Research on the Structural Features and Inﬂuence Mechanism of the Low-Carbon Technology Cooperation Network Based on Temporal Exponential Random Graph Model

: China actively promotes cross-regional low-carbon technology cooperation to improve low-carbon technologies and remove technological barriers to sustainable development. In this process, a cross-regional low-carbon technology cooperation network (LCTCN) has been developed and evolved. To help China rationalize the allocation of innovation resources and promote the cross-regional exchange of low-carbon technologies, we measured the LCTCN using low-carbon technology co-patents from 2011 to 2020. We investigated changes in the network structure using social network analysis. In addition, we examined the endogenous structures and exogenous factors that inﬂuence the formation of cooperation relationships in the network using a time exponential random graph model (TERGM). We came to the following conclusions: (1) The LCTCN develops toward complexity, showing prominent characteristics of spatial imbalance, heterogeneity, and core-periphery. (2) Among the endogenous structural variables, the coefﬁcient of geometrically weighted degree (Gwdegree) is signiﬁcantly negative, suggesting that regions within LCTCN tend to form partnerships with already well-connected regions. On the other hand, a positive coefﬁcient of geometrically weighted dyad shared partner statistic (GWDSP) suggests that regions tend to link in multiple ways to each other. (3) Among the exogenous variables, the coefﬁcient of the digital economy is signiﬁcantly positive. As a result, for every level of digital economy development in a region, the probability of establishing low-carbon technology cooperation between that region and other regions increases by 87.39%. (4) External openness and geographical proximity can also facilitate establishing partnerships. The formation of low-carbon partnerships in the network results from a combination of endogenous structures and exogenous variables.


Introduction
With a series of problems such as global warming, environmental pollution, and resource depletion becoming increasingly serious, the "high pollution, high emissions, high consumption" approach to economic development has seriously affected the survival of humankind [1]. Reducing carbon emissions and energy consumption is an inevitable choice to alleviate environmental problems and achieve sustainable development [2]. At COP26, China committed to reducing emissions and elaborated its strategy and long-term plan [3]. Green innovation can reduce energy consumption and contribute to economic sustainability [4]. Low-carbon technologies can effectively control carbon emissions and thus mitigate climate change, so they are widely considered to be the key to solving existing environmental problems [5]. Therefore, to achieve the goal of reducing emissions, China must improve its innovation capability in low-carbon technologies. Since low-carbon technology innovation has higher risks and uncertainties than other technology innovation [6], it becomes increasingly difficult to rely on a region alone to make technological breakthroughs and improve innovation capability. Regions cooperate in low-carbon technologies India, and China as sub-nuclear participants in regional technology collaboration networks in Europe and Asia.
The reasons affecting R&D cooperation can be attributed to the following aspects. First, a group of scholars studied the influence of the external environment on cooperative relationships. Fan et al. [19] studied the dynamic influence of government policies on the diffusion of green innovation. Han et al. [20] investigated the influence of policy shifts on the evolution of the R&D strategy of collaborative innovation networks of new energy vehicles. Some other scholars studied the role of the interaction between innovation agents for innovation cooperation. For example, Yi et al. [21] proposed the interaction of universities, research institutions, supply chains, intermediaries, and consumers, which jointly drive the evolution of the system. Multidimensional proximity is widely considered as the driving mechanism of R&D collaboration. Scholars summarized these proximity levels: physical, institutional, cognitive, social, and organizational [15,22].
In addition, the current research on the factors influencing the formation of network relationships involves methodological issues. The existing literature generally uses conventional regression methods to study the factors influencing the formation of cooperative relationships. For example, Corrocher and Mancusi [23] used pooled Poisson and negative binomial regression to analyze the influencing factors of international cooperation in green energy technologies. Linear regression models require all interference items to be independent of each other [24]. However, network data are inherently interdependent, so regression models are not applicable in studying network data. Li et al. [18] used the quadratic assignment procedure (QAP) to explore the impact mechanisms of the global green information and communications technology (ICT) cooperation network from 2000-2019. Although the QAP method can identify formation mechanisms by converting attribute data into relationship data [25], it ignores the influence of network structures on relationship formation. Social network theory values the embeddedness of individuals in the network. It considers that they do not exist in isolation, which means that the structures in the network can influence the formation of relationships [26]. Ma et al. [27] used the exponential random graph model (ERGM) to analyze the determinants affecting international green R&D collaboration networks. The ERGM is based on social network theory. ERGM overcomes the limitations of traditional regression models and can analyze both endogenous variables (network structure) and exogenous variables (node attributes, edge attributes, etc.) [28]. However, ERGM ignores the dynamic correlations between networks in different periods and can only reveal the factors affecting relationship formation from static cross-sectional data, which may lead to bias in the model fitting results [29].
Based on the above literature review, we found several gaps in the existing literature: (1) Although there is a wealth of research on green innovation collaboration networks, previous studies neglected low-carbon technology collaboration. There are differences in the R&D in different technology areas [27], so it is necessary to distinguish the technology areas of green innovation, further investigating how cooperation in lowcarbon technology innovation evolves. (2) Most researchers have examined the impact of traditional economic variables on collaboration. However, previous studies neglected digitalization's transformation of the traditional economy. There is no direct evidence that the digital economy impacts inter-regional low-carbon technology cooperation. However, some literature on technology matching and information seeking provides theoretical support. The network externalities and economies of scale brought by the digital economy alleviate the problems of distance constraints for technology cooperation [30] and also provide an optimization method for the supply and demand matching problem of technology collaborators [31]. Therefore, it is necessary to study the impact of the digital economy on the formation of low-carbon technology partnerships. (3) Finally, in the choice of methods for the analysis of network formation mechanisms, most of the researchers choose traditional linear models. The temporal exponential random graph model (TERGM) recognizes the interdependence between and attributes of variables and the relationships among variables, treating them as explanatory variables [32]. TERGM can encompass both endogenous and exogenous factors [33]. Endogenous factors refer to characteristic substructures constituting a network, and exogenous factors are attributes of nodes constituting a network or the attributes of links [34]. Analyzing the influence of endogenous structural variables on network formation is something that traditional network models and QAP cannot do, although ERGM can also analyze the effect of endogenous structure on network relationship formation [35]. ERGM is only for explaining the network formation mechanisms observed at a point in time [36]. Relative to ERGM, TERGM analyzes multi-period networks as a whole and fully considers the influence of network patterns in different periods.
To fill the above gap, first, we further filtered the green patents. We kept the patent data with the number of invention organizations greater than two and related to low-carbon technologies. Then, based on the patent data, we crawled the geographical locations of the inventing organizations using Python to build an LCTCN. Next, we studied the network's changes in topological structure and spatial dynamics using some metrics. In addition, we proposed that the digital economy would impact the establishment of collaborative relationships in the LCTCN based on theories such as technology matching. Then, based on previous studies, we sort out other factors that can influence the establishment of cooperative relationships in the network. Finally, we used TERGM to examine the factors that affect low-carbon technology cooperation, especially the digital economy and endogenous structures.

Low-Carbon Technology Collaboration Network Construction
The patent data for this study were obtained from the Himmpat database [37]. First, we download the green patent data for the period 2011-2020 based on the classification provided by the International Patent Classification Green Inventory (IPC Green Inventory) developed by the World Intellectual Property Office (WIPO) and the corresponding patent classification number of each category. After that, we kept the patent data containing the keyword about low-carbon and filtered out the patents whose applicants were individuals and the number of applicants was less than two. We ended up with 7225 patent data. Figure 1 shows the annual distribution of our data (collaborative patents for lowcarbon technologies), reflecting the change in the maturity of low-carbon technologies in China yearly. Overall, from 2011 to 2020, the number of patents is generally a tortuous upward trend. The number of co-patents for low-carbon technologies in 2011 and 2012 was around 500, and the number of co-patents started to increase, over 700 in 2013 and 2014. There was a brief decline in the number of patent publications in 2015, but it began to grow again in 2016 and 2017. After that, in 2018, the number of patents declined again and gradually remained stable. It shows that China's low-carbon technology is developing and moving forward in a tortuous manner.
We used Python to crawl the geographical location of the patent application organizations. We determined the regions of patent cooperation according to the area of patent application organizations. We constructed undirected networks with weights, where nodes represent provinces or municipalities directly under the central government and links represent cooperative relationships. Specifically, v i denotes the ith region (province or province-level municipality). The adjacency matrix A = [a ij ] represents the patent flow between different regions, where a ij = 1 means that the ith region and the jth region have common patents; otherwise, a ij = 0. The weight matrix is W = [w ij ], where w ij represents the number of patents for cooperation between the ith region and the jth region. The LCTCN of 31 provinces and municipalities directly under China (excluding Hong Kong, Macao and, Taiwan) is an undirected weighted network consisting of V, A and, W. We used Python to crawl the geographical location of the patent application orga zations. We determined the regions of patent cooperation according to the area of pat application organizations. We constructed undirected networks with weights, wh nodes represent provinces or municipalities directly under the central government a links represent cooperative relationships. Specifically, v i denotes the ith region (provi or province-level municipality). The adjacency matrix A = [a ij ] represents the patent fl between different regions, where a ij =1 means that the ith region and the jth region h common patents; otherwise, a ij =0. The weight matrix is W = [ ], where represe the number of patents for cooperation between the ith region and the jth region. T LCTCN of 31 provinces and municipalities directly under China (excluding Hong Ko Macao and, Taiwan) is an undirected weighted network consisting of V, A and, W.

Low-Carbon Technology Collaboration Network Characteristic
We processed the data into three phases from 2011 to 2014, 2015 to 2017, and 2018 2020 to observe the temporal changes in the network. We use a series of network statist indicators to characterize the network in the three phases. The meanings and formula these metrics are shown in Table 1.  N represents the number of nodes; l ij represents the shortest path connecting the i-th node to the j-th nod N represents the number of nodes; E i represents the a tual degree value of the neighboring nodes of i-th nod k i represents the degree value of i-th node.

Low-Carbon Technology Collaboration Network Characteristic
We processed the data into three phases from 2011 to 2014, 2015 to 2017, and 2018 to 2020 to observe the temporal changes in the network. We use a series of network statistical indicators to characterize the network in the three phases. The meanings and formulas of these metrics are shown in Table 1.  Average path length L = 2 N(N−1) ∑ i>j l ij N represents the number of nodes; l ij represents the shortest path connecting the i-th node to the j-th node.
N represents the number of nodes; E i represents the actual degree value of the neighboring nodes of i-th node; k i represents the degree value of i-th node.
Average degree <k> = 1 N ∑ N i k i N represents the number of nodes; k i represents the number of edges connected by the i-th node.
We used the social network analysis software UCINET 6.645 to calculate these indicators. As shown in Table 2, the values of edge and average degree increase gradually with time, indicating that the network's cooperation intensity is rising and the breadth of cooperation is expanding. The network structure becomes more complex as the connections between regions are enriched. The network density and clustering coefficient values also increase over time, indicating that the tightness and cohesiveness of LCTCN have improved. In addition, the average path length of the network increases gradually with time, which suggests that the accessibility of LCTCN is decreasing and the efficiency of information dissemination is decreasing, which is not conducive to the rapid communication and dissemination of information in the whole network. We analyzed the evolutionary trends of LCTCN from spatial perspectives. We used ArcGIS 10.7 to plot the spatio-temporal evolution of each of the three stages. The colors of the lines indicate the strength of the linkage intensity. From Figure 2, we can see that the geographical distribution of LCTCN is uneven in all three stages. Most low-carbon technology cooperation is concentrated in the east and central regions, while collaboration is sparse in the northwest, northeast, and southwest regions. From 2011 to 2020, the inter-regional ties are getting closer and closer; especially the innovation ties in the backward western areas are obviously enhanced. The number of core nodes is also gradually increasing, meaning that more and more regions are moving from participants to leaders.
tions between regions are enriched. The network density and clustering coefficient values also increase over time, indicating that the tightness and cohesiveness of LCTCN have improved. In addition, the average path length of the network increases gradually with time, which suggests that the accessibility of LCTCN is decreasing and the efficiency of information dissemination is decreasing, which is not conducive to the rapid communication and dissemination of information in the whole network. We analyzed the evolutionary trends of LCTCN from spatial perspectives. We used ArcGIS 10.7 to plot the spatio-temporal evolution of each of the three stages. The colors of the lines indicate the strength of the linkage intensity. From Figure 2, we can see that the geographical distribution of LCTCN is uneven in all three stages. Most low-carbon technology cooperation is concentrated in the east and central regions, while collaboration is sparse in the northwest, northeast, and southwest regions. From 2011 to 2020, the interregional ties are getting closer and closer; especially the innovation ties in the backward western areas are obviously enhanced. The number of core nodes is also gradually increasing, meaning that more and more regions are moving from participants to leaders. We calculated each node's degree and its neighboring nodes' average degree and drew and fitted a scatter plot using Stata 15.0. Exploring how nodes with different degrees are connected helps understand whether nodes have assortativity. In other words, we examined whether nodes with similar degree values tend to be connected. As shown in Figure 3, the coefficient of assortativity in LCTCN is negative in all three phases, meaning the network exhibits heterophily. This means that regions always tend to cooperate with those that already have a lot of cooperation. The absolute value of the assortativity coefficient decreases from the first to the third stage, which indicates that the dependency of regions We calculated each node's degree and its neighboring nodes' average degree and drew and fitted a scatter plot using Stata 15.0. Exploring how nodes with different degrees are connected helps understand whether nodes have assortativity. In other words, we examined whether nodes with similar degree values tend to be connected. As shown in Figure 3, the coefficient of assortativity in LCTCN is negative in all three phases, meaning the network exhibits heterophily. This means that regions always tend to cooperate with those that already have a lot of cooperation. The absolute value of the assortativity coefficient decreases from the first to the third stage, which indicates that the dependency of regions on core regions is decreasing. Regions are gradually moving away from path dependency and actively expanding the breadth of cooperation.
A community is a sub-structure of a network. Nodes in the same community are tightly connected, but nodes in different communities are very loosely connected to each other. Performing community detection allows studying the clustering changes of nodes. In this study, Louvain algorithm was used for community detection and visualized with Gephi 0.9.2. Figure 4 shows the three stages of community detection, where different colors are used to distinguish different communities. From Figure 4, we can see that there are only two major communities in the first stage of LCTCN. The green community has a small but frequently connected number of nodes, and the red community has a large number of nodes. In the second stage, the boundary between red and green communities starts to become blurred, indicating that the two communities have started to integrate. As the depth and breadth of cooperation between the regions grow, the flow of technology between the communities is further enhanced. In the third stage, the red and green communities are  A community is a sub-structure of a network. Nodes in the same community are tightly connected, but nodes in different communities are very loosely connected to each other. Performing community detection allows studying the clustering changes of nodes. In this study, Louvain algorithm was used for community detection and visualized with Gephi 0.9.2. Figure 4 shows the three stages of community detection, where different colors are used to distinguish different communities. From Figure 4, we can see that there are only two major communities in the first stage of LCTCN. The green community has a small but frequently connected number of nodes, and the red community has a large number of nodes. In the second stage, the boundary between red and green communities starts to become blurred, indicating that the two communities have started to integrate. As the depth and breadth of cooperation between the regions grow, the flow of technology between the communities is further enhanced. In the third stage, the red and green communities are further integrated, but at the same time, new communities (purple communities) are also differentiated.  According to the core-periphery structure theory, core nodes in LCTCN have the most cooperative relationships. Strong semi-peripheral nodes are characterized by strong ties with core nodes and other strong semi-peripheral nodes. Their number of relationships and strength of ties is higher than the average. Semi-peripheral nodes differ from   A community is a sub-structure of a network. Nodes in the same community are tightly connected, but nodes in different communities are very loosely connected to each other. Performing community detection allows studying the clustering changes of nodes. In this study, Louvain algorithm was used for community detection and visualized with Gephi 0.9.2. Figure 4 shows the three stages of community detection, where different colors are used to distinguish different communities. From Figure 4, we can see that there are only two major communities in the first stage of LCTCN. The green community has a small but frequently connected number of nodes, and the red community has a large number of nodes. In the second stage, the boundary between red and green communities starts to become blurred, indicating that the two communities have started to integrate. As the depth and breadth of cooperation between the regions grow, the flow of technology between the communities is further enhanced. In the third stage, the red and green communities are further integrated, but at the same time, new communities (purple communities) are also differentiated.  According to the core-periphery structure theory, core nodes in LCTCN have the most cooperative relationships. Strong semi-peripheral nodes are characterized by strong ties with core nodes and other strong semi-peripheral nodes. Their number of relationships and strength of ties is higher than the average. Semi-peripheral nodes differ from According to the core-periphery structure theory, core nodes in LCTCN have the most cooperative relationships. Strong semi-peripheral nodes are characterized by strong ties with core nodes and other strong semi-peripheral nodes. Their number of relationships and strength of ties is higher than the average. Semi-peripheral nodes differ from strong semi-peripheral nodes in that they have lower metrics than strong semi-peripheral nodes and their collaborative links are mainly with the core nodes. Peripheral nodes are isolated and have the lowest network metric values in the LCTCN. We used Citespace 5.3.R4 for visualization to observe how the core-periphery structure of the network evolves. Figure 5 shows that all three phases of the LCTCN show a distinct core peripheral structure. The core group regions are few but strongly connected, indicating that the core regions are mostly reciprocally linked. The peripheral group regions are widely distributed, and numerous, but the network links depend on the core regions, which is a lack of lowcarbon technology cooperation among the peripheral regions, and with time, regions once located in the core group would continue to maintain their core position, which suggests that path-dependent mechanisms may influence the evolution of core regions. The core regions that have occupied the core position would further strengthen their network locational advantages through their resource control advantages and information advantages. In the second and third stage phase, some regions shift from strong semi-perimeter groups to core groups, and the number of core group nodes rises yearly. In addition, we can see that the gap of each regional degree is getting smaller and smaller, which indicates that the core-periphery structure is gradually easing. In conclusion, network evolution is influenced by path dependence to a certain extent. The nodes in the core group would further strengthen their core position. However, the peripheral structure is also boosting the connection with other regions, the gap is gradually narrowing, and the dependence on the core region is relatively decreasing.
gests that path-dependent mechanisms may influence the evolution of core regions. The core regions that have occupied the core position would further strengthen their network locational advantages through their resource control advantages and information advantages. In the second and third stage phase, some regions shift from strong semi-perimeter groups to core groups, and the number of core group nodes rises yearly. In addition, we can see that the gap of each regional degree is getting smaller and smaller, which indicates that the core-periphery structure is gradually easing. In conclusion, network evolution is influenced by path dependence to a certain extent. The nodes in the core group would further strengthen their core position. However, the peripheral structure is also boosting the connection with other regions, the gap is gradually narrowing, and the dependence on the core region is relatively decreasing.  Table 3 shows the degree centrality and betweenness centrality of the nodes (only the top 10 are shown), making it easier to see the regions that occupy the core and how it changes over time. The degree centrality is the number of a node in the network connected to other nodes, which can directly reflect the "power" of a region in LCTCN. The degree of centrality is calculated as C = ∑ x (i≠j), where x represents the number of direct links between node i and node j. Betweenness centrality measures a region's "bridging" role in the LCTCN, which reflects the node's ability to communicate and control other regions. Betweenness centrality is calculated as C = ∑ ∑ b (i) (j ≠ k ≠ i and j < k), where b denotes the control ability of node i over node j. As seen from Table 3, as the network continues to grow, the degree centrality of most node regions has increased, implying that the inter-regional cooperation on low-carbon technologies has increased year by year. The top ranking of degree centrality of the network in each phase is Beijing and Shanghai, which reflects the dominant role of these two regions in low-carbon technologies. Liaoning and Shandong are closely linked to the other areas too. As shown by the betweenness centrality, Beijing and Shanghai also play a vital intermediary role in the network and  Table 3 shows the degree centrality and betweenness centrality of the nodes (only the top 10 are shown), making it easier to see the regions that occupy the core and how it changes over time. The degree centrality is the number of a node in the network connected to other nodes, which can directly reflect the "power" of a region in LCTCN. The degree of centrality is calculated as C D = ∑ n j=1 x ij (i =j), where x ij represents the number of direct links between node i and node j. Betweenness centrality measures a region's "bridging" role in the LCTCN, which reflects the node's ability to communicate and control other regions. Betweenness centrality is calculated as C E = ∑ n j ∑ n k b jk (i) (j = k = i and j < k), where b jk denotes the control ability of node i over node j. As seen from Table 3, as the network continues to grow, the degree centrality of most node regions has increased, implying that the inter-regional cooperation on low-carbon technologies has increased year by year. The top ranking of degree centrality of the network in each phase is Beijing and Shanghai, which reflects the dominant role of these two regions in low-carbon technologies. Liaoning and Shandong are closely linked to the other areas too. As shown by the betweenness centrality, Beijing and Shanghai also play a vital intermediary role in the network and have great control in LCTCN. Second, Hubei also has a high betweenness centrality value, indicating that it has a lot of direct cooperation with other regions. The betweenness centrality values of Beijing and Shanghai increase in the second stage but decline in the third stage. It indicates that regions' dependence on the single connection of core nodes, such as Beijing and Shanghai, is decreasing, and independence is increasing. It is worth mentioning that the values of degree centrality in Liaoning and Shandong are high, but the betweenness centrality values are not outstanding. It indicates that the depth of regional cooperation in these two regions is strong, but the breadth of collaboration is not enough, and collaboration with more areas is needed in the future.

Digital Economy
Existing studies rarely include the emerging macro element of the digital economy in the research framework of low-carbon technology cooperation drivers. Although there is a lack of research on this issue in the academic community, studies on the impact of the digital economy on technology searching and technology matching provide the theoretical basis for this paper. Digital infrastructure development has changed how information is transmitted [38], providing efficient access to information for technical cooperation activities. Therefore, when conducting cross-regional low-carbon cooperation, the digital economy reduces information asymmetry caused by geographical and administrative boundaries [39] and can quickly and accurately match supply and demand sides [40]. In addition, digital finance can reduce the information asymmetry between capital supply and demand, thereby alleviating the financing constraints of low-carbon technology cooperation [41]. We reasonably speculate that regions with high digital economy development will have their technological advantages and technological features showcased first, so they will start to accumulate links (cooperation) first in LCTCN and are more likely to have more links and become central nodes. However, the digital economy also has the potential to further widen the imbalance of cooperation between regions. Regions with a high level of digital economy are more likely to monopolize information resources and continuously crowd out existing resources in regions with a low level of digital economy [42], which further widens the imbalance in the development of low-carbon technologies and increases the technical barriers to cooperation. As a result, it leads to the fact that things are clustered together, and regions with the same level of digital economy are more inclined to cooperate.
To measure the level of digital economy development, we build on previous research results [43,44] and measure five dimensions. The specific index system is shown in Table 4. Drawing on relevant research [45,46], we used the Entropy-based Technique for Order Preference by Similarity to Ideal Solution (Entropy-based TOPSIS) to calculate the regional digital economy level. The Entropy-based TOPSIS is an organic combination of the entropy-weighted and Technique for Order Preference by Similarity to Ideal Solution (TOP-SIS). The weights of evaluation indicators are first determined by the entropy-weighted method. Then the ranking of evaluation indicators is directly determined by the TOP-SIS [47]. Therefore, it can not only reduce the interference of subjective factors in the assignment of indicators but also effectively judge the relative merits of each observation, thus improving the objectivity and rationality of the measurement results of the digital economy development level.
The homophily effect is mainly used to measure whether the homogeneity of attributes of different nodes will impact the formation of network relationships. Therefore, after obtaining the digital economic development level, we divided the digital economy development level into regions with high digital economy levels (1-10), regions with medium digital economy levels (11)(12)(13)(14)(15)(16)(17)(18)(19)(20), and regions with low digital economy levels (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31) according to the ranking. We included three homophily variables in the model to examine whether these sample regions with close levels of the digital economy are more inclined to form cooperation with each other.
The data were mainly obtained from the 2011-2020 China Urban Statistical Yearbook and the China Stock Market & Accounting Research (CSMAR) Database [48]. Figure 6 shows the changes in each Chinese region's comprehensive digital economy index in 2014, 2017, and 2020. In the three selected years, the top three regions are Beijing, Jiangsu, and Guangdong, which reflects their absolute strength and leading position in the digital economy. Overall, the eastern coastal regions have higher levels of digital economy, while the western and central regions have relatively weaker levels. It is highly consistent with the spatial distribution characteristics of the core nodes in our LCTCN. opment level into regions with high digital economy levels (1-10), regions with medium digital economy levels (11)(12)(13)(14)(15)(16)(17)(18)(19)(20), and regions with low digital economy levels (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31) according to the ranking. We included three homophily variables in the model to examine whether these sample regions with close levels of the digital economy are more inclined to form cooperation with each other.
The data were mainly obtained from the 2011-2020 China Urban Statistical Yearbook and the China Stock Market & Accounting Research (CSMAR) Database [48]. Figure 6 shows the changes in each Chinese region's comprehensive digital economy index in 2014, 2017, and 2020. In the three selected years, the top three regions are Beijing, Jiangsu, and Guangdong, which reflects their absolute strength and leading position in the digital economy. Overall, the eastern coastal regions have higher levels of digital economy, while the western and central regions have relatively weaker levels. It is highly consistent with the spatial distribution characteristics of the core nodes in our LCTCN.

Other Variables
We included three geometrically structural terms in our model: Geometrically weighted edgewise shared partner (Gwesp), Geometrically weighted degree (Gwdegree), and Geometrically weighted dyadwise shared partners (Gwdsp) [49]. Gwesp is a measure of the transitivity structure of the network. It captures the tendency for two regions that share a collaborative tie to also be connected in the network [50]. It measures whether the network prefers to form closed triangles structures. Gwdegree captures the tendency of regions with higher degrees to form collaborative relations with others. It measures whether the network prefers to form star structures [51]. Gwdsp captures the tendency of dyads (a pair of regions) to have identical ties with other regions in the network [52]. It measures whether the network prefers to form intermediary paths.
In addition to the digital economy, other node attribute variables are included in the temporal exponential random graph model (TERGM). The current literature suggests that government environmental controls can promote green innovation in different contexts

Other Variables
We included three geometrically structural terms in our model: Geometrically weighted edgewise shared partner (Gwesp), Geometrically weighted degree (Gwdegree), and Geometrically weighted dyadwise shared partners (Gwdsp) [49]. Gwesp is a measure of the transitivity structure of the network. It captures the tendency for two regions that share a collaborative tie to also be connected in the network [50]. It measures whether the network prefers to form closed triangles structures. Gwdegree captures the tendency of regions with higher degrees to form collaborative relations with others. It measures whether the network prefers to form star structures [51]. Gwdsp captures the tendency of dyads (a pair of regions) to have identical ties with other regions in the network [52]. It measures whether the network prefers to form intermediary paths.
In addition to the digital economy, other node attribute variables are included in the temporal exponential random graph model (TERGM). The current literature suggests that government environmental controls can promote green innovation in different contexts [53,54]. Therefore, we included two nodal attribute variables regarding government environmental control: government ecological attention and regional environmental regulation intensity. Government attention represents the attention of government decisionmakers to a particular issue. Ecological governance attention is a prerequisite for environmental governance to introduce policies and implement management [55]. Regarding other literature [56,57], we selected 101 keywords related to environmental governance in our study. The frequency of these keywords appearing in the Government Work Report of each province or municipality directly under the central government in previous years was used as the ecological attention of that government. Environmental regulation is an effective way for the government to use administrative means to restrain the production behavior of enterprises and reduce pollutant emissions. In this study, the share of industrial pollution control investment completed in the secondary sector measures environmental regulation. The original data are taken from the China Statistical Yearbook.
Trade is also an essential factor in promoting sustainable development. Trading green products can impact environmental degradation [58] and decrease carbon emissions, increasing human well-being [59]. Trade is considered to be an important source of green technology spillovers [27]. Trade has positive spillover effects on technology innovation in emerging markets [60]. External openness was therefore included as a nodal variable. The degree of external openness is calculated as total exports and imports divided by regional GDP. The original data are taken from the China Statistical Yearbook.
Network evolution is also related to exogenous network effects [61]. Multidimensional proximity has always been the focus of evolutionary economic geography [62]. Since the study was conducted at the provincial level rather than at the organizational level, geographical proximity and institutional proximity were finally chosen as exogenous network variables. Geographic proximity refers to territorial and spatial proximity. We determine whether regions are bordering or not and then construct a 0-1 geographic proximity matrix between regions. The geographic proximity matrix is used to measure geographic proximity.
The institutions related to technological innovation include environmental regulations and innovation government support. As variables responding to environmental policies are already available in the previous section, government R&D investment is chosen to measure the proximity of institutions in this study [15]. The specific calculations are as follows: The inv i and inv j refer to the R&D inputs of region i and region j. The closer the value is to 1, the more similar the system is between the two provinces. Finally, we used the mean value as a threshold to transform it into a 0-1 matrix. This matrix is used to measure institutional proximity. The original data are taken from the China Science and Technology Statistical Yearbook. Table 5 shows all the variables and their meanings.            Whether technology cooperation is more likely to occur between regions with lower levels of digital economy development Table 5. Cont.

Variables Configuration Measurement
Exogenous network covariates Edgecov_geo Homophily (High-dige) tween regions with higher levels of digital economy development Whether technology cooperation is more likely to occur between regions with moderate levels of digital economy development Whether technology cooperation is more likely to occur between regions with lower levels of digital economy development Exogenous network covariates Edgecov_geo geo Whether regions with relationships in geographic proximity networks are more likely to cooperate Edgecov_inst inst Whether regions with relationships in institution proximity networks are more likely to cooperate

Temporal Exponential Random Graph Model
Before the estimation of TERGM coefficients, the LCTCN was first binarized. The mean value of the network weights is used as the threshold to determine whether there is a connection between the two provinces. If it is greater than the mean value, the connection is said to exist; otherwise, it does not exist.
Whether regions with relationships in geographic proximity networks are more likely to cooperate Edgecov_inst ment Homophily (Mid-dige) Whether technology cooperation is more likely to occur between regions with moderate levels of digital economy development Whether technology cooperation is more likely to occur between regions with lower levels of digital economy development Exogenous network covariates Edgecov_geo geo Whether regions with relationships in geographic proximity networks are more likely to cooperate Edgecov_inst inst Whether regions with relationships in institution proximity networks are more likely to cooperate

Temporal Exponential Random Graph Model
Before the estimation of TERGM coefficients, the LCTCN was first binarized. The mean value of the network weights is used as the threshold to determine whether there is a connection between the two provinces. If it is greater than the mean value, the connection is said to exist; otherwise, it does not exist.
Whether regions with relationships in institution proximity networks are more likely to cooperate

Temporal Exponential Random Graph Model
Before the estimation of TERGM coefficients, the LCTCN was first binarized. The mean value of the network weights is used as the threshold to determine whether there is a connection between the two provinces. If it is greater than the mean value, the connection is said to exist; otherwise, it does not exist.
TERGM is an extended dynamic ERGM. The following is how ERGM is expressed in its generic form: Y stands for all possible networks, and y stands for observed networks. k(θ, y) is a constant that ensures that the probability of a new network structure is in the range of 0 to 1. Z A (y) represent the potential influencing factor of network formation and θ A represent parameter vectors.
ERGM can be modified to include K-order temporal dependencies of the observed network y [63]: P(y t |y t−k , . . . , y t−1 , θ) = exp ∑ θ T A Z A y t−k , . . . , y t−1 k θ, y t−K , . . . , y t−1 Equation (3) only specifies TERGM for a single network at a single time, the joint probability of observing the networks between time k+1 and T is formulated as follows [63]: P(y k+1 , . . . , y T |y 1 , . . . , y K ) = ∏ T t=K+1 P y t−K , . . . , y t−1 , θ For the estimation of TERGM parameters, scholars believe that the maximum pseudo likelihood estimation (MPLE) suffers from insufficient sample randomness and less accurate estimation of parameter confidence intervals, so the MPLE method based on the bootstrap method is proposed [64]. Instead of conditioning the MPLE estimation function on the rest of the network after removing the network relationships, the method conditions the samples drawn by the bootstrap method. More random sample data are obtained by the bootstrap method, so the parameter interval estimation is more accurate. Therefore, we estimate coefficients and confidence intervals of our model with 1000 bootstrap replications.

Results
We included endogenous network structure, node attribute covariates, and exogenous network covariates in the model in turn [65]. We judged whether the variable would impact the evolution of LCTCN according to the significance of the coefficients of the variables. Table 6 shows the TERGM results on the sample from 2011 to 2020. Model A1 in Table 6 shows the effect of endogenous structural variables on the evolution of LCTCN. The coefficient of Edges is significantly negative, indicating that the network structure's density is low, the network as a whole is loose, and the rate of tie growth is much lower than the theoretical number. It is consistent with the findings of some ERGM studies [66]. The coefficient of Gwdegree is significantly negative, suggesting that the network has a precise preferential attachment mechanism. Preferential attachment describes a process where regions in LCTCN seek connections with already well-connected regions [67]. As a result, the rich get richer, and the poor get poorer. The coefficient of Gwesp is significantly negative, which indicates that the network does not tend to form a closed triangle structure. In other words, transitive closure occurs less often in our empirical networks [68]. The coefficient of Gwdsp is significantly positive, a consequence of organizations tending to seek a diverse portfolio of partners [69]. In other words, regions may connect to others in multiple ways to decrease their dependency on individual links.
Model A2 demonstrates the effect of the node variables on the evolution of the LCTCN. The estimated coefficient of environmental regulation intensity is significantly positive. Stricter environmental regulations stimulate regional cross-regional cooperation to seek breakthrough innovations to offset compliance costs [70]. Governmental ecological attention is insignificant, which may be because some local governments have "verbal commitment" and do not implement government environmental protection measures, resulting in a separation between governmental eco-attention and actual environmental protection measures. The study by Hao et al. [71] demonstrated that the current environmental control regulations of local governments in China do not achieve the desired pollution control and reduction goals. The estimated coefficient of external openness is significantly positive. Trade has been shown to have a positive impact on knowledge dissemination [72]. A higher degree of openness means that more heterogeneous technologies from other countries are likely to be available. Therefore, regions are more inclined to cooperate with regions that have a higher degree of openness to the outside world. The estimated coefficient of the level of digital economy development is significant, with a coefficient value of 4.4818. It proves the speculation we presented in the previous section. The probability of establishing low-carbon technology cooperation with other regions increases by about 87.39% (EXP (4.4818) − 1) for each level of regional digital economy development. Among the digital economy homophily variables, only the estimated coefficient of homophily (Low-dige) is significant. It indicates that low-carbon technology cooperation is more likely to occur between regions with lower levels of digital economy development. This result may be due to the following reasons. The regions with low digital economy may have technical barriers to the regions with high or moderate digital economy because of the backward information infrastructure, and it is more difficult to match technology supply and demand. It makes the less developed digital economy regions fall into the "technology silo" dilemma, so they can only cooperate with the same digital economy level.
Model A3 demonstrates the effect of network covariates on the evolution of LCTCN. The estimated coefficient of geographic proximity is significantly positive, meaning that regions seeking low-carbon technology cooperation prefer to cooperate with neighboring regions. This result agrees with the findings of Milani et al. [73]. The shorter geographic distance can enhance communication and interaction between the cooperating parties, which can increase the efficiency of technical cooperation. Notably, institutional proximity was not found to impact inter-regional collaboration in low-carbon technology.
To avoid the mean value being pulled up or down by a single maximum or minimum value, we binarized the LCTCN again, using 120% and 80% of the mean value as thresholds.
We then re-estimated the coefficients of the two newly obtained binarization matrices to perform robustness tests [34]. The results are presented in model A4 and model A5. In addition, we refer to other scholars' literature [65], we adjust the time step from 1 to 2 for the robustness test, and the results are presented in Model A6. We can see that the direction and significance of the coefficients of the other variables, except for the strength of environmental regulation, do not change much compared to Model A3. It indicates the reliability of our results to some extent. The results of model A4, model A5, and model A6 all show that environmental regulation does not affect the formation of the LCTCN relationship. Although the coefficient of environmental regulation intensity is still positive, it is no longer significant. So, the impact of environmental regulation intensity on low-carbon technology cooperation does not pass the robustness test.
To observe the dynamics of the coefficient values of the variables, we estimated the parameters of the LCTCN separately by the periods classified in the previous section. Model B1, Model B2, and Model B3 in Table 7   The coefficient values of the endogenous structures (Gwdegree, Gwesp, and Gwdsp) are getting smaller and gradually become insignificant from significant, which indicates a gradual stabilization of the network structure. The role of structures in network relationship formation is decreasing. The coefficient of environmental regulation is negatively insignificant in the first stage and positively significant in the second and third stages. Based on other scholars' studies, we speculate that there may be an inflection point in the process of environmental regulation intensity [74]. Only if the intensity of environmental regulation exceeds the inflection point can it play a facilitating effect. The coefficient value of external openness is increasing, which indicates that external openness plays a more critical role as a facilitator over time.
The digital economy is not significant in the first stage, which may be because China's digital economy just started in 2011-2014, which has a limited contribution to low-carbon technology cooperation. In the second and third stages, the digital economy starts to become significant, but the absolute value of the coefficient is decreasing. It indicates that the higher the level of digital economy development, the easier it is for the region to establish cooperation with other regions. However, the digital economy's impact is getting smaller. The coefficient of homophily (High-dige) is negatively significant in the second and third stages but decreases in absolute value. It suggests that regions with high digital economies do not tend to cooperate, but this tendency is diminishing. The coefficient of homophily (Mid-dige) is insignificant to positively significant. It indicates that regions with intermediate levels of digital economy are also beginning to prefer to cooperate with regions with similar levels of digital economy. The coefficient of homophily (Low-dige) has been positively significant, and its absolute value gradually increased with time. It suggests that low-carbon technology partnerships are more likely to be established between regions with low levels of digital economy, and this trend is increasingly evident. In conclusion, the digital economy's homophily plays an increasingly significant role in LCTCN formation. While the digital economy has increased the efficiency of cooperation, the uneven development of the digital economy has further widened the technological barriers between different digital economy levels, leading to the increasing tendency of regions with similar levels of the digital economy to cooperate.
The geographic proximity has a positive and significant effect on cooperative networks in all periods and plays an increasingly important role in the formation of LCTCN.
Next, we included temporal variables in the model to test the state of the LCTCN. Autoregression checks whether the network edges at stage t-1 transfer to the network at stage t. Stability tests whether the edges and non-edges in phase t-1 and phase t are stable. Innovation checked whether each regional cooperation relationship increased from the previous year. From Table 8, we can see that the parameter estimates for both Autoregression and Stability are positively significant, and those for Innovation are negatively significant. It indicates that LCTCN is more stable and less innovative, reflecting more incremental development than leapfrogging in the evolutionary path.  Next, we checked the reliability of the model. First, we generated many simulated networks using the observations of the variables and the coefficient values of the variables estimated by the model. The metrics of the generated networks were then compared with the actual observed networks' metrics. The results are shown in Figure 7. The thick black lines in the first five subplots in Figure 7 are the distributions of the metrics from the observed network. The grey areas are the corresponding distribution intervals for the network simulated by the model. The closer the grey area's midpoint is to the actually observed eigenvalue points, the more reliable the model is. Second, the area under the curve (AUC) is also one of the model evaluation metrics [75]. The value of AUC indicates the distance between y = 1 and y = 0. The larger the AUC, the more accurately our model predicts whether cooperation is generated between regions. In the sixth subplot of Figure 7, The above figure shows blue and red curves, which present receiver operating characteristics (ROC) and precision-recall (PR) curves, respectively. The area enclosed by the receiver operating characteristic curve (ROC) in the sixth subplot of Figure 7 is the AUC. The closer the ROC is to the upper left corner, the more accurate the model prediction is [76]. As can be seen, in Figure 7, our ROC curve is very close to the upper left corner. Note: * represents 5% of the parameter significance levels.
Next, we checked the reliability of the model. First, we generated many simulated networks using the observations of the variables and the coefficient values of the variables estimated by the model. The metrics of the generated networks were then compared with the actual observed networks' metrics. The results are shown in Figure 7. The thick black lines in the first five subplots in Figure 7 are the distributions of the metrics from the observed network. The grey areas are the corresponding distribution intervals for the network simulated by the model. The closer the grey area's midpoint is to the actually observed eigenvalue points, the more reliable the model is. Second, the area under the curve (AUC) is also one of the model evaluation metrics [75]. The value of AUC indicates the distance between y = 1 and y = 0. The larger the AUC, the more accurately our model predicts whether cooperation is generated between regions. In the sixth subplot of Figure  7, The above figure shows blue and red curves, which present receiver operating characteristics (ROC) and precision-recall (PR) curves, respectively. The area enclosed by the receiver operating characteristic curve (ROC) in the sixth subplot of Figure 7 is the AUC. The closer the ROC is to the upper left corner, the more accurate the model prediction is [76]. As can be seen, in Figure 7, our ROC curve is very close to the upper left corner. In addition, we also checked the fitting effect of TERGM when the network was phased. Figures 8-10 show the fit of the TERGM model for LCTCN in the 2011-2014 phase, 2015-2017 phase, and 2018-2020 phase, respectively. It can be seen that the fit of In addition, we also checked the fitting effect of TERGM when the network was phased. Figures 8-10 show the fit of the TERGM model for LCTCN in the 2011-2014 phase, 2015-2017 phase, and 2018-2020 phase, respectively. It can be seen that the fit of the model for the 2018-2020 phase is the best.

Conclusions and Enlightenment
With increasingly severe energy and environmental problems, China is paying more attention to developing low-carbon technologies. In this study, we used co-patent data on low-carbon technology from 2011 to 2020 to investigate the network topology and spatial association of LCTCN. Then, we empirically tested the determinants of the inter-regional establishment of cooperation relationships in the network using a TERGM.
Our statistical analysis and visualization of the LCTCN reflect the latest dynamics and development direction of low-carbon technology cooperation in China to a certain extent. It provides substantial empirical evidence for realizing the rational allocation of innovation resources. Studying the reasons for establishing cooperation relationships in LCTCN can provide some policy guidance to help China crack the barriers to cooperation, promoting the absorption and integration of low-carbon technologies and improving China's independent innovation capability of low-carbon technologies.

Main Conclusions
We explored the network structure and spatial distribution of the LCTCN. We came to the following conclusions: (1) Overall, the LCTCN has evolved from simple to complex, and the breadth of each regional cooperation and the depth of cooperation are increasing yearly. It reflects the importance that each region in China attaches to low-carbon technologies and continuously strengthens the cooperation and exchange of low-carbon technologies. (2) Low-carbon technology cooperation is unevenly distributed geographically, showing that the east is strong and the west is weak. However, the spatial imbalance is weakening with the increase of time. It indicates that the western region is also actively promoting the enhancement of low-carbon technologies and striving to promote the exchange of the low-carbon technologies with other regions. (3) In the LCTCN, regions with small degrees are more willing to trust regions with high degrees and cooperate with them to build partnerships, which makes the network show prominent heterogeneous characteristics. It indicates that the pattern of low-carbon technology cooperation in China is mainly a division of labor between strong and weak regions rather than a union between

Conclusions and Enlightenment
With increasingly severe energy and environmental problems, China is paying more attention to developing low-carbon technologies. In this study, we used co-patent data on low-carbon technology from 2011 to 2020 to investigate the network topology and spatial association of LCTCN. Then, we empirically tested the determinants of the inter-regional establishment of cooperation relationships in the network using a TERGM.
Our statistical analysis and visualization of the LCTCN reflect the latest dynamics and development direction of low-carbon technology cooperation in China to a certain extent. It provides substantial empirical evidence for realizing the rational allocation of innovation resources. Studying the reasons for establishing cooperation relationships in LCTCN can provide some policy guidance to help China crack the barriers to cooperation, promoting the absorption and integration of low-carbon technologies and improving China's independent innovation capability of low-carbon technologies.

Main Conclusions
We explored the network structure and spatial distribution of the LCTCN. We came to the following conclusions: (1) Overall, the LCTCN has evolved from simple to complex, and the breadth of each regional cooperation and the depth of cooperation are increasing yearly. It reflects the importance that each region in China attaches to low-carbon technologies and continuously strengthens the cooperation and exchange of low-carbon technologies.
(2) Low-carbon technology cooperation is unevenly distributed geographically, showing that the east is strong and the west is weak. However, the spatial imbalance is weakening with the increase of time. It indicates that the western region is also actively promoting the enhancement of low-carbon technologies and striving to promote the exchange of the low-carbon technologies with other regions. (3) In the LCTCN, regions with small degrees are more willing to trust regions with high degrees and cooperate with them to build partnerships, which makes the network show prominent heterogeneous characteristics. It indicates that the pattern of low-carbon technology cooperation in China is mainly a division of labor between strong and weak regions rather than a union between strong regions or a union between weak regions. However, this heterogeneous feature is weakening over time, which indicates that the regions are also actively exploring other cooperation patterns. (4) Beijing and Shanghai are always in the core positions and intermediary positions in LCTCN and have absolute power and control force in the LCTCN. With increased time, the dependence of other regions on the core nodes of Beijing and Shanghai is decreasing, and their independence is growing gradually. Jiangsu, Guangdong, and other regions gradually shift from strong semi-peripheral regions to core regions, from participants to leaders. It shows they can rely on their development advantages to drive other regions.
We empirically test the effects of endogenous structural variables and exogenous variables of the network on the establishment of regional low-carbon partnerships. (1) The regions in LCTCN prefer to seek connections with already well-connected regions and the network does not tend to form a closed triangle structure. Instead, regions prefer to connect to others in multiple ways to decrease their dependency on individual links. (2) The digital economy will positively and significantly promote the establishment of the low-carbon technology cooperation between regions. It suggests that the higher the regional digital economy's development, the more opportunities for low-carbon technology cooperation are available to the region. However, we also verify that the imbalance in the digital economy's growth further widens the low-carbon technology barriers between different levels, leading to a gradual preference for regions to engage in low-carbon technology cooperation with regions that have similar levels of digital economy. (3) We also verify that openness and geographic proximity also affect the establishment of interregional low-carbon technology cooperation relationships, validating previous findings.

Policy Implications
The government should fully understand the role of the network structure. Interregional low-carbon technology cooperation relationships form on the effect of endogenous structures and exogenous factors. Therefore, if China wants to improve the overall efficiency of inter-regional low-carbon technology cooperation, it should formulate different development policies according to the region's position in the network. For regions at the core positions, the government should control the quantity of low-carbon technology cooperation and pay more attention to the quality of collaboration. For regions at the periphery positions, the government should provide more policy assistance to help them establish broader cooperation relationships. Regions with high cooperation depth but insufficient cooperation breadth need to actively expand new partners to be able to absorb more heterogeneous technologies. In conclusion, China can improve the development of low-carbon technologies by optimizing the structures.
Imbalance in the development of the regional digital economy has become an important reason for expanding the barriers to low-carbon technology cooperation between developed and backward regions. Inter-regional competition for critical resources has exacerbated the imbalance in the development of the digital economy. There are also significant differences between different areas in their ability to access digital resources and seize opportunities and benefits. Therefore, it is necessary to address these issues if we want to break down the technological barriers between developed and backward regions. The government should improve the digital economy's top-level design and overall planning and provide policy support for developing the digital economy in lagging areas. In addition, the government needs to fully use the backward regions' low-cost advantage, helping it build digital infrastructure to pull the level of the digital economy. Finally, the government should establish a digital economy exchange platform to spread the successful experience of digital economy development in developed regions to the backward areas.

Limitations and Opportunities
The limitations of this study provide opportunities for future research to improve. This paper constructs an inter-provincial low-carbon technology cooperation network. If we change the geographical scale, some conclusions may change. In the future, we will consider constructing inter-municipal low-carbon technology cooperation networks at a smaller scale. In addition, the data used in this paper are cooperative patents, and we may consider using co-authored papers or corporate alliance data to enrich the empirical findings in the future.