Spatial Network Structure of China’s Provincial-Scale Tourism Eco-Efficiency: A Social Network Analysis

While tourism eco-efficiency has been analyzed actively within tourism research, there is an extant dearth of research on the spatial network structure of provincial-scale tourism eco-efficiency. The Super-SBM was used to evaluate the tourism eco-efficiency of 30 provinces (excluding Tibet, Hong Kong, Macao and Taiwan). Then, social network analysis was employed to examine the evolution characteristics regarding the spatial network structure of tourism eco-efficiency. The main results are shown as follows. Firstly, tourism eco-efficiency of more than two thirds’ provinces witnessed an increasing trend. Secondly, the spatial network structure of tourism eco-efficiency was still loose and unstable during the sample period. Thirdly, there existed the multidimensional nested and fused spatial factions and condensed subsets in the spatial network structure of tourism eco-efficiency. However, there was still a lack of low-carbon tourism cooperation among second or third sub-groups. These conclusions can provide references for policymakers who expect to reduce carbon emissions from the tourism industry and to achieve sustainable tourism development.


Introduction
Tourism has solidified its role as the strategic-pillar industry in China [1], accounting for 6.69% of the total gross domestic product (GDP) in 2019. For a long time, tourism has been regarded as an industry with low-carbon and environmental protections [2]. Therefore, adequate attention is not paid to the pollution brought by tourism industry in China. With the expansion and improvement of the tourism economy, the negative environment impacts of the tourism industry have gradually been exposed [3]. The Fourteenth Five Year Plan, issued by the central government in March 2021, emphasized the high-quality development is the main direction of the tourism industry in the next five years. Tourism eco-efficiency is defined as creating more economic value in tourism products and service, while eliminating negative environmental effects and reducing resource consumption [4][5][6]. The improvement of tourism eco-efficiency cannot only be in accordance with the goal of carbon emission peaking and carbon neutrality (Two Carbon) but also promote the high-quality development of tourism industry [7].
With the exposure of the negative impacts of tourism development on ecological environment, quite a few scholars have gradually begun to concentrate how to achieve low-carbon development in tourist destinations. Moreover, the Sustainable Tourism Development Action Strategy (STDAS) put forward the concept of sustainable tourism, and pointed out that both ecological environment and economic benefit should be taken into Section 3, in which this study evaluated the tourism eco-efficiency and explored the evolution characteristics regarding the spatial network structure of tourism eco-efficiency. The discussion and conclusions were presented in Section 4, in which this study discussed the empirical results, summarized the literature contributions, and provided recommendations for tourist destination management.

Materials and Methodology
2.1. Method 2.1.1. Super-SBM Data envelopment analysis (DEA) is a model that evaluates multiple decision units with similar inputs and outputs [21]. However, there are two main shortcomings in the traditional DEA morel. First, the slack variables may affect the accuracy of the evaluation results. Second, there solely exists expected output, and the undesirable output is not fully taken into account. In order to make up the for above-mentioned deficiencies, Tone [22] proposed the slack-based model (SBM) based on the undesirable output, which not only takes into consideration the issue of slack, but also includes undesirable output. There is no doubt that the modifications of the model can make the evaluation more accurate. Nevertheless, when the SBM is employed to assess the efficiency of several decision-making units (DMUs), it is easy to generate the phenomenon wherein the efficiency values of DMUs all reach the optimal frontier production surface [23]. In other words, the efficiency values of multiple DMUs are 1, which makes the comparison of DMUs' efficiency impossible. Considering this issue, Tone [24] put forward the Super-SBM model based on the traditional SBM. The formula of Super-SBM is as follows. x ≥ x k ; y d ≤ y d k ; y u ≥ y u k ; λ j ≥ 0, i = 1, 2, . . . , m j = 1, 2, . . . , n; j = 1, 2, . . . , n; q = 1, 2, . . . , r 2 (1) where, ρ is the tourism eco-efficiency; x, y d and y u are input, expected output and undesirable output, respectively. m, r 1 , and r 2 are the quantities of inputs, expected outputs and undesirable outputs, respectively. A value of tourism eco-efficiency greater than or equal to 1 indicates that the tourism eco-efficiency is in an effective state; otherwise, it is in an invalid state.

Modified Gravity Model
A province is a point in the spatial network structure of tourism eco-efficiency, and the spatial connection of tourism eco-efficiency among provinces is the line [25]. At present, the vecto autoregressive (VAR) model, and the modified gravity model are universally used to establish the spatial correlation matrix of tourism eco-efficiency. Given that the sensibility regarding the choice of lag order may reduce the accuracy of examining the network structure characteristics [26], the modified gravity model has been universally applied to construct the spatial correlation matrix. More importantly, this model can take consideration into the "quality" and "distance", and reflect the evolution characteristics regarding the spatial network structure [27]. Based on the above-mentioned advantages, this study applied the modified gravity model. The formula is as follows. where F ij denotes the gravity between province i and province j. E i and E j represent the tourism eco-efficiency in province i and province j, respectively. D ij represents the distance between province i and province j, which is represented by the shortest straightline distance among two provincial capitals [25]. K ij is the correction coefficient. Generally speaking, provinces with high tourism eco-efficiency possess a stronger radiation effect on provinces than that of provinces with low tourism eco-efficiency, through radiation of tourism low-carbon technology and spillovers of tourism low-carbon information [2]. In this study, K ij is calculated by the proportion of tourism eco-efficiency of province i in the sum of tourism eco-efficiency of province i and province j.

Social Network Analysis
Social network analysis (SNA), an interdisciplinary research method, aims to describe the relationship among members in a network and the influence of different relationship patterns on the characteristics regarding network structure based on graph theory and algebra [1,28]. Due to the advantages of intuitive graphics and accurate characterization, the application of SNA has been gradually expanded from sociology to economics, management, psychology, geography and other disciplines [27,29,30]. This study mainly adopted the SNA to explore the overall and individual characteristics regarding spatial network structure of tourism eco-efficiency in China and to reveal the actual or potential relationship between provinces. The relevant formulas can be seen in Table 1.
Where D is the network density, L is the actual relationship number, and N is the number of research areas.

Network hierarchy
Where H is the network hierarchy, K is the symmetric reachable points, and max(K) is the maximum possible point logarithm.
Network efficiency Where E is the network efficiency, M is the number of redundant lines, and max(M) is the maximum number of possible redundant lines.

Clustering coefficient
Where C i is the clustering coefficient, e i represents the number of edges between k neighbors of province I, k i is the number of edges of node i.

Average path length
Where N is the total of network nodes, d ij is distance between province i and province j.

Degree centrality
Where De is the point centrality, n is the number of nodes connected with the province, and N is the maximum number of nodes connected with the province.

Betweenness centrality
Where Cb i is betweenness centrality; b ij is the number of the shortcuts between city i and city j; and b ij (l) represents the number of shortcuts between province i and province j.

Closeness centrality
Where C −1 APi is closeness centrality; and d ij is the shortest distance between province i and province j. more rigid the network structure, and more provinces play the role of edge in the spatial network structure. Network efficiency mainly reflects the connection efficiency among nodes in the spatial network structure. If the network efficiency is lower, there will be more spillover channels among various provinces, and the more stable the network structure is. The clustering coefficient and the average path length are used to mirror the characteristics of "small-world" regarding the spatial network structure [31], among which, the clustering coefficient mainly represents the cohesion of the spatial network structure. The higher the clustering coefficient is, the more frequent the network connections are. The average path length can indicate the distance between nodes.
(2) The individual network structure characteristics. The individual network structure characteristics are mainly reflected by three indexes, namely degree centrality, betweenness centrality and closeness centrality. Specifically, the point centrality reflects the central position of the node in the network structure. The greater power in the network structure, and the more prominent the central position of the node in the network structure. Betweenness centrality mirrors the degree to which nodes control the connections among other nodes. The higher the betweenness centrality, the greater the priority and control of the node. Closeness centrality reflects the ability a node to be controlled by other nodes. The greater closeness centrality, the more direct spatial associations among nodes, and the easier it is for the node to play the role of the center.
(3) Network cohesive sub-groups analysis. Cohesive sub-groups can explain the substructure within a group, which is a broad concept of sub-group [28]. Nodes in a subgroup possess relatively strong, relatively close and relatively direct relationships, whose fundamental purpose is to reveal the actual or potential relationship between nodes [32].

Index System Selection
This study regards capital, labor and energy as the tourism input indicators. Land is one of the most basis production factors in economic activities, but it is not a decisive factor affecting the intensive or extensive management of tourism industry in the process of tourism economic development [33]. More seriously, there is a dearth of the dataset on the number of tourism land-use [1]. Therefore, the land is not seen as the basis input in this study. Capital input has a significant influence on the development pathway to a certain extent, thus, playing an indispensable role in the low-carbon tourism development. In this study, the total of fixed asset investment regarding tourist attractions, travel agencies and star-hotels is used to represent the level of tourism capital investment [28]. Additionally, tourism industry is regarded as a labor-intensive industry with significant employment attributes. In this study, the number of tourism employees is used to represent the labor input of tourism [34]. Tourism energy input is of great importance in evaluating tourism eco-efficiency; this study selects tourism energy consumption to represent tourism energy input [13].
With respect to the expected output index, the total tourism revenue is the direct embodiment of economic benefits from tourism. Moreover, the total number of tourists can better reflect the spillover effect of the tourism industry [35]. In terms of undesired output, this study adopts carbon emissions from the tourism industry to reflect the negative impact of tourism-related economic development on the ecological environment [7,13].

Data Source
In this study, 30 provinces (excluding Tibet, Hong Kong, Macao and Taiwan) were taken as the case studies. The data on inbound tourism revenue, inbound tourist arrival, and fixed asset investment in the tourism industry were mainly received from the China Statistical Yearbook (2001~2018) and China Tourism Statistical Yearbook (2001~2018). Domestic tourism revenue and domestic tourist arrival were mainly taken from the statistical yearbooks of 11 provinces during the period of 2001~2018. Quite a few data were supplemented and improved by the statistical bulletins of national economic and social development of each province. With regard to carbon emissions and energy consumption, this study adopted the "bottom-up" method, including decomposition and summation based on determining the key areas, overall tourism energy consumption and carbon emissions [36,37]. The specific calculation process was played in Appendix A. The data involved in the calculation of energy consumption and carbon emissions from the tourism industry were mainly received from the China Transport Statistical Yearbook (2001~2018) and the China Energy Statistical Yearbook (2001~2018). A part of the data is collected from the Tourism Sample Survey Data (2001~2018) and the Statistical Bulletin of National Economic and Social Development. Additionally, in order to avoid the interference of price factors on the empirical results, the data of income nature is adjusted, with year 2000 as the baseline period.

Measurement of Tourism Eco-Efficiency
China's tourism eco-efficiency, shown in Table 2, witnessed a fluctuating growth trend during the study period, which increased from 0.441 in 2000 to 0.525 in 2017, with an average annual growth rate of 1.1%. This indicated that tourism-related economic development in China still relied on resources and harmed the environment; thus, there is tremendous room for progress in low-carbon tourism development. According to the partition criterion, formulated by the National Bureau of Statistics in 2011, 30 provinces were divided into four areas, namely Eastern area, Central area, Western area, and Northeastern area. From the perspective of the sub-area, the tourism eco-efficiency in the Eastern, Central, Western and Northeastern areas all showed a fluctuating growth trend, with the largest growth rate (32.70%), and the smallest growth rate (14.31%), respectively ( Figure 1). The order of the spatial heterogeneity distribution pattern regarding the mean of tourism ecoefficiency by area was Eastern (0.740), Northeastern (0.440), Central (0.429) and Western (0.217) during the period of 2000~2017. At the provincial level, except for Beijing, Tianjin, Liaoning, Henan, Hunan, Chongqing, Sichuan, Qinghai and Ningxia, tourism eco-efficiency of the remaining 21 provinces experienced varying degrees of increase during the study period; the largest increase was in Jilin Province (197.18%); the largest decrease was in Qinghai Province (43.33%), indicating that, due to the differences in the input of the material elements of the tourism economy, there was great spatial heterogeneity in the tourism eco-efficiency among these provincial areas in China.  Table 2.  In this study, ArcGIS10.3 software was used to draw the network structure of China's provincial-scale tourism eco-efficiency, which can reflect the overall network structure characteristics of tourism eco-efficiency in China. Figure 2 showed that with the implementation of the ecological civilization strategy and the high-quality development strategy, the cooperation among different provinces in promoting the transformation of the tourism development mode has been deepening. Therefore, the spatial network structure of tourism eco-efficiency was complex and dense. The overall network structure of China's tourism eco-efficiency, shown in Figure 2, was relatively loose during the study period. The average number of network relationships in each province was 107; the average network density was 0.123; the average clustering coefficient was 0.417, and the average path length was 2.98. Low network agglomeration, connectivity, and closeness were not only conducive to the diffusion and spillovers of tourism low-carbon production factors, such as technologies, talents and capital among provinces, but also affected the stability of the spatial network structure of tourism eco-efficiency.

Individual Network Characteristics
In this study, three indexes, i.e., degree centrality, betweenness centrality ness centrality, were used to analyze the characteristics regarding individua structure of tourism eco-efficiency. Furthermore, the spatio-temporal evolution istics of the above-mentioned three indicators, adopting the ArcGIS10.2 softw visually played by the inverse distance weight (IDW) method ( Figure 4).

(1) Point Degree
Out-degree centrality and in-degree centrality can reflect the interaction ships among provinces in the spatial network structure of tourism eco-efficienc cally, the out-degree centrality and the in-degree centrality represents the spillo and agglomeration effect from tourism eco-efficiency, respectively. The average in-degree centrality and out-degree centrality, shown in Figure 4a,b, experience all growth trend during the sample period, which indicated that the inflow an of tourism eco-efficiency among provinces were strengthening constantly, an mutual connection of tourism eco-efficiency between provinces was strengthen more specific, in 2000, there were 14 provinces with higher out-degree centr mean value, in which Heilongjiang, Hunan, Hainan, Guangxi, Guangdong, Zhe Yunnan ranked TOP 7, while Ningxia, Gansu, Guizhou and other regions exh spillover effect for other provinces. Moreover, there were nine provinces with erage in-degree centrality, with Beijing, Tianjin, Liaoning and Henan in the top In terms of the evolution trend, the network density, and the number of network relationships, were both increasing slowly in the fluctuation; however, the increase degree was still small, which indicated that the scale, level and standard of low-carbon tourism cooperation among these provinces were still low ( Figure 3). It was noteworthy that the clustering coefficient witnessed a slight downward trend, while the average path length experienced a slight upward trend, revealing that the connectivity of the tourism ecoefficiency transmission and the cohesion of the overall network structure among provinces have decreased. Additionally, this highlights that the low-carbon technology between provinces used to promote low-carbon tourism development still faces obstacles and constraints, such as administrative boundaries.

Individual Network Characteristics
In this study, three indexes, i.e., degree centrality, betweenness centrality ness centrality, were used to analyze the characteristics regarding individu structure of tourism eco-efficiency. Furthermore, the spatio-temporal evolution istics of the above-mentioned three indicators, adopting the ArcGIS10.2 soft visually played by the inverse distance weight (IDW) method ( Figure 4).
(1) Point Degree Out-degree centrality and in-degree centrality can reflect the interactio ships among provinces in the spatial network structure of tourism eco-efficien cally, the out-degree centrality and the in-degree centrality represents the spil  the network hierarchy always remained above the value of 0.57, indicating that there was a hierarchical network structure in the spillover effect of tourism eco-efficiency among provinces and that this hierarchical structure was becoming increasingly intense. Additionally, the spatial equilibrium of tourism eco-efficiency in each province was relatively poor; the internal environment in which the spill occurred was as terrible as the radiation.
On the contrary, while the network efficiency experienced a downward trend in the fluctuation, decreasing from 0.803 in 2000 to 0.764 in 2017, which revealed that the connectivity of network structure of tourism eco-efficiency has increased, the routes of tourism ecological resource elements spillovers among provinces has been raised, and the stability of spatial correlation has been improved. However, there was also a risk that with the increase of redundant cables, the transmission efficiency of the network structure would be reduced. Therefore, maintaining reasonable network efficiency can optimize the allocation of network resources.

Individual Network Characteristics
In this study, three indexes, i.e., degree centrality, betweenness centrality and closeness centrality, were used to analyze the characteristics regarding individual network structure of tourism eco-efficiency. Furthermore, the spatio-temporal evolution characteristics of the above-mentioned three indicators, adopting the ArcGIS10.2 software, were visually played by the inverse distance weight (IDW) method ( Figure 4). spatial distribution pattern of point centrality has been expanded from a high value ar in 2000 (with Beijing and Tianjin as the core) to two high value areas in 2017 (with Beiji as the core of the Northern area around Bohai Sea and Urumqi as the core of the northe Xinjiang region). While the coverage of the low-value areas of point centrality has be shrinking, its spatial distribution pattern has been reduced from a continuous low-va area in 2000 (the continuous low-value area with the core of Urban Agglomeration alo the Yellow River in Ningxia and the Lanzhou-Xining Urban Agglomeration) and th scattered-point areas with low-value (Shanxi, Shandong and Guizhou) to one low-va area in 2017 (the low-value area with the core of Urban Agglomeration along the Yello River in Ningxia). Some of the provinces with high point centrality, such as Tianjin, w able to share modern low-carbon tourism technology and management experience w other provinces, and, thus, improve their point centrality by increasing out-degree ce trality. Other provinces, such as Xinjiang, become the province with high point central in 2017, which was mainly due to the deep implementation of the Aid-Xinjiang progra Xinjiang can absorb the management experience of developing low-carbon tourism pro ucts, designing low-carbon tourism routes, establishing low-carbon tourism enterpri and so on, which improved the point centrality by strengthening in-degree centrality.  (1) Point Degree Out-degree centrality and in-degree centrality can reflect the interaction relationships among provinces in the spatial network structure of tourism eco-efficiency. Specifically, the out-degree centrality and the in-degree centrality represents the spillover effect and agglomeration effect from tourism eco-efficiency, respectively. The average values of indegree centrality and out-degree centrality, shown in Figure 4a,b, experienced an overall growth trend during the sample period, which indicated that the inflow and outflow of tourism eco-efficiency among provinces were strengthening constantly, and that the mutual connection of tourism eco-efficiency between provinces was strengthening. To be more specific, in 2000, there were 14 provinces with higher out-degree centrality than mean value, in which Heilongjiang, Hunan, Hainan, Guangxi, Guangdong, Zhejiang and Yunnan ranked TOP 7, while Ningxia, Gansu, Guizhou and other regions exhibited less spillover effect for other provinces. Moreover, there were nine provinces with above-average indegree centrality, with Beijing, Tianjin, Liaoning and Henan in the top tier, and Hubei, Hainan and Shanxi in the lowest tier. In contrast, the number of provinces that exhibited an above-average out-degree centrality dropped by two in 2017, with Hainan, Fujian, Jiangxi and Sichuan still remaining in the top ranks, whereas the number of provinces with above-average in-degree centrality increased to 12, showing that China's provincial-scale tourism eco-efficiency network was more closely structured; the number of provinces that can receive other radiation effects is increasing, and the cooperation and exchanges among different provinces in low-carbon tourism technologies were also continuously strengthening.
In 2000 and 2017, the interval of point centrality was [3.482, 55.149] and [3.455, 48.202], respectively. The interval range of point centrality saw a narrow trend, indicating that the spatial differences of point centrality among various provinces witnessed a trend of constant balance. The spatial network structure of tourism eco-efficiency tended to be balanced; provinces increasingly played a core role. As can be seen from Figure 4c,d, the spatial distribution pattern of point centrality has been expanded from a high value area in 2000 (with Beijing and Tianjin as the core) to two high value areas in 2017 (with Beijing as the core of the Northern area around Bohai Sea and Urumqi as the core of the northern Xinjiang region). While the coverage of the low-value areas of point centrality has been shrinking, its spatial distribution pattern has been reduced from a continuous low-value area in 2000 (the continuous low-value area with the core of Urban Agglomeration along the Yellow River in Ningxia and the Lanzhou-Xining Urban Agglomeration) and three scattered-point areas with low-value (Shanxi, Shandong and Guizhou) to one low-value area in 2017 (the low-value area with the core of Urban Agglomeration along the Yellow River in Ningxia). Some of the provinces with high point centrality, such as Tianjin, were able to share modern low-carbon tourism technology and management experience with other provinces, and, thus, improve their point centrality by increasing out-degree centrality. Other provinces, such as Xinjiang, become the province with high point centrality in 2017, which was mainly due to the deep implementation of the Aid-Xinjiang program. Xinjiang can absorb the management experience of developing low-carbon tourism products, designing low-carbon tourism routes, establishing low-carbon tourism enterprise, and so on, which improved the point centrality by strengthening in-degree centrality.
(2) Closeness Centrality In 2000 and 2017, the ranges of closeness centrality were (32.957, 64.430) and (33.727, 64.390), respectively. On the one hand, the overall provincial closeness centrality tended to increase. On the other hand, the regional differences of closeness centrality among provinces gradually contracted. This indicated that more provinces can make full use of the transmission effect of the spatial network structure, quickly generate spatial connections with other provinces, and play the role of "central actors" in the spatial network structure of tourism eco-efficiency. As shown in Figure 5, similar to the geographical distribution pattern of point centrality, the areas covered with high closeness centrality were mainly distributed around the northern part of the Bohai Sea with Beijing and Tianjin as the core; the low-value areas were mainly distributed along the urban agglomeration along the Yellow River in Ningxia. With the spatial association of the tourism eco-efficiency among the provinces increasing, the spatial scope of the high closeness centrality saw an expanding trend to a certain extent, while the coverage of the low closeness centrality was reduced to a certain extent. On the one hand, the low-value areas with the core of the urban agglomeration along the Yellow River in Ningxia were difficult to spill over into the surrounding provinces due to the behindhand low-carbon tourism technology. On the other hand, due to their unfavorable transport accessibility, it was difficult to connect with the provinces located in the Central area or the Eastern area. Therefore, it played the role of marginal actor in the spatial network structure of tourism eco-efficiency. saw an expanding trend to a certain extent, while the coverage of the low closeness centrality was reduced to a certain extent. On the one hand, the low-value areas with the core of the urban agglomeration along the Yellow River in Ningxia were difficult to spill over into the surrounding provinces due to the behindhand low-carbon tourism technology. On the other hand, due to their unfavorable transport accessibility, it was difficult to connect with the provinces located in the Central area or the Eastern area. Therefore, it played the role of marginal actor in the spatial network structure of tourism eco-efficiency. (

3) Betweenness Centrality
The ranges of the provincial betweenness centrality were (0, 33.334) and (0.001, 25.612) in 2000 and 2017, respectively. The betweenness centrality saw a decreasing trend during the sample period, indicating that the spatial equilibrium of the betweenness centrality tended to be intensive, and the spatial network structure of tourism eco-efficiency gradually transformed from simple to complex ( Figure 6). In 2000, the high-value areas of betweenness centrality were mainly located in Beijing, Tianjin, Guangdong, Hainan and Yunnan, which controlled at least two communication channels for tourism eco-efficiency, showing that the above-mentioned provinces played a role of bridge and intermediary in the transmission of low-carbon tourism technologies, and were the key nodes of the tourism eco-efficiency network structure. Significantly, some of the above provinces are provinces with a developed tourism economy in China, such as Beijing and Guangdong, which possess favorable low-carbon tourism technologies and management. Moreover, the other provinces were pilot low-carbon tourism provinces in China, such as Hainan and Yunnan, with a relatively perfect regulation of the tourism-related ecological environment; they can take on the role of intermediary to other provinces' tourism ecological protection resource elements. (

3) Betweenness Centrality
The ranges of the provincial betweenness centrality were (0, 33.334) and (0.001, 25.612) in 2000 and 2017, respectively. The betweenness centrality saw a decreasing trend during the sample period, indicating that the spatial equilibrium of the betweenness centrality tended to be intensive, and the spatial network structure of tourism eco-efficiency gradually transformed from simple to complex ( Figure 6). In 2000, the high-value areas of betweenness centrality were mainly located in Beijing, Tianjin, Guangdong, Hainan and Yunnan, which controlled at least two communication channels for tourism eco-efficiency, showing that the above-mentioned provinces played a role of bridge and intermediary in the transmission of low-carbon tourism technologies, and were the key nodes of the tourism eco-efficiency network structure. Significantly, some of the above provinces are provinces with a developed tourism economy in China, such as Beijing and Guangdong, which possess favorable low-carbon tourism technologies and management. Moreover, the other provinces were pilot low-carbon tourism provinces in China, such as Hainan and Yunnan, with a relatively perfect regulation of the tourism-related ecological environment; they can take on the role of intermediary to other provinces' tourism ecological protection resource elements.

Cohesive Sub-Group
The convergent correlation (CONCOR) model in UCINET (University of California at Irvine Network) software was used for the cluster analysis. Figure 7 shows that the spatial network structure of tourism eco-efficiency in 2000 and 2017 was divided into four secondary sub-groups and eight tertiary sub-groups, forming multidimensional nested and fused spatial cliques and condensed subsets. The boundary of each sub-group faced with several obstacles due to the large number of sub-groups; the spatial connection and overflow of tourism eco-efficiency among provinces were not close. From the perspective of time evolution, the constituent provinces of each subgroup were constantly changing on the whole; however, the individual provinces under most sub-groups remained unchanged, such as Beijing and Hebei in the first sub-group, Hainan and Xinjiang in the

Cohesive Sub-Group
The convergent correlation (CONCOR) model in UCINET (University of California at Irvine Network) software was used for the cluster analysis. Figure 7 shows that the spatial network structure of tourism eco-efficiency in 2000 and 2017 was divided into four secondary sub-groups and eight tertiary sub-groups, forming multidimensional nested and fused spatial cliques and condensed subsets. The boundary of each sub-group faced with several obstacles due to the large number of sub-groups; the spatial connection and overflow of tourism eco-efficiency among provinces were not close. From the perspective of time evolution, the constituent provinces of each subgroup were constantly changing on the whole; however, the individual provinces under most sub-groups remained unchanged, such as Beijing and Hebei in the first sub-group, Hainan and Xinjiang in the seventh sub-group, and Qinghai, Ningxia and Gansu among the eighth sub-group, which fully demonstrated that the sub-groups of the spatial network structure of tourism eco-efficiency had gradually become stable, and the functions and roles of some provinces had not changed a lot, especially the eighth sub-group, except that Guizhou moved to other subgroups. Qinghai, Ningxia and Gansu provinces were always located in the eighth subgroup. These three provinces were mainly restricted by geographical location and held weak connections with other provinces; they were situated at the edge of the tourism eco-efficiency network.

Cohesive Sub-Group
The convergent correlation (CONCOR) model in UCINET (University of California at Irvine Network) software was used for the cluster analysis. Figure 7 shows that the spatial network structure of tourism eco-efficiency in 2000 and 2017 was divided into four secondary sub-groups and eight tertiary sub-groups, forming multidimensional nested and fused spatial cliques and condensed subsets. The boundary of each sub-group faced with several obstacles due to the large number of sub-groups; the spatial connection and overflow of tourism eco-efficiency among provinces were not close. From the perspective of time evolution, the constituent provinces of each subgroup were constantly changing on the whole; however, the individual provinces under most sub-groups remained unchanged, such as Beijing and Hebei in the first sub-group, Hainan and Xinjiang in the seventh sub-group, and Qinghai, Ningxia and Gansu among the eighth sub-group, which fully demonstrated that the sub-groups of the spatial network structure of tourism ecoefficiency had gradually become stable, and the functions and roles of some provinces had not changed a lot, especially the eighth sub-group, except that Guizhou moved to other sub-groups. Qinghai, Ningxia and Gansu provinces were always located in the eighth sub-group. These three provinces were mainly restricted by geographical location and held weak connections with other provinces; they were situated at the edge of the tourism eco-efficiency network.

General Discussion
Tourism eco-efficiency is an important indicator to assesses the degree of low-carbon development in the tourism industry. Additionally, the low-carbon development of the tourism industry is one of the most important goals of the high-quality development of tourism. Against the background of high-quality development, it is imperative that tourism eco-efficiency should be explored. Although increasing attention has been paid to tourism eco-efficiency, there is scant work on the spatial network structure of tourism ecoefficiency in China. Therefore, the practical background and theoretical gap have driven us to concentrate on this topic. This study adopted Super-SBM, considering undesired output and social network analysis to explore the evolution characteristics of spatial network structure of tourism eco-efficiency.
There was been a slight rise of tourism eco-efficiency in China; the order of spatial distribution characteristics by areas were Eastern, Northeastern, Central, and Western. From the perspective of a single province, tourism eco-efficiency of more than two thirds of the provinces presented an increasing trend, indicating that provinces have increasingly begun to pay more attention to the quality improvement of the tourism industry rather than solely to quantity growth [5]. More specifically, improving tourism eco-efficiency has been a crucial strategy that coordinates tourism-related economic development and eco-environmental protection in tourists' destinations in China [7,38].
There are significant spatial connections of tourism eco-efficiency among various provinces, which is in accordance with the findings of Wang, Xia, Dong, Li, Li, Ba and Zhang [15]. In terms of overall network, although spatial connection of tourism ecoefficiency among various provinces has heightened during the sample period to a certain extent, the spatial network structure of tourism eco-efficiency was still loose and unstable.
Moreover, there existed rigid stratification in the spillover relationship of tourism ecoefficiency among different provinces. More seriously, the above-mentioned phenomenon has not been profoundly changed. From the perspective of the small-world characteristic, there was a lack of cohesive force and connection convenience in spatial network structures of tourism eco-efficiency, demonstrating that it is imperative that the central government establish tourism eco-environmental protection and supervision mechanisms across provinces, which is in line with the conclusion of Sun, Hou, Huang and Zhong [7].
With regard to an individual network, the spatial network structure of tourism ecoefficiency has become more compact, complicated, and balanced, which demonstrates that, increasingly, provinces can rapidly generate connections between other provinces and play the role of intermediary in the spatial network structure of tourism eco-efficiency. Generally, due to the limitation of geographical location, provinces located in the Western area play a marginal role in the network structure, which results from the fact that there is a lack of modern low-carbon tourism technology, and not enough investment in environmental protection in the Western area [17]. With respect to the results of the cohesive group, there existed the multidimensional nested and fused spatial factions and condensed subsets in the spatial network structure of tourism eco-efficiency; however, there was a dearth of effective connection among second or third sub-groups, which further confirmed that the spatial network structure of tourism eco-efficiency was incompact.

Theoretical Contributions
Our study makes three contributions to the new body of knowledge. To our knowledge, our research may be among the first study efforts to explore the evolution characteristics of the spatial network structure of provincial-level tourism eco-efficiency. Firstly, the extant literature mainly concentrates on a single tourism sector, such as scenic spots and hotels; this study can enrich and broaden the literature about the tourism efficiency of all tourist destinations. Secondly, this study grasps the spatial relationship of tourism eco-efficiency among different tourist destinations based on the relational data, providing new research perspectives for other scholars who expect to investigate spatiotemporal characteristics of tourism eco-efficiency. Thirdly, our research constructs the spatial connection matrix of tourism eco-efficiency by using the modify gravity model. Although the empirical investigation takes 30 provinces of China as a case study, this model is universal and applicable across other countries.

Practical Implications
This conclusion of our research is of great significance to the sustainable development of the tourism industry in China. Based on these conclusions, this study put forward recommendations for destination management organizations (DMOs). First, the spatial differences of tourism eco-efficiency across four areas must be taken into account by the central government. More capital investment and policy support should be brought into the Central and Western areas by the implementation of the Western Development Strategy and Central Risen Strategy, thus, achieving the coordinated improvement of tourism ecoefficiency. Second, the spatial network structure of tourism eco-efficiency was still loose and unstable. Therefore, the spatial connection of tourism eco-efficiency must be strengthened by accelerating the flow of information and technology among different provinces. For example, Anhui Province can gain the spillover of technology and the radiation of management from the other provinces in Yangtze River Delta Urban Agglomeration. Third, the barrier of administrative division needs to be broken by combining macroeconomic regulation and market disposition, which aims to generate more channels of the communication regarding low-carbon development. Given that there was a dearth of connections of tourism eco-efficiency among the second or third sub-groups, the cooperation and connection of sustainable tourism development should also be optimized by the construction of a low-carbon tourism market and the decrease of connection cost.

Limitations and Future Research
This study is not without limitations, which should not be overlooked; however, it also paves the potential road for future study. Firstly, with tourism-related economic development, the coefficients or the calculation method of carbon emissions from the tourism industry need to be adjusted in future research. Secondly, the data on the use of tourism land cannot be included in an input-output index system due to the size of the dataset. Therefore, the index system must be improved in future research. Thirdly, future scholars should explore the factors driving the spatial network structure of tourism eco-efficiency.  Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Data available from the authors upon request.

Acknowledgments:
We acknowledge the precious advice of the referees and editors. Meanwhile, we thank An Shi for his contribution that he modified all pictures.

Conflicts of Interest:
The authors declare no conflict of interest.

Evaluation on Carbon Dioxide Emission and Energy Consumption from the Tourism Industry
Based on the existing results at home and abroad, this study chose to use the "bottomup" method to calculate energy consumption and carbon dioxide emissions from the tourism industry. This study calculated the energy consumption/carbon dioxide emissions in three key tourism sectors, namely tourism transportation, tourism accommodation and tourism activities, and then summarized the total energy consumption/carbon dioxide emissions. The calculation formula is as follows: where, C t represents the total energy consumption/carbon dioxide emissions of tourism industry in year t; C t j represents the energy consumption/carbon dioxide emissions of department j in year t; C t 1 represents energy consumption/carbon dioxide emissions of tourism and transportation sectors in year t; C t 2 represents energy consumption/carbon dioxide emissions of tourism and accommodation sector in year t; C t 3 represents energy consumption/carbon dioxide emissions from tourism activities in year t.
where, C t i1 represents the energy consumption/carbon dioxide emissions of tourism and transportation sectors in region i in year t; Q t ix represents the passenger turnover of category x mode of transportation in region i in year t; f x represents the proportion of tourists in the passenger traffic volume of class x mode. The values of highway, civil aviation, railway and water transportation can be determined as 13.8%, 64.7%, 31.6%, and 10.6%, respectively, by referring to the existing research results. α x represents the energy consumption/carbon dioxide emissions coefficient of class x transportation mode, where the α value of highway is 133 g CO 2 /pkm, the value of civil aviation is 137 g CO 2 /pkm, and the railway and water transport are 27 g CO 2 /pkm and 106 g CO 2 /pkm.
where, C t i2 represents the energy consumption/carbon dioxide emissions of the tourism and accommodation sector in region i in year t; N t i is the number of beds in tourist hotels in region i in year t; l t i represents the average room occupancy rate in region i in year t; β is the energy consumption/carbon dioxide emissions coefficient (g/p visitor-night) per bed per night, and the value is 2.458 g/p visitor-night.
where, C t i3 represents the energy consumption/carbon dioxide emissions of regional tourism activities in year t; P t iS denotes the number of tourists participating in category s tourism activities in region i in year t; γ S is the energy consumption/carbon dioxide emissions coefficient of class s tourism activities, and the energy consumption/carbon dioxide emissions coefficient of tourism, vacation tourism, business trip, visiting friends and relatives and other tourism activities are, respectively, 417 g/p visitor, 1670 g/p visitor, 786 g/p visitor, 591 g/p visitor and 172 g/p visitor.