could only analyze the ECTN caused by inter-provincial trade in the past years, which is difficult to effectively predict the future change situation.How to assess the possible future CO 2 transfer situation and analyze the "roles" of key provinces in ECTN would undoubtedly provide meaningful references for the formulation of carbon reduction policies.
According to the above analysis, this study mainly attempted to solve the following three problems: (1) based on the existing CMRIOs of 2002,2007,2010,2012,2015 and 2017, the missing CMRIOs during 2002-2017 were updated through the RAS method under the premise of unified sectors; (2) based on the CMRIOs from 2002 to 2017 after price reduction, this study calculated the CO 2 transfer among provinces in China, and Particle Swarm Optimization -Support Vector Machine (PSO-SVM) was employed to calculate the CO 2 transfer data of provinces to other provinces, so as to construct ECTNs from 2018 to 2025; (3) complex network analysis (CNA) was used to analyze the temporal and spatial evolution of ECTNs from 2002-2025, which aimed to identify the key provinces and regional community divisions from the perspective of CO 2 transfer.Finally, this study provided theoretical reference for CO 2 emission reduction policies according to the research findings.
The remainders of this study is organized as follows: we comb the relevant research on carbon transfer, compex network and support vector machines in Section Literature Review.The study methodology and data are presented in Section Materials and Methods.The results are presented in Section Results.The analysis and practical applications of this case are presented in Section Discussion.Finally, Section Conclusions are the conclusion and research limitations of this study.

Literature review
Not only does China's large economic activity make it active in international carbon transfer networks, but the increasingly fine-grained domestic value chains and differences in development structure also make inter-regional CO 2 transfers within China increasingly abundant [13].Similar to the transfer of CO 2 from developed countries to developing countries, developed provinces in China also transfer large amounts of CO 2 to resource-rich, but economically undeveloped regions [14].According to CO 2 of China's provinces from 2007 to 2012, economic development would increase carbon emissions transfer [15].For example, energy-rich provinces such as Hebei and Inner Mongolia export energy resources and industrial products to developed coastal provinces, thus, becoming the largest carbon outflow provinces, while economically-developed coastal provinces are the largest carbon inflow areas in China [16].Taking geographic region as the scope of study, what was found is that the inter-provincial EC transfer in the middle and lower reaches of the Yellow River, where the economy is relatively developed, was much higher than that of the inter-provincial EC transfer in the upper reaches, where the economy is relatively undeveloped [17].Thus, a complex inter-provincial transfer network containing much inward and outward CO 2 was formed under the domestic economic cycle, and the analysis of this network provided perspectives and theoretical tools to understand the basic features of inter-provincial carbon transfer systems [18].
Complex networks, as tools for the effective structural analysis of integrated economic systems, are centered on abstracting real individuals with complex relationships as nodes in a network and exploring their interactions using network metrics [19].CNA has been widely used in economic, resource, and environmental fields [12,20].Considering the impact of provincial community structure on energy imports and exports, Gao et al. [21] combined energy/emissions embodied in bilateral trade and CNA to visualize the transfer and clustering characteristics of interregional energy, which helps to understand the heterogeneous distribution of different types of energy flows and the possibility of potential impacts of province-specific policy interventions.The scale of CO 2 transfer in 31 provinces is unevenly distributed, but the overall spatial network structure is relatively stable, and the network relevance is increasingly close.Policy changes in a single province could quickly spread and affect the entire ECTN [22].The temporal and spatial evolution of ECTN is relatively obvious.Around 2002, CO 2 emissions transferred mainly from the eastern and central regions to the northern provinces.By 2012, due to the relocation of heavy polluting industries in the eastern region, CO 2 was transferred to the southwest and central regions [23].From the analysis of ECTN's nodes, North China was dominated by heavy industry, and some provinces that played the role of intermediary transmission were mostly located in Northwest China in 2012-2017 [24].However, Jiangsu, Guangdong, Hebei, Zhejiang and other provinces are key nodes in China's ECTNs, with strong local closeness centrality [25].In addition, the division of provincial community was geographically dependent, which is basically consistent with the development of national urban agglomeration, such as Chengdu-Chongqing urban agglomeration, Harbin-Changchun urban agglomeration and mid-Yangtze River urban agglomeration [26].The above findings demonstrate the superiority of CNA in revealing the hidden features of ECTN.Therefore, this study combined CMRIOs with CNA to explore the structural features of the ECTN between Chinese provinces under the domestic economic cycle and provided theoretical references for collaborative carbon emission reductions.
In studies of carbon emission prediction, the general methods can be divided into two categories: econometric models, which usually include linear regression [27] and grey models [28] and artificial intelligence models, which are commonly used by neural networks [29], random forests [30]and SVM [31].Due to the continuous availability of energy-related CO 2 emissions data, prediction of carbon emissions has been studied extensively [32,33].However, there are relatively few predictions on embodied carbon (EC) emissions, which are either discussed from the sources of material [34]or analyzed from the perspective of industry carbon transfer [35].
Compared with traditional econometric models, machine learning excels in self-learning, generalization, computational speed [36], and associative memory.The SVM, based on statistical learning theory and structural risk minimization, has been typically used to address nonlinear problems.It is also good at accommodating small sample training data sets and high-dimensional pattern recognition problems, and performs well with classification and regression features [37].For example, Sun and Huang [38]built a CO 2 emission intensity prediction model based on factor analysis and extreme learning machine.Zeng et al. [39], based on China's energy-related CO 2 emissions data from 1980 to 2019, determined 17 factors that affect the energy consumption structure to predict China's advanced index of energy consumption structure from 2020 to 2030 through SVM.However, the SVM still requires parameter optimization to further improve prediction accuracy, such as the improved lion swarm optimizer [40], grey wolf optimizer-based [41], particle swarm optimization algorithm [42], and firefly search algorithm [43].
Among such algorithms, the high-speed convergence and global search capability of PSO make PSO-SVM good for prediction.Rui et al. [38] compared three parameter optimization models of cross-validation, grid search, and found that PSO optimized SVM has the best prediction effect.Therefore, in this study, the PSO-SVM model was used to predict carbon emissions.
There have been many studies on EC, which provide ideas for the study.However, the prior studies are mostly based on the existing MRIOs to analyze the ECTN of provinces or sectors in past years, ignoring future changes of carbon transfer networks.What could be found from the existing literature is that due to the incoherent compilation of CMRIOs and the lack of available data, there is greater uncertainty and difficulty in ECTN prediction.In response to the above issues, this study might make the following contributions: (1) Based on the existing CMRIOs, it took the lead in updating the CMRIOs from 2002 to 2017, systematically analyzing the spatial and temporal evolution trend of China's ECTNs, and providing ideas for the continuous and systematic research on topics such as embodied energy, virtual water, and ecological footprint related to interprovincial trade.(2) According to China's ECTNs from 2002 to 2017, this study tentatively predicted and constructed the ECTNs from 2018 to 2025.Combined with the CNA, the key provinces in China's carbon transfer network were identified, and the "role" changes of each province in the future ECTN were analyzed, providing a theoretical reference for formulating carbon emission reduction policies and phased adjustment of collaborative carbon emission reduction strategies.

Multi-regional input-output table
Input-output tables (IOs) created by Leontie [44]explained the economic transfer relationships between production sectors and regions.MRIOs extended with environmental data have been widely used to study carbon emissions or energy transfers, as well as other environmental relationships between regions or sectors [45].CMRIO is divided into competitive CMRIO and non-competitive CMRIO [46].The CMRIO used in this study in 2002 is a competitive CMRIO, and the other years are non-competitive CMRIOs.
In a non-competitive CMRIO, the row balancing relationships is where r and s denote provinces, i and j denote sectors; z rs ij denotes intermediate inputs from sector i in region r to sector j in region s; f rs i denotes final demand from region s to sector i in region r; ex r i denotes exports from sector i in region r; x r i denotes total output of sector i in region r.
The total output of region r is where x r , z r , f r and ex r denote the total output, total intermediate input, total final demands and total exports of region r, respectively; z rs denotes the intermediate goods input from region r to region s; A d is the domestic input-output coefficient matrix, among which a rs ij ¼ z rs ij =x s j ;ðI À A d Þ À1 is the domestic Leontief inverse matrix.The carbon transfer form region r to region s is ee rs , as follows: where e r i is carbon emissions coefficient of sector i in region r and e r i ¼ c r i =x r i , c r i denotes carbon emissions of sector i in region r.
In a competitive CMRIO, the total output in region r is as follows: where z r im denotes the import of intermediate products in region r, A ¼ Z d þ Z im is the total input-output coefficient matrix, im r denotes the taotal import in region r, L ¼ ðI À AÞ À1 is the total input-output coefficient matrix.
Considering the share of imported products in intermediate demands im Z ¼ ðim Z ij Þ nÃn and final demands im Z ¼ ðim Z ij Þ nÃn , the proportion of domestic products used for intermediate demand and final demand are defined as s , respectively [8].Combined with Eq. (3), carbon transfer ee rs from r to s in the competitive CMRIO is as follows：

RAS analysis
The RAS method is also called the Bi-proportional Scaling Method, or the Timely Correction Method.The "total intermediate input" of the target year is used as the column control vector, and the "total intermediate demand" of the target year is used as the row control vector.The IOs' intermediate input-output structure of the base year is modified to obtain that of the target year.Substitution multiplier matrix R and manufacturing multiplier matrix S are constructed as follows respectively: The base period is assumed as period 0 and the direct consumption coefficient matrix is A 0 ; The target period is assumed as the period t, and the direct input-output coefficient matrix is A t , then R and S exist to make A t ¼ RA 0 S tenable.The objective error function was as follows: where a r 0ij is the input-output coefficient in the base period 0; v r tj is the value-added of sector j region r in target period t; y s ti , im s ti and x s ti represent the final product demand, import and total output of sector i in region s in target period t.Eq. (7) shows that the sum of squares of errors between the horizontal and vertical evaluation values and the known values of the input-output table is minimized.Under this goal, the IO data will converge and the direct input-output coefficient matrix of the target period t will be obtained through repeated iteration.
Specifically, take the existing CMRIO of the reference year as the benchmark table, and update the intermediate demand matrix and final demand matrix through the data of the benchmark table, such as total industrial output value, import and export, rural residents' consumption, urban residents' consumption, government consumption, inventory investment, and fixed assets investment.The total output value and value-added of the industry in the target year are taken as the columns' sum control vectors, and the intermediate demand is taken as the rows' sum control vectors of the intermediate input flow

Support vector machine model and prediction
The SVM was first proposed by Cores and Vapnik [47], and has been typically used to solve small sample, nonlinear, and high dimensional pattern recognition problems.The basic approach of the SVM is to construct a hyperplane as a decision line in the sample space to classify the samples.Currently, SVMs are classified into support vector classification machines, which are usually used for classification problems, and support vector regression machines, which are used for prediction.The latter was used in this study.

Support vector machine model
For training samples ðx i , y i Þ ði ¼ 1, 2, . . ., nÞ, x i 2 R n , y i 2 R n represent the input and output respectively to obtain their regression functions： Where w represents the weight vector, ðw Á xÞ is the dot product operation in high-dimensional space.If all samples within the accuracy e can be estimated by f ðxÞ, the above problem will be transformed into a quadratic programming problem: Considering the influence of noise, relaxation variables n i and n Ã i are introduced, and the optimization equation is as follows: where the first term is used to maximize the classification interval, the second term is used to reduce the error; C is the penalty coefficient of the sample exceeding the error e, and it is between (0,1).If the error is less than e, C will not be recorded, otherwise the epsilon loss function would be recorded as: SVM needs to map the input quantity to the feature vector of higher dimensions to solve the nonlinear problem.In order to avoid the problem of too high dimensions, the kernel function jðx i , x j Þ is introduced, and the Gaussian radial basis kernel function is selected in this study: where parameter r affects the mapping from sample space to feature space.Eq. ( 10) is a convex optimization problem.Lagrangian multipliers are introduced to obtain Lagrangian functions: Then, the original problem is transformed into the corresponding dual problem, and the expression of f ðxÞ obtained after solving a is: Parameter optimization of support vector machine Cross-validation.The performance of SVM largely depend on the type of SVM used, kernel function, penalty coefficient, and selection of kernel parameters.However, there is no theoretical method to determine the penalty coefficient and kernel parameters, and the Cross-validation method is commonly used.The original data are first divided into training and test sets.The training set is then fitted with an SVM.Lastly, the validation set is used to verify the prediction accuracy and generalization of the model.The method searches for parameters with good fitness to the SVM through iterative validation and prevented overtraining.However, the cross-validation method is complex and not time-sensitive, which usually leads to local optima and overfitting of the model.
Particle swarm optimization algorithm.The PSO algorithm proposed by Kennedy and Eberhart [48] is a stochastic search algorithm constructed by combining evolutionary theory and the features of bird foraging behavior.The core idea is to first form a group of random particles into a population, then change the position of particles through the set information, and gradually optimize the search in an iterative manner, so as to achieve the goal of finally finding the optimal solution.

Design predictive model
Referring to the model design of Hu and Lv [49], this study tested PSO-SVM and SVM using the cross-validation method for parameter search (referred to as traditional SVM), respectively, with the following modeling process. Step where y i Ù and y i represent the predicted and actual values, respectively.
Step 4: From 2004, a time window of size 14 was constructed, and the data inside the window were the input data of the optimal model selected according to Step 3 for out-of-sample data prediction (Figure 1).

Complex networks analysis
In the economic system, CO 2 flows between provinces and sectors through input-output relationships, thus constituting a weighted directed complex network.In which provinces are network nodes, transfers in and out between provinces are directions, and transfers are assigned weights.The constructed transfer network is as follows.
T ¼ where T is embodied carbon transfer network, w rs ðr ¼ 1, 2, . . ., m; s ¼ 1, 2, . . ., mÞ denotes the amount of carbon transferred between province r and province s, m is the amount of nodes in ECTN.Using a series of parameters of complex networks, this study described the features and laws of carbon transfer system.The relationship between China's provincial carbon transfer caused by economy and trade was further analyzed from the perspectives of the features of small world, the network nodes and provincial community.

Small-world features
Average path length is average steps of EC transfer between any two regions in a complex network, which indicates network connectivity [50] Its calculation equation is as follows: where L represents average path length; d rs represents the number of shortest path edges of r and s nodes; m is the number of nodes.Average clustering coefficient is the ratio of all adjacent nodes to the potential maximum number of edges, which is used to evaluate the degree of node aggregation [51].If a node in the network has a high clustering coefficient, it means that there is a close relationship between the node and its neighbors.Its calculation equation is as follows: where C is average clustering coefficient; Q r represents the actual number of connections between nodes; q r denotes the number of adjacent nodes r, and these adjacent nodes have at most q r ðq r À 1Þ=2 potential connections.

Analysis of network node features
Weighted degree is total flow of EC in a region.In directed networks, weighted degrees are divided into weighted in degrees and weighted out degrees [52].Their calculation equations are as follows: where Y in r and Y out r represent the weighted in degree and weighted out degree of region r respectively.
Betweenness centrality is defined as the ratio of the number of shortest paths passing through the node to all shortest paths in the network, reflecting the node's ability to control other nodes as an intermediary [53].The calculation equation of the betweenness centrality of node i is as follows: where b i represents betweenness centrality; g rs is the number of shortest paths of nodes r and s; g ras is the number of shortest paths of the above paths through node a.
Closeness centrality is defined as the average weighted distance between one node and other nodes in the network.The greater the closeness centrality, the better the efficiency and independence of the nodes [54].The equation for calculating the closeness centrality of node r is as follows: Network community structure In a complex network, the clustering represents the close relationship between nodes.The community formed by these clustering nodes is called community structure.A complex structure is divided into several sub blocks to more succinctly describe the entire network, which could be used to mine the deep characteristics of ECTNs [55].The equation of modularity Q is as follows: where, C r is the community to which node r belongs; w represents the total EC transfer, w ¼ The algorithm is divided into two parts.First, each node is assigned to a different community.Node r is placed in community j to evaluate the added value of modularization DQ considering the neighboring node s.If DQ is positive, node r would be placed in the largest community; otherwise, node r is placed in the original community.Modularization DQ is expressed as: where P in w is the sum of the weights of the internal connections of community C; P tot w is the sum of the weights of the nodes connected to C; k r is the strength of node r; k r, in is the sum of the weights of node r to the nodes in community C, and h is the sum of the weights of all connections in the network.emissions data of Tibet, it is assumed that the carbon emission intensity of all industries in Tibet is 0, which will not affect the mutual carbon transfer between other provinces.The research of Wang et al. [22] also confirmed that there is almost no EC transfer between Tibet and other provinces.When dividing communities, Tibet was always divided into a separate community, thus Tibet was deleted from their ECTN.Finally, the ECTN among 30 provinces required for this study was extracted from the ECTN among 31 provinces.

Data
Since CMRIO for 2002 contains 21 sectors, CMRIOs for 2007 and 2010 contain 30 sectors, CMRIOs for 2012, 2015 and 2017 contain 42 sectors, energy-related CO 2 data contains 45 sectors in CEADs, it is necessary to classify the sectors uniformly.In the department aggregation, the "data treatment scheme 2" proposed by Su et al. [61] was adopted.Referring to the sectoral divisions of Wang et al. [62], Yan et al. [63], and Zhou et al. [64], the sectors were aggregated into 21 based on the maximum number of sectoral division retained, as shown in Appendix A in the Supplementary Materials.
In the process of updating CMRIOs, the data of agricultural gross output value, agricultural valueadded, rural residents' consumption, government final consumption and inventory in each province are from China Statistical Yearbook and Statistical Yearbook of each province.The industrial gross output and value-added are from the China Industrial Statistics Yearbook and the provincial statistical yearbooks, while the gross output value and value-added of the construction industry are from the China Construction Statistics Yearbook and the provincial statistical yearbooks.The gross output value and value-added of the service industry are calculated according to the value-added rate and the value-added rate of CMRIOs.The provincial industrial and agricultural import and export data are divided into four HS customs codes from National Research Network, with a total of more than 1000 commodities.First, the corresponding relationship between the HS code and the ISIC industry classification standard was established according to the industry corresponding relationship between the four quantile HS code and ISIC Rev. 3.According to the National Economic Industry Classification Standard (GB/T4754-2002), we divided the four HS codes into corresponding industries and more details were presented in Appendix B in the Supplementary Materials.The total import and export data of service industry by province are obtained from China Business Yearbook, China's service trade guide, statistical yearbook, papers and statistical annual reports.For imports and outputs of missing years, they were calculated according to the CMRIOs of known years.Taking 2002 as the base period, the updated CMRIOs were subject to price reduction.The production price indexes of agriculture, industry and construction are from the National Research Network and China Statistical Yearbook, while the production price indexes of service industry are from China Statistical Yearbook.

Simulation of support vector machine
In order to compare the cross validation and PSO algorithm-optimized SVM which is more suitable for the CO 2 emission prediction, this study took the 2017 CO 2 emission prediction as an example, and the RMSE and MAE of the two models are shown in Figure 2. It is obvious that PSO-SVM performs better in CO 2 emission prediction of this study.The CO 2 transfer prediction results of Beijing, Jiangsu, Guangdong and Xinjiang in 2017 were randomly selected (see Appendix C in Supplementary Materials for the rest of the provincial prediction results).As shown in Figure 3, the SVMs of the above two algorithms could predict the data trends, but the prediction effects are different.In the predictions of each province, most of the predictions of PSO-SVM have a relative error distribution between [-0.2,0.2], and only a few predictions have a relative error greater than 0.2 which are mostly for paths with relatively small CO 2 transfer.Since this study mainly incorporated the paths with larger CO 2 transfer volume but did not include smaller CO 2 transfer paths when constructing the complex network, the above error distribution is in an acceptable state overall.

Construction of embodied carbon transfer network
Based on the carbon transfer calculated from the existing data, we predicted the carbon emission data using the PSO-SVM, constructed the future ECTNs which were analysed by CNA.Too many linear relationships made it challenging to reveal the network's essence, and critical paths must be selected to explore the embodied carbon flow relationships, rather than all of the inter-provincial trade linkages.A threshold value was set for the magnitude of the embodied carbon flow, and the transfer path can be ignored when the carbon flow between provinces was extremely small [21].To reasonably select carbon transfer paths, the 870 edges in the network were arranged according to the weights of the edges (i.e. the EC flows) from smallest to largest, and the cumulative sum of the edge weights was calculated, as shown in Figure 4.When the cumulative probability was less than 90%, the cumulative probability increased rapidly as the number of edges increased; when the cumulative probability was greater than 90%, the cumulative probability increased at a slower rate as the number of edges increased, thus, indicating that 90% of the embodied carbon flows occurred on a few edges.Therefore, the paths covering the top 90% of carbon fluxes were selected as edges of the complex network in this study, and the rest performed the deletion process.Thus, the number of complex network edges were 329,328, 321, 385,388, 382, 387, 386 and 392 for 2002-2010, 494,493, 507, 517, 502, 500 and 514 for 2011-2017, and 526,528, 532, 533, 536, 537, 535 and 533 for 2018-2025, respectively.Small-world features of the complex network In the complex network, the small-world features indicated that most nodes were not directly connected, but rather, established relationships through other nodes in a small number of steps [65].The average path length and the aggregation coefficient were usually used to reflect the smallworld features.If the small-world features existed in a complex network, it indicated that the network was well connected and the control of a key node quickly affected the other nodes [66].As shown in Figure 5, compared with the ECTN of Song et al. [25] in China from 2002 to 2017, the average clustering coefficient of this study is relatively low as a whole, which may be because Song et al. [25] used all paths when building a complex network, while this study only used the CO 2 transfer path with the first 90% contribution rate.From 2002 to 2012, the average clustering coefficient showed an upward trend, which was consistent with the research conclusion of Wang et al. [22] and Lv et al. [23].During 2012-2017, the average clustering coefficient decreased first and then increased.The average path length was relatively stable and fluctuated slightly.

Key regions in the embodied carbon transfer network
Regions with high carbon flow The distribution of the contribution of degree strength by province is shown in Figure 6.Degree did not change significantly during the study period.A total of 23% of the provinces controlled half of the carbon flows, while less than 50% of the provinces controlled 80% of the carbon flows.This means that both PE and CE are distributed in a few provinces.If total carbon emissions control is implemented in these provinces, it will have an important impact on the total carbon emissions of the country.
Figure 7 shows the distribution of in-degree and out-degree CO 2 between 30 provinces in 2002, 2010, 2017 and 2015, and that of the rest are represented in Appendix C in Supplementary Materials.Consistent with the findings of Pu et al. [13] and Dong and Zhang [67], there was a significant imbalance in the distribution of PE and CE across Chinese provinces, and this imbalance was increasing over time.From the perspective of indegree CO 2 , Hebei, Heilongjiang, Jilin and other northern industrial provinces, as well as Beijing, Shanghai and other cities with earlier industrial development, ranked top in the initial stage of the study.In the middle and later stages of the study, the in-degree CO 2 of central and eastern coastal provinces, such as Jiangsu, Henan, Guangdong and Zhejiang, accounted for an important share in the country.From the perspective of out-degree CO 2 distribution, the overall change in the study period was relatively small.Hebei, Henan, Jiangsu and other industrial developed provinces, as well as Inner Mongolia, Shanxi and other resource-oriented provinces, have always ranked in the forefront of the country in terms of out-degree CO 2 .As for Qinghai, Ningxia, Hainan and other provinces, their in-and out-degree CO 2 are at a low level due to the small economic aggregate and less trade in goods.
Regions with large betweenness centrality In complex networks, betweenness centrality has been used to explore the intermediary capacity of nodes.These nodes act as bridges to transfer embodied carbon among sectors or regions.The larger the betweenness centrality, the stronger the node's ability to control the carbon emissions flow.Figure 8 shows the betweenness centrality in some years (the others are presented in Appendix E in Supplementary Materials).In general agreement with Sun et al. [7], Wang et al. [22], provinces such as Henan, Jiangsu, Hebei, and Guangdong are key bridges in China's trade and economic linkages.In the pre-study, Guangdong ranked first in terms of betweenness centrality and eigenvector centrality, indicating that Guangdong is not only influential in connecting multiple regions, but also central in connecting the most influential regions, and has a prominent position in the national carbon flow network.However, the betweenness centrality of Guangdong gradually weakened and, together with Shandong, were gradually exceeded by Henan and Jiangsu.As for Sichuan, Ningxia, Xinjiang, Qinghai and Hainan, betweenness centrality has been at a very low level due to their relatively remote location and small trade volume.
The competition for betweenness centrality between Jiangsu and Henan has been intense, with Jiangsu ranking ahead of Henan in 2010 and earlier, while the two remained nearly the same in 2012 and 2015.However, in 2017 and after, Henan was significantly ahead of Jiangsu in controlling carbon emissions in other provinces.Through the above analysis, it can be found that China's industry has been transferred from the eastern coastal provinces to the central and western provinces, which confirms the findings of Ran et al. [68].
Regions with large closeness centrality Regions with high closeness centrality usually have close economic interactions with other regions.Once the above regions are affected, the impact will be extended to other regions with the shortest path, thus, affecting the complete trade network [69].As can be seen from Figure 8, the value gap of closeness centrality among most regions was small and did not change substantially over time.Among the regions, Hebei, Henan, Jiangsu and Inner Mongolia had consistently higher closeness centrality, indicating that those provinces had higher carbon emission transmission efficiencies and higher uncontrolled capacities.This was followed by Shandong and Liaoning, which were second only to the above provinces in terms of closeness centrality.

Division of communities
The association structure indicated that provinces in ECTN could be divided into multiple small communities, with closer inter-regional linkages within the same association.Unlike the inter-provincial associations in 2002 and 2010, which were geographically clustered, the provincial associations in 2017 and 2025 are relatively geographically dispersed, which was confirmed by Zhu et al. [26].C1 mainly included 7 provinces including Beijing-Tianjin-Hebei, Shanxi, Inner Mongolia, Hubei and Jiangxi; C2 was scattered, including 3 provinces -Liaoning, Jiangsu and Anhui; C3 was concentrated in the southwest, southeast coast and Shandong, totaling 8 provinces.C4's provinces are mainly concentrated in the upper-and mid-Yellow River, eastern coastal provinces (Shanghai, Zhejiang, Fujian) and northeast provinces (Heilongjiang and Jilin), totaling 12 provinces.By 2030, the provinces of each community were more decentralized.C1 mainly included the provinces in North China, Jiangsu and Anhui.C2 was loosely distributed where provinces were scattered in the northeast, southwest coastal areas, Xinjiang, Shandong and other regions.C3 contained the largest number of provinces, concentrated in the southwest, then the upper Yellow River, and some provinces in the lower and mid-Yangtze River.
Through the division of regional communities, it can be clearly observed that China's inter-provincial trade communities were more consistent with the division of China's urban agglomerations and economic zones.The inter-regional embodied carbon linkages showed a trend of increasing geographical dispersion, indicating the strengthening of trade links between non-contiguous provinces and cities, and the gradual integration of China's trade development.

Discussions on inter-provincial carbon transfer
The large-scale development of China's industry has only been nearly 40 years.It has gone through the stages of scale from small to large, process from rough to economic, and environmental protection from contempt to attention.To some extent, carbon emissions reflect its development process.The total amount of inter-provincial carbon transfer in China has been on the rise due to the continuous expansion of production scale.In 2002, it was 1128.48 million tons.With China's accession to the WTO and the improvement of rail transit, inter-provincial trade and total production increased rapidly, followed by an accelerated increase in the total carbon transfer.Due to the global financial crisis in 2008, the reduction of China's trade sharply reduced the growth rate of total carbon transfer until 2010, when the trade situation improved, the growth rate of total carbon reached the maximum.In 2015, the concept of green development was first put forward at the fifth plenary session of the 18th Central Committee of the CPC, and the total amount of It can be seen from Figure 5 that the average path length and average clustering coefficient fluctuated significantly before and after 2012, and the small world characteristics of complex networks increased.For the above phenomena, we guess the reasons are as follows: on the one hand, 494 paths were included in the carbon transfer network in 2011, an increase of 26.02% compared with 392 paths in 2010.From the calculation method of average path length and average clustering coefficient, it may lead to a large shortterm growth of their calculated values; On the other hand, after 2010, China's transport infrastructure has entered a stage of rapid development, such as the average growth rate of highway mileage is more than 20%; With the popularity of smart phones and "Four Connections and One Access" and other express companies becoming bigger and stronger, third-party Internet payment has grown at a "takeoff" speed.The national express business volume has grown from 26% in 2010 to 57% in 2011, and maintained a growth rate of more than 50% until 2016 (China Economic Data).All of these have led to the flourishing of China's inter-provincial trade after 2010, strengthening the inter-provincial carbon transfer link.

Discussions on key provinces of carbon transfer
A small number of provinces controlled the vast majority of carbon transfers nationwide, a finding consistent with Gao et al. [19].Provinces with large carbon outflows were divided into two main types: those rich in energy resources (Shanxi, Inner Mongolia, etc.) and those with developed industrial industries (Hebei, Shandong, Jiangsu, Liaoning, etc.), which undertook the task of transporting energy or carbon-intensive products to other provinces.Analysis of Figure 7 and Appendix D in Supplementary Information showed that the provinces with the highest carbon inflow ranking have a trend of moving south -in the early stage of the study, most of them were northern provinces such as Shanxi, Hebei, Jilin, etc., but gradually moved to south after 2010, most of them were Henan, Shandong in the central region, Jiangsu, Anhui and other places in the south of the central region.Such changes were closely related to the decline of the northeast heavy industry base and the southward shift of the economic center [70].
As for the provinces with large carbon inflows, they were also divided into two main types: those with developed industrial industries (Hebei, Jiangsu, Zhejiang, Guangdong, Henan, etc.) and those with developed tertiary industries (Beijing, Shanghai, Chongqing, etc.).The relative backwardness of Hebei's industrial technology has led to its decreasing ranking of carbon flow incomings year by year.While Jiangsu, Zhejiang, Guangdong and Henan, etc. imported a large amount of energy or primary processed products to meet the needs of industrial production and become the key areas of carbon inflows.As for cities such as Beijing and Shanghai, the reason for their large carbon inflows is different from the above.Beijing and Shanghai have almost abandoned secondary industries and fully promoted the development of tertiary industries such as Internetþ, biotechnology and finance, and their industrial systems have basically achieved green mode transformation [71].These two most economically developed cities with over 20 million people have the highest per capita material consumption in terms of quantity and quality demand and the majority of products for living and production needs have been imported from other provinces, resulting in their carbon flow intake ranking consistently in the middle and upper reaches of the country.
Based on the betweenness centrality and closeness centrality of each province, it is found that Jiangsu has always been a key node in the flow of carbon emissions.The closeness centrality of Hebei Province has always ranked first, but the betweenness centrality ranking was relatively low.Inner Mongolia also showed a similar ranking distribution, mainly because Hebei and Inner Mongolia were both provinces with large energy and CO 2 emissions output, but their economic control ability was relatively weak compared with Jiangsu, Guangdong and Zhejiang.As an important province with large population, emerging economy, industry, comprehensive transportation hub and logistics center, Henan's central position in CO 2 emission flow path has been highlighted [25].As shown in Figure 7 and the Appendix D in Supplementary Information, Henan's carbon inflows ranking has been increasing year by year, ranking 3rd in 2017 and climbing to 1st by 2025. Figure 8 and Appendix E in Supplementary Information showed that Henan' betweenness centrality has been the first in ECTN since 2017, mainly due to its precise development positioning -giving full play to its unique location advantage of "being in the middle of the China", Henan' General Office of the provincial government issued the "Henan Province Logistics Industry Transformation and Development Plan (2018 $ 2020)" in 2017, and the "Henan Province "14th Five-Year" Modern Circulation System Development Plan" issued in 2022 initially established the status of Henan's modern trade circulation center, and the trade of goods entered a rapid development track.Since January 2010, the State Council officially approved Anhui's inclusion in the "Wanjiang City Belt to Undertake Industrial Transfer Demonstration Zone Plan", Anhui has taken advantage of its Yangtze River Economic Belt and proximity to Jiangsu, Zhejiang and Shanghai to strengthen its trade with eastern and central-western provinces, resulting in its betweenness centrality ranking rising, and its position in the carbon flow network becoming more and more critical.As for Hainan, Fujian, Qinghai, Ningxia and Gansu, their betweenness centrality and closeness centrality rankings were not high in all years, indicating that these provinces were not efficient in transmitting carbon emissions in the national network and are in the position of being controlled by other provinces in the EC flow [69].

Discussions on the division of communities
Analysis of Figure 9 and Appendix F in the Supplementary Materials revealed that the division of communities under China's CO 2 transfer network has changed more significantly since 2011.The trend of modularity level, as an indicator of inter-provincial economic trade closeness, reflects to some extent the closeness of China's economic trade from 2002-2025.The level of modularity declined over the study period, a finding that supported the study by Song et al. [25], with a larger decline in 2012 and a flattening trend thereafter.The above results indicated that under the macroeconomic regulation of national economic policies, the economic development and environment of Chinese provinces have undergone more changes and entered a new normal after high economic development.
During the period 2002-2006, China's economic integration was at a primary stage, with serious homogenization of industrial structure between provinces.Due to geographical location, transportation costs and market demand for products, inter-provincial trade usually occurred between neighboring provinces within a large area, leading to a local spatial aggregation of EC by interprovincial trade, at which time the division of communities was more in line with the "geographic adhesiveness" proposed by Lv et al. [23].After the fifth and sixth high-speed railway speed increases in 2004 and 2007, China's accessibility space was extended to the southwest and northwest, the inter-provincial trade distance was lengthened.The provinces covered by the community were gradually extended in a north-south or east-west direction in terms of geographical distribution, specifically in the form of strengthening carbon transfer links between the provinces in the northeast and northern China, and strengthening links between the provinces in the northwest and the central region In 2011 and later, with the improvement of transportation and information network accessibility, inter-provincial trade gradually broke the geographical barriers, which led to regional economic integration accelerating.The refinement of domestic value chains has led to increasingly frequent inter-provincial trade and carbon transfer, as is amply confirmed by the division of community in 2017.The completion of the West-East Gas Transmission Line II at the end of 2012 has unblocked the trade channels between the east and west regions, and linked the east-west provincial trade across geographical locations.Along with the Beijing-Tianjin-Hebei synergistic development, the Yangtze River Economic Belt, the Pearl River Delta Economic Zone and other major development strategies proposed, the development radiation effect of Beijing, Shanghai, Guangdong, Hubei and other provinces and cities was increasingly obvious.
Analysis of the forecasted ECTNs from 2018-2025 revealed that China's domestic economic cycle would be gaining momentum.During the 14th Five-Year Plan period, inter-provincial carbon transfer due to trade will be more closely linked along with the completion of the third west-east gas transmission line and other transportation construction.The energy-oriented provinces in northwest China would become key controllers in China's ECTNs as energy suppliers to ensure national energy security.The rise of the central region is crucial to the success of the whole country in the 14th Five Year Plan period, to form a strong domestic market and to build a new pattern of development.The central inland provinces, represented by Henan and Anhui, as a "backbone" in the Chinese hinterland, would play an increasingly important role in the communities, and any emission reduction policy would have a fundamental and effective impact on other regions [72].

Practical applications
Based on the existing and updated CMRIOs, China's inter-provincial ECTNs during the 14th Five Year Plan period were predicted.According to the analysis results, this study proposed relevant policy implications: First, the central government should attach great importance to the imbalance of CO 2 emissions caused by trade and think about the rational allocation of carbon emission reduction tasks among provinces.For example, most of the CO 2 emissions in Inner Mongolia and Shanxi are generated to provide the energy for other provinces.Henan, Hebei and other provinces emit CO 2 to provide industrial products, while Beijing, Shanghai, Zhejiang and other developed provinces transfer out of their local CO 2 emissions responsibility by purchasing the above high energy-consumption and low value-added products, resulting in carbon inequality and ultimately affecting the realization of national CO 2 emissions reduction goals.In the face of such problems, the central government's attention and policy formulation are the fundamental way to alleviate the problem of carbon inequality.Therefore, when calculating the regional emission reduction responsibilities during the 14th and 15th Five Year Plan, government should comprehensively consider the CO 2 transfer caused by trade.
Second, China's ECTN has the characteristics of a small world, showing a growing trend.Therefore, the central government ought to effectively identify the role of provinces in the ECTN to develop targeted CO 2 emission reduction programs.For example, Jiangsu and Guangdong with high betweenness centrality and closeness centrality, should continue to optimize the secondary industrial structure and accelerate the layout of the tertiary industry.More attention ought to be paid to improve the carbon emission efficiency in Hebei, Inner Mongolia and other provinces with large centrality closeness.For provinces such as Henan and Anhui, which play an increasingly important role in the carbon transfer network, their carbon emission reduction tasks should be adjusted periodically.Taking Henan as an example, it has caused a large amount of CO 2 emissions during the 12th and 13th Five-Year Plan periods due to the transfer of industries from the eastern provinces.However, with the continuous establishment and consolidation of the status of logistics center, the carbon emission of the transportation sector would be an important challenge to carbon emission reduction during the 14th or 15th Five Year Plan period.Therefore, we should pay close attention to the changes in the role and position of each province in the ECTN, as well as the key sectors of future carbon emissions, and formulate long-term dynamic differential emission reduction policy strategies.
Third, as China's transportation construction and communication technologies develop and improve, inter-regional trade flows are frequent.Therefore, it is necessary to identify the division of community in provinces where trade leads to close linkage of carbon transfer in order to achieve the goal that can maximize the effect of policy intervention.On the one hand, since the spillover effect of regional policies within associations was more obvious, promoting the integration of trade between provinces within associations could maximize the effects of policy interventions.On the other hand, a collaborative drainage platform could be built based on regions to share pollution data and emission reduction technology and experience.Such activities would improve resource utilization through scale effect.In addition, from the results of prediction analyses, it can be seen that future trade between Chinese provinces will no longer be limited to geographical location after 2010, as inter provincial economic exchanges have become increasingly close.Therefore, it is necessary to implement the central idea of a national strategy when policymakers formulate the 14th Five-Year Plan inter-regional cooperation policy and actively adjust the inter-provincial carbon reduction synergy strategy according to the actual situation.

Conclusions and research limitations
In the context of accelerated domestic economic cycles, China's inter-provincial trade is frequent, resulting in carbon leakage becoming more and more serious.Based on the existing CMRIOs, the CMRIOs for the period 2002-2017 were updated and used to forecast China's inter-provincial carbon transfer between 2018 and 2025.The position and role of each province in the ECTN was analyzed through complex networks.The main conclusions are as follows.

The total inter-provincial carbon transfer in
China shows an overall upward trend and is in a rapid rise between 2002 and 2010.With the deepening of the green development concept and the goal of reaching the carbon peak proposed, the total trade carbon transfer grows at a low rate after 2015.With the accelerated and more frequent circulation of trade in goods nationwide, the key path of carbon transfer is no longer limited to trade between individual provinces, and more and more provinces are occupying an important position in the national trade induced carbon transfer network.2. Due to the continuous adjustment of the economic development structure and strategic positioning of each province, the provinces with great closeness centrality have experienced the process of transferring from northern industrial provinces, such as Hebei and Liaoning, to southern manufacturing developed provinces, such as Jiangsu, Zhejiang and Guangdong, and finally to central provinces, such as Henan and Anhui.Although Xinjiang, Gansu and other northwest provinces are the main suppliers of natural gas, oil and other energy in China, their impact on the ECTN is small because the limitation of economic volume, which may be different from our previous understanding of the distribution of carbon emissions in China's provinces.3. The inter-provincial carbon transfer links caused by trade have broken through the geographical restrictions due to the rapid development of the Internet and logistics.The "geographic stickiness" of the provincial community division under the carbon transfer network has been gradually disintegrating since 2011.Therefore, it may be difficult to maximize the policy effect when considering the cooperative carbon emission reduction policy purely from the geographical location.Under the background of the strengthening of China's integration, the coordinated emission reduction strategy should be adjusted in a timely manner from the perspective of inter provincial carbon transfer links caused by trade links.
The limitations of this study deserve further research.First of all, the CMRIOs used in this study for the year 2002, 2007, 2010, 2012, 2015 and 2017 came from three research institutions, and the preparation caliber or method was different among provinces, which may lead to deviation in the carbon emission results, thus affecting the analysis results.Second, although this study updated the MRIO from 2002 to 2017 through RAS method, the prediction accuracy still needs to be improved due to the limited data available.For future prediction research, on the one hand, efforts should be made to improve the time length of available data, and on the other hand, relevant policies such as future development planning ought to be included in the prediction index system.Third, the share of import and export in total output varies greatly among different provinces.Scholars should also focus on carbon emissions caused by foreign trade and future trends when analyzing key provinces or sectors of carbon emissions.

Figure 1 .
Figure 1.Schematic diagram of predictive model.Note: CE(s,r) (s 5 1,2, … ,29, s and r represent region) indicates the EC transfer from region r to region s.

Figure 2 .
Figure 2. Validation indicators of SVM prediction results optimized by cross validation and PSO.

Figure 3 .
Figure 3.The prediction effect of SVM optimized by cross validation and PSO in some provinces.

Figure 4 .
Figure 4. Cumulative contribution rate of edges of complex networks in 2002-2025.

Figure 5 .
Figure 5. Small-world features of the complex network in 2002-2025.

Figure 6 .
Figure 6.Cumulative contribution of in-degree and out-degree in 2002-2025.

Figure 9
represents the community division of Chinese provinces according to EC transfer in 2002, 2010, 2017 and 2025.The community division in other years are presented in Appendix F in Supplementary Materials.In 2002, 30 provinces in China were divided into 4 communities according to the situation of carbon transfer.Each community's provinces were closely related in location.Community 1 (C1) included five northwest provinces of Xinjiang, Ningxia, Qinghai, Gansu and Shaanxi, while community 2 (C2) included three northeast provinces of Jilin, Liaoning and Heilongjiang.The community 3 (C3) contained the six provinces and cities, Beijing-Tianjin-Hebei, Inner Mongolia, Shanxi and Henan.The number of community 4 (C4) was 16, which included Shandong and all southern provinces.In 2010, the division of communities was still closely related to the geographical location, which was basically consistent with the finding of Gao et al. [21] on energy transfer in 2009.C1 covered the three northeastern provinces, Shandong and

Figure 9 .
Figure 9. Community division of embodied carbon transfer network in China in 2002, 2010, 2017 and 2025.
This study mainly used CMRIOs from 2002, 2007, 2010, 2012, 2015, and 2017, where the 2002 MRIO was from Shi and Zhang [56], 2007 and 2010 MRIOs were from Liu et al. [57] and Liu et al. [58].The MRIOs for 2012, 2015, and 2017, as well as energyrelated CO 2 emission data were from China Emission Accounts and Datasets [59,60].Since CMRIOs contain 30 sectors in 2002, 2007 and 2010, and 31 sectors in 2012, 2015 and 2017, we only measured the CO 2 transfer of other 30 provinces, municipalities and autonomous regions excluding Tibet, Taiwan, Hong Kong and Macao.When measuring the carbon transfer between provinces in 2012-2017, this study measured the 31 provinces involved, including Tibet.Since the CEADs lack the energy-related CO 2