Spatial Association Network and Driving Factors of Agricultural Eco-Efﬁciency in the Hanjiang River Basin, China

: Reducing agricultural emissions and promoting carbon sequestration are vital for China to achieve its dual carbon goals. Achieving the green transformation of agricultural watersheds requires a thorough understanding of the internal transmission relationships within the watersheds and the underlying spatial correlation structures. This paper used the SBM-3E model to calculate the agricultural ecological efﬁciency of 17 prefecture-level cities in the Hanjiang River Basin (HRB) from 2010 to 2020, taking agricultural carbon emissions and a comprehensive non-point source pollution index as the unexpected output. The Gravity model and social network analysis methods were used to analyze the evolution characteristics of the network structure of agricultural ecological efﬁciency, and the secondary assignment procedure method was used to identify the driving factors from the planting structure, water use structure, and resource endowment. First, from 2010 to 2020, the overall agricultural ecological efﬁciency in the HRB demonstrates a declining trend, with efﬁciency values of 12.15, 9.40, and 6.67 in the upper, middle, and lower reaches, respectively. Second, the spatial correlation network density of agricultural ecological efﬁciency in the HRB is 0.17, with a network efﬁciency of 0.89. The correlation among units within the basin is relatively low, but stability is high. Moreover, the individual network spillover absorption capacity exhibits heterogeneity, and the status of each subject within the watershed follows a “core-edge” structure. Third, total water consumption and corn cultivation have a positive impact on the agricultural ecological efﬁciency network in the HRB, whereas agricultural water use and rice cultivation negatively inﬂuence the network. We propose policy recommendations to facilitate the advancement of green development in China’s agricultural watersheds and the achievement of the dual carbon goals.


Introduction
The challenges of greenhouse gas emissions and pollution have become critical [1,2]. Agriculture is a major contributor to global carbon emissions, with emissions from the agricultural sector accounting for 13.5% of the global total [3,4]. Non-point source pollution from agricultural activities is highly detrimental to the water environment, soil quality, and ecosystems, and also poses a range of environmental and human health risks [5]. China has achieved remarkable progress in agricultural development since the reform and opening-up policy [6]. However, it cannot be ignored that China has become the world's largest emitter of carbon, with agricultural greenhouse gas emissions accounting for approximately 17% of the country's total emissions [7,8]. At the same time, a particularly striking contradiction between China's agricultural development and the environment is the problem of non-point source pollution from agriculture [9,10]. Therefore, taking into account the adverse impacts of carbon emissions and non-point source pollution on efficient agricultural development will be a key element of low carbon, green, and sustainable agricultural development.
Eco-efficiency offers a new perspective for measuring environmental quality and sustainable development. [11]. It is the ratio of economic value to environmental impact and was first proposed by Schaltegger in 1990 [12]. In the field of agricultural research, agricultural eco-efficiency refers to the production of maximum agricultural products with minimum resource consumption and least environmental impact, thus promoting a sustainable agricultural development model [13,14]. Non-point source pollution is the problem of pollution caused by soil erosion, the use of fertilizers and pesticides, and agricultural waste from agricultural activities, and it is one of the main pressures on the development of environmentally friendly agriculture. When measuring agricultural eco-efficiency, research needs to take into account the negative environmental impacts of undesirable outputs. However, studies have considered both non-point source pollution and carbon emissions to a limited extent [4,5,8,10,13,14]. In general, the average level of agricultural efficiency decreases when a broader consideration of non-desired outputs is taken into account, but this is a more accurate reflection of efficiency. Furthermore, the analysis of structures and interactions between agricultural eco-efficiency units is a research gap, the absence of which hampers regional cooperation and the development of synergies [15][16][17][18][19]. Therefore, more research needs to be completed on agricultural eco-efficiency and its spatial characteristics.
The Han River Basin (HRB) is one of China's major agricultural producing areas. Despite the advantages of the HRB's agricultural resources, inefficient agricultural development and severe environmental pollution pose challenges to green development and meeting people's aspirations for a better life. It is necessary to understand the current situation and spatial characteristics of agro-ecological development in the HRB, which can provide a theoretical and practical basis for agricultural development in key areas. Therefore, this paper first introduces the 3E system into the SBM model and discusses the current development of agricultural eco-efficiency; second, it investigates the spatial characteristics of each unit's efficiency using the gravity model and social network analysis methods; and finally, it identifies the factors driving the spatial network of agricultural eco-efficiency and provides policy recommendations. The study finds that agricultural ecoefficiency in the HRB has a spatial distribution pattern and "core-edge" spatial structure. This paper makes a marginal contribution to the analysis of agricultural eco-efficiency by filling a gap in research that does not sufficiently consider unanticipated outputs, using agricultural carbon emissions and a composite surface pollution index as unanticipated outputs, and discussing the structural and interactive characteristics of efficiency in space. With a view to providing theoretical and practical insights into the design of agricultural green development policies and collaborative regional governance, the study provides insights into watersheds where fundamental agricultural resource advantages exist, and we have made policy recommendations to help green the Basin's agriculture and achieve the dual carbon goal.

Literature Review
At present, scholars at home and abroad have conducted extensive studies on agricultural eco-efficiency, focusing on different measurement techniques, the analysis of drivers, and study scales. One of the key aspects of measuring agricultural ecological efficiency is the method. Commonly used to assess agricultural environmental efficiency include life cycle assessment (LCA) [20], ecological footprint analysis (EF) [21], stochastic frontier analysis (SFA) [22], and data envelopment analysis (DEA). LCA is used to assess the potential environmental impacts of resource use and waste emissions throughout the life cycle of crop production processes [23]. It has been applied to integrated agro-ecosystem assessment, providing an important methodological contribution to environmental impact assessment [24]. However, defining research boundaries for methodological applicability is difficult, and the complexity of agricultural systems poses a challenge for assessment [20]. SFA has been used to estimate changes in crop and smallholder production efficiency [25]. The shortcomings of this method are the large errors in the assessment results when faced with complex correlations between input indicators [26]. There are also studies that combine EF and DEA to measure eco-efficiency [21], but the EF approach does not cover a comprehensive range of accounts, such as the lack of estimation of underground resources, which may underestimate the true carrying capacity [27]. DEA is a nonparametric relative probability analysis method. Scholars have gradually improved the model based on research needs [28][29][30][31], such as research based on zero-sum game theory to construct the ZSG-DEA model, which overcomes the shortcomings of evaluating indicator systems that need to be weighted to address the issue of water-energy-food efficiency relationships. It is the most widely used research method because it is less restrictive in data handling [32].
The second aspect focuses on regional heterogeneity. Most studies are at the macronational and micro-city levels, and fewer are at the catchment scale. There are studies that compare agricultural performance between countries [33]. There are also studies that examine the spatial and temporal variability of agricultural sustainability in a given region [34,35]. Some studies have used spatial spillovers and agglomeration effects to analyze regional heterogeneity in agricultural eco-efficiency [36]. Others have used Moran's I and the Local Indicators of Spatial Association (LISA) index to analyze the spatial and temporal patterns [13]. Some studies have analyzed the convergence of spatial differences in agricultural eco-efficiency and concluded that the efficiency values in the study area do not exhibit absolute α-convergence and absolute β-convergence characteristics [37], but that geographically adjacent regions influence the surrounding areas through efficiency spillovers. Besides analyzing agricultural eco-efficiency time series evolution, spatial distribution differences, and trends, social network analysis methods are often used to analyze the structural and interactive nature of different spatial units [38,39]. Based on current cutting-edge research measuring agroecological efficiency dynamics, the spatial correlation of interprovincial agroecological efficiency in China was further investigated by Chen et al. [39]. Differences in industrial structure, economic development, spatial proximity, urbanization, and transport development in different provinces influence the spatial network formed by the level of green agricultural development.
The third aspect focuses on the analysis of factors influencing. It has been argued that, beyond a certain level, increases in agricultural resource inputs are no longer accompanied by increases in eco-efficiency [16]. Considering the renewable element of each input, substituting organic and renewable materials for conventional crops improves the sustainability of the system, albeit at reduced economic profitability [40]. It was also found that the use of fertilizers is a serious constraint to sustainable agricultural development, although technological progress has been made in recent years in terms of agricultural yields, energy use, and the treatment of pollutants [30]. The level of socio-economic development also has a significant impact on the green eco-efficiency of agriculture. Gross regional product, industrial structure, and urbanization-which can mobilize the transfer of human, material, and financial resources and information technology within a catchment area-affect agricultural efficiency through economies of scale and structural effects [17,31,38,41]. Natural resource endowment and crop acreage share have a significant positive effect on agricultural efficiency [42,43].

SBM-3E Model for Agricultural Ecological Efficiency
The Super-SBM model is one of the extension methods of DEA. Tone improved it to effectively solve the relaxation problem of input-output variables [44] and considered environmental constraints to include unexpected outputs in the model estimation. However, traditional DEA may result in efficiency values greater than 1 when evaluating effective or weakly effective decision units, resulting in multiple decision units exhibiting a fully efficient state. The Super-SBM model can further compare effective decision units to achieve effective ranking, thereby correcting potential efficiency bias in traditional DEA model estimation. The 3E (Energy-Environment-Economy) system represents a dynamic and complex whole with a unified functional structure formed by the coupling of energy, environment, and economy. Introducing 3E into the efficiency measurement model of green water resource utilization under environmental constraints can dynamically reflect the efficiency state that efficient energy utilization can still protect the water ecological environment under reasonable economic relations [45]. The basic idea is to treat each city in the HRB as a decision-making unit, each of which includes energy subsystem elements, environmental subsystem elements, and economic subsystem elements. The properties of the elements are divided into input, expected output, and unexpected output. Assuming each city uses N inputs x = (x 1 , . . . x n . . . x N ) ∈ R + N , and produces M "good outputs" y = (y 1 , . . . y m . . . y M ) ∈ R + M , and Q "bad outputs" z = z 1 , . . . z q . . . z Q ∈ R + Q . Based on this, this article constructs an SBM-3E model that considers unexpected outputs and the system elements of the "energy-environment-economy" to measure agricultural eco-efficiency in the HRB. The specific formula is as follows: In Formula (1), → S is the effective value of the decision-making unit DMU, and the higher the value, the higher the level of agricultural ecological efficiency; the input, expected output, and non-expected output vectors of each city in the HRB are respectively x o t , y o t , z o t . Among them, o represents the administrative units involved in the watershed; t represents the year; a, b, and c respectively represent the energy subsystem elements, environmental subsystem elements, and economic subsystem elements in the 3E system; The positive vector of expected output expansion, non expected output, and input compression is (g x , g y , g z ); S x n , S y m , S z q is the relaxation vector of the nth factor input, the m-th expected output, and the q-th non-expected output; ω t o is the weight of the cross-sectional observations.

Determination of Spatial Correlation of Agricultural Ecological Efficiency: Modified Gravity Model
The gravity model depicts the radiation capacity of the central area and the surrounding area by measuring the strength of regional connections and reflects the acceptance of the surrounding area by the radiation capacity, so it is widely used in the study of distance attenuation effects and spatial interaction [38]. This article constructs a correction force model based on existing research to examine the spatial correlation of agricultural ecoefficiency among various administrative units within the watershed. The specific formula is as follows: In the equation, V ij represents the gravitational relationship between city i and city j in the HRB; α ij represents the gravitational coefficient, which is the contribution rate of city i in the agricultural eco-efficiency correlation between city i and j; U represents the agricultural eco-efficiency value considering the impact of the three subsystems of energy, environment, and economy; G is the Gross Domestic Product of the region, representing the level of local economic development, and P is the total population at the end of the year; the product of U, G, P represents the "quality" of agricultural eco-efficiency in the HRB; the value of attenuation parameter b is 2 [46]. This article uses Matlab R2022a software to calculate Equation (2) and obtains a 17 × 17 gravitational matrix Wij. In order to facilitate the analysis of the spatial characteristics of agricultural eco-efficiency in the HRB, the spatial correlation matrix was transformed into a binary matrix to determine the spatial correlation relationship of agricultural ecoefficiency between cities. The gravity matrix takes the average correlation strength of each administrative unit every year as the threshold. If the threshold is greater than or equal to 1, it indicates that there is a spatial correlation between agricultural eco-efficiency in the HRB. If it is less than the threshold, it is marked as 0, indicating that there is no spatial correlation between the two watersheds.

Social Network Analysis Methods
The essence of Social Network Analysis (SNA) is to treat "relationships" as statistical units, use matrix methods and mathematical models to process relationships, and examine the impact of social background factors such as the nature and content of relationships on behavioral subjects. This paper analyzes the agricultural eco-efficiency of the HRB from two aspects: the whole network and the egocentric network. The network density reflects the degree of closeness of administrative units within the basin in the related network structure, and the larger the value, the closer the connection between the two; The network efficiency reflects the stability of the connection between two administrative units in the network structure within the watershed. A low network efficiency value indicates that the two are more likely to promote factor flow through the spatial correlation network of agricultural ecological efficiency, reducing the comparative advantage between cities; the degree of network hierarchy reflects the asymmetric order of the network, and the higher the degree, the more obvious the hierarchical distinction between members; the characteristics of an egocentric network include degree centrality, betweenness centrality, and closeness centrality. In an individual network, degree centrality reflects the dominant position of a node in the entire network. The higher the degree of a node, the more individuals it is associated with, and the more individuals it represents in the center of the network; The intermediate centrality reflects the degree of separation between a node and other points in the network, indicating the degree to which a point becomes an "intermediary" among other points in the structure; the closeness centrality reflects the centrality of the distance between nodes in a network. The shorter the total distance, the higher the centrality of the network. The specific calculation formula is shown in Table 1.

Data Source and Explanation
This article analyzes the energy, environment, and socio-economic data of 17 cities in the HRB from 2010 to 2020. In the process of measuring agricultural ecological efficiency, land, labor, water resources, energy, machinery, fertilizers, agricultural films, and pesticides are selected as input factors; economic output is the expected output; pollution emissions and carbon emissions are unexpected outputs [19], as detailed in Table 2. Based on the summary of existing research and taking into account the impact of the "energy-environment-economy" subsystem on the spatial network of agricultural ecological efficiency, this article selects the difference matrix between the proportion of rice planting area, wheat planting area, corn planting area, industrial water use, agricultural water use, total water use, annual precipitation, water resources, and industrial structure between cities i and j in the HRB as indicators to characterize the planting structure. The impact of water use structure and water resource endowment on the spatial network of agricultural eco-efficiency is detailed in Table 3

Indicators Formula Definition
Whole network Density m is the actual number of relationships that exist in the network; n is the number of administrative units in the watershed. Efficiency Q is the number of redundant connections in the network. Hierarchy P is the number of units of symmetric nodes.
Egocentric network This equation represents the spatial correlation between i and j, if x ij = 1, there is a relationship, otherwise, it is 0.
Betweenness centrality is the number of shortest paths passing through i between administrative units j and k; l ik is the number of shortest paths between i and k.

Closeness centrality
z ij z ij is the shortcut distance between administrative units at two nodes. Total carbon emissions from fertilizers, pesticides, agricultural film, agricultural diesel, agricultural irrigation, and agricultural sowing 10 4 t Table 3. Driving factors of spatial correlation network for agricultural eco-efficiency in the HRB. Industrial structure Difference matrix of the proportion of total agricultural output value to regional GDP

Temporal and Spatial Analysis of Agricultural Eco-Efficiency in the HRB
Overall, as shown in Figure 1, the agricultural eco-efficiency value in the HRB shows a decreasing trend from 2010 to 2020. Specifically, from 2010 to 2012, the agricultural eco-efficiency value in the HRB was at a relatively high level, with an average efficiency value of about 0.98; the fluctuation of agricultural eco-efficiency in the HRB decreased from 2013 to 2020, with an average efficiency value of approximately 0.79. Among them, cities in the upper reaches of the HRB have shown a trend of increasing efficiency values, such as Ankang City, Baoji City, Shangluo City, and Wuhan City, which has a higher level of economic development in the lower reaches. There is a general trend of declining agricultural efficiency levels in other cities, especially Suizhou City, Tianmen City, and Xiantao City. Analyzing the reasons for the decline in agricultural eco-efficiency level from the perspective of input-output relaxation variables, it may be due to production congestion caused by excessive input factors, which leads to a decrease in output, i.e., the factor crowding phenomenon, making production factors unable to be fully and effectively utilized [15,47]. The obvious redundancy of diesel, pesticide, and agricultural film input in these areas indicates that the input of agricultural means of production is not fully utilized, which leads to an increase in agricultural non-point source pollution and carbon emissions, thus worsening agricultural ecological efficiency. From the perspective of the watershed, the spatial distribution of agricultural ec efficiency in the HRB is as follows: upstream > middle reaches > downstream (Figure The average efficiency in the upstream, middle, and downstream areas is 12.15, 9.40, a 6.67, respectively. Among them, from the perspective of input-output factor redundanc the reason for the lowest agricultural eco-efficiency value in downstream cities is an lyzed. Tianmen City, Xiantao City, and Xiaogan City have a high degree of redundan in energy input. Insufficient utilization of diesel can lead to energy waste and enviro mental pollution, which create dual pressure on the local economy and environme Since 2016, the state has actively implemented crop seed subsidies, direct subsidies f grain farmers, and comprehensive agricultural subsidies (called "three subsidies") f farmers, which mobilized production enthusiasm and eased economic pressure [4 However, there is serious spatial differentiation of agricultural eco-efficiency in the HR with generally high efficiency in the upper reaches and serious agricultural land, air, a carbon pollution problems in the lower reaches. Based on the analysis of the data in th study, it appears that cities in the upper HRB use fewer inputs of agricultural producti materials, such as agricultural films, pesticides, and mechanical power. This may be d to the rugged terrain in the upper reaches and the different grain cultivation structu between the middle and lower reaches, with a higher proportion of corn and a lower pr portion of rice in the upper reaches of the HRB. At the same time, the large number laborers employed in the cities also directly leads to a decrease in agricultural efficien [49]. And the downstream cities, such as Suizhou, Jingmen, Tianmen, and Xiantao, ha not yet undergone any fundamental changes in their highly resource-intensive agricu tural operations, and there is a lack of green production and low-carbon technologi Therefore, in 2018, the country launched the Han River Ecological Economic Belt Dev opment Plan, which aims to promote the high-quality development of the ecological ec nomic belt in the middle and lower reaches. From the perspective of the watershed, the spatial distribution of agricultural ecoefficiency in the HRB is as follows: upstream > middle reaches > downstream ( Figure 2). The average efficiency in the upstream, middle, and downstream areas is 12.15, 9.40, and 6.67, respectively. Among them, from the perspective of input-output factor redundancy, the reason for the lowest agricultural eco-efficiency value in downstream cities is analyzed. Tianmen City, Xiantao City, and Xiaogan City have a high degree of redundancy in energy input. Insufficient utilization of diesel can lead to energy waste and environmental pollution, which create dual pressure on the local economy and environment. Since 2016, the state has actively implemented crop seed subsidies, direct subsidies for grain farmers, and comprehensive agricultural subsidies (called "three subsidies") for farmers, which mobilized production enthusiasm and eased economic pressure [48]. However, there is serious spatial differentiation of agricultural eco-efficiency in the HRB, with generally high efficiency in the upper reaches and serious agricultural land, air, and carbon pollution problems in the lower reaches. Based on the analysis of the data in this study, it appears that cities in the upper HRB use fewer inputs of agricultural production materials, such as agricultural films, pesticides, and mechanical power. This may be due to the rugged terrain in the upper reaches and the different grain cultivation structure between the middle and lower reaches, with a higher proportion of corn and a lower proportion of rice in the upper reaches of the HRB. At the same time, the large number of laborers employed in the cities also directly leads to a decrease in agricultural efficiency [49]. And the downstream cities, such as Suizhou, Jingmen, Tianmen, and Xiantao, have not yet undergone any fundamental changes in their highly resource-intensive agricultural operations, and there is a lack of green production and low-carbon technologies. Therefore, in 2018, the country launched the Han River Ecological Economic Belt Development Plan, which aims to promote the high-quality development of the ecological economic belt in the middle and lower reaches. In summary, there is heterogeneity in the development path of agricultural eco-efficiency values among individuals in the HRB from 2010 to 2020, showing a decreasing trend overall with a spatial distribution of differentiation in the upper, middle, and lower reaches. The current situation of large internal disparities in the level of agricultural ecoefficiency in the HRB requires policy makers to have a vision of promoting integrated regional development and coordinating green agricultural development according to the resource and environmental carrying capacity and agricultural production conditions of each city [23]. Therefore, to find ways to improve agricultural eco-efficiency as a whole and on an individual basis, we need to further focus on the information about each city's agricultural eco-efficiency in spatial interactions.

Whole Network Analysis
The spatial relationship matrix of agricultural eco-efficiency in the Hanjiang River basin is constructed through the modified Gravity model, and the evolving structure of the network relationship of agricultural eco-efficiency is characterized by the indicators of the social network analysis method (Figures 3 and 4). The overall network structure is able to express rules and resources, which in the spatial network of agricultural eco-efficiency in the HRB refers to the rules used by urban actors to reproduce social relations in a longer space and time period and the resource dominance of cities in authoritative positions. The mean value of the spatial density of agricultural eco-efficiency in the HRB from 2010 to 2020 is 0.17, and the network hierarchy increases from 0.34 to 0.48, which indicates that the degree of closeness among administrative units in the basin is low and does not form a complex network, making it difficult to bring inter-individual reciprocity into play, and the structural role of the network has less impact on individual cities. The average efficiency of the agricultural eco-efficiency spatial network in the HRB from 2010 to 2020 was 0.89, indicating that individuals within the basin have high stability in connecting to the network structure. This means that the mobility of factors between the two cities is poor, making it difficult to promote factor flow through the agricultural eco-efficiency spatial correlation network and reducing the comparative advantage between cities [32]. This requires synergistic basin-wide policies. To promote overall efficiency, cities must interact to facilitate the flow of capital, labor, information technology, and other factors. In summary, there is heterogeneity in the development path of agricultural ecoefficiency values among individuals in the HRB from 2010 to 2020, showing a decreasing trend overall with a spatial distribution of differentiation in the upper, middle, and lower reaches. The current situation of large internal disparities in the level of agricultural ecoefficiency in the HRB requires policy makers to have a vision of promoting integrated regional development and coordinating green agricultural development according to the resource and environmental carrying capacity and agricultural production conditions of each city [23]. Therefore, to find ways to improve agricultural eco-efficiency as a whole and on an individual basis, we need to further focus on the information about each city's agricultural eco-efficiency in spatial interactions.

Whole Network Analysis
The spatial relationship matrix of agricultural eco-efficiency in the Hanjiang River basin is constructed through the modified Gravity model, and the evolving structure of the network relationship of agricultural eco-efficiency is characterized by the indicators of the social network analysis method (Figures 3 and 4). The overall network structure is able to express rules and resources, which in the spatial network of agricultural eco-efficiency in the HRB refers to the rules used by urban actors to reproduce social relations in a longer space and time period and the resource dominance of cities in authoritative positions. The mean value of the spatial density of agricultural eco-efficiency in the HRB from 2010 to 2020 is 0.17, and the network hierarchy increases from 0.34 to 0.48, which indicates that the degree of closeness among administrative units in the basin is low and does not form a complex network, making it difficult to bring inter-individual reciprocity into play, and the structural role of the network has less impact on individual cities. The average efficiency of the agricultural eco-efficiency spatial network in the HRB from 2010 to 2020 was 0.89, indicating that individuals within the basin have high stability in connecting to the network structure. This means that the mobility of factors between the two cities is poor, making it difficult to promote factor flow through the agricultural eco-efficiency spatial correlation network and reducing the comparative advantage between cities [32].
This requires synergistic basin-wide policies. To promote overall efficiency, cities must interact to facilitate the flow of capital, labor, information technology, and other factors.

Egocentric Network Analysis
The Egocentric network index can reveal the spillover absorption ability, trading ability, and control ability of 17 cities in the HRB in the spatial relationship of agricultural ecological efficiency. This paper selects three specific indicators, namely degree centrality, intermediate centrality, and closeness centrality, for evolutionary analysis.
1. Degree centrality. According to Figure 5, it can be found that Baoji City ranked high in terms of degree between 2010 and 2020, with a value of 37.5. Baoji City is located in the upper reaches of the HRB and belongs to Shaanxi Province. Generally speaking, as the core city where the agricultural eco-efficiency generates the spatial correlation of factors, the mobility of agricultural means of production, technology, capital, and other factors makes the ecological efficiency of the region play a positive role, and through spatial spillover to neighboring provinces, it improves the degree of output, thus obtaining a higher degree of centrality. However, the overall ranking of the lower reaches of the Han River is relatively low, and its efficiency and spatial trading ability are poor. This may be due to the geographical edge of downstream areas and the high level of industrial and economic development, resulting in a significant difference in agricultural eco-efficiency values from surrounding provinces and less spatial correlation behavior.

Egocentric Network Analysis
The Egocentric network index can reveal the spillover absorption ability, trading abi ity, and control ability of 17 cities in the HRB in the spatial relationship of agricultura ecological efficiency. This paper selects three specific indicators, namely degree centrality intermediate centrality, and closeness centrality, for evolutionary analysis.
1. Degree centrality. According to Figure 5, it can be found that Baoji City ranked hig in terms of degree between 2010 and 2020, with a value of 37.5. Baoji City is locate in the upper reaches of the HRB and belongs to Shaanxi Province. Generally speak ing, as the core city where the agricultural eco-efficiency generates the spatial corre lation of factors, the mobility of agricultural means of production, technology, cap tal, and other factors makes the ecological efficiency of the region play a positive rol and through spatial spillover to neighboring provinces, it improves the degree o output, thus obtaining a higher degree of centrality. However, the overall ranking o the lower reaches of the Han River is relatively low, and its efficiency and spati trading ability are poor. This may be due to the geographical edge of downstream areas and the high level of industrial and economic development, resulting in a sig nificant difference in agricultural eco-efficiency values from surrounding province and less spatial correlation behavior.

Egocentric Network Analysis
The Egocentric network index can reveal the spillover absorption ability, trading ability, and control ability of 17 cities in the HRB in the spatial relationship of agricultural ecological efficiency. This paper selects three specific indicators, namely degree centrality, intermediate centrality, and closeness centrality, for evolutionary analysis.

1.
Degree centrality. According to Figure 5, it can be found that Baoji City ranked high in terms of degree between 2010 and 2020, with a value of 37.5. Baoji City is located in the upper reaches of the HRB and belongs to Shaanxi Province. Generally speaking, as the core city where the agricultural eco-efficiency generates the spatial correlation of factors, the mobility of agricultural means of production, technology, capital, and other factors makes the ecological efficiency of the region play a positive role, and through spatial spillover to neighboring provinces, it improves the degree of output, thus obtaining a higher degree of centrality. However, the overall ranking of the lower reaches of the Han River is relatively low, and its efficiency and spatial trading ability are poor. This may be due to the geographical edge of downstream areas and the high level of industrial and economic development, resulting in a significant difference in agricultural eco-efficiency values from surrounding provinces and less spatial correlation behavior. 2.
Betweenness centrality. The average betweenness centrality of the spatial relationship between agricultural eco-efficiency in the HRB is 36.13, indicating that the factor exchange capacity of the entire basin is in a low state; that is, each administrative unit has weak dominance over the direction of efficiency flow in other cities. At the same time, the correlation relationship within the basin shows regional differences. Baoji City, Ankang City, and Xiangyang City control the communication path of spatial correlation of agricultural ecological efficiency and are important transfer stations for spatial correlation of agricultural eco-efficiency in the HRB; the agricultural ecoefficiency measured by agricultural economic output and pollution as output factors reflects the stronger influence of provinces with faster economic development in the HRB on agricultural eco-efficiency in the network. At the same time, they promote their interaction ability with other regions through their dominance of resources and production factors, presenting the role of an "information bridge" in space. As a central city in the HRB, Xiangyang City connects the eastern and western regions of the basin, becoming a hub for the exchange and communication of economic, energy, technological, and other elements throughout the entire basin and playing a mediating role as a "middleman" in the agricultural eco-efficiency correlation network.

3.
The closeness centrality of some cities in the middle and lower reaches of the agricultural ecology in the HRB from 2010 to 2020 was 0, indicating that some cities in the agricultural eco-efficiency correlation network of the HRB can directly establish connections with other collaborating entities without intermediary provinces. The action distance of Luoyang City, Shennongjia Forest District, Wuhan City, Qianjiang City, and Xiaogan City is 0, which means that there is no spatial effect of agricultural eco-efficiency in these administrative regions. This means that the positive effects generated by high-efficiency areas are difficult to flow into the surrounding areas with low efficiency through all factors; meanwhile, the negative effects caused by low efficiency are difficult to flow into areas with higher efficiency through absorption relationships. 2. Betweenness centrality. The average betweenness centrality of the spatial relationship between agricultural eco-efficiency in the HRB is 36.13, indicating that the factor exchange capacity of the entire basin is in a low state; that is, each administrative unit has weak dominance over the direction of efficiency flow in other cities. At the same time, the correlation relationship within the basin shows regional differences. Baoj City, Ankang City, and Xiangyang City control the communication path of spatia correlation of agricultural ecological efficiency and are important transfer stations for spatial correlation of agricultural eco-efficiency in the HRB; the agricultural eco-efficiency measured by agricultural economic output and pollution as output factors reflects the stronger influence of provinces with faster economic development in the HRB on agricultural eco-efficiency in the network. At the same time, they promote their interaction ability with other regions through their dominance of resources and production factors, presenting the role of an "information bridge" in space. As a central city in the HRB, Xiangyang City connects the eastern and western regions of the basin, becoming a hub for the exchange and communication of economic, energy

Group Analysis
To further explore the stability of agricultural eco-efficiency in the spatial correlation network structure of the HRB, this article uses non-overlapping clustering analysis and the iterative correlation convergence method (CONCOR) in social network analysis methods to calculate (Table 4) and characterize the stability of the local structure of the correlation network by the results of the condensed subgroups. Condensed subgroups refer to subsets within a network structure that have certain characteristics that are homogeneous, closely related, or have positive relationships. In the key network of agricultural eco-efficiency in the HRB, subgroups are clustered subsets of several provinces with similar governance levels. The condensed subgroup analysis reflects the number of condensed subgroups in each block and the provinces involved in each condensed subgroup. The network is analyzed based on two-phased structures generated from 2010 to 2013 and 2014 to 2020. From 2010 to 2013, two identical condensed subgroups were generated, subgroup I being Baoji City, Hanzhong City, Jingmen City, Nanyang City, Sanmenxia City, Shangluo City, Shennongjia Forest District, Suizhou City, Xiangyang City, and subgroup II being Qianjiang City, Shiyan City, Tianmen City, Wuhan City, Xiantao City, Xiaogan City, and Luoyang City. This indicates that the spatial correlation of agricultural eco-efficiency in the HRB formed two homogeneous relationship circles during this stage. On the one hand, the degree of relationship density between cities within the subgroup and other cities is similar, that is, their network positions are similar; on the other hand, the agricultural development level, energy consumption capacity, and pollutant discharge capacity of each administrative unit within the subgroup are similar in the agricultural eco-efficiency network of the HRB. From 2014 to 2020, there were changes in the number and structure of condensed subgroups. Ankang City, Jingmen City, Shennongjia Forest District, Suizhou City, and Xiangyang City withdrew from subgroup I, while the network locations of other cities remained unchanged. During this period, the two homogeneous relationship circles were significantly impacted, and the structure of the efficiency network shifted from a "flat" to a "pointed tower". This indicates that the balance of the agricultural eco-efficiency network structure in the HRB has weakened, the interaction ability and correlation between provinces have deteriorated, and the position of the "core edge" structure has gradually been strengthened. Currently, there is no trend toward regionally coordinated development.

Driving Factors of Spatial Correlation Network for Agricultural Eco-Efficiency in the HRB
This article uses the Quadratic Assignment Procedure (QAP) regression method to analyze the driving factors of the spatial correlation network of agricultural ecological efficiency. This method first needs to compare the values of each element in the matrix to determine the correlation coefficient and perform a non-parametric test on the correlation coefficient. Furthermore, based on the significance judgment, select the variable indicators that will participate in the next step of inter-matrix regression. Finally, perform a standardized multiple regression analysis on the independent variable matrix and the dependent variable matrix. When discussing the influencing factors of the correlation network, the effectiveness of parameter estimators of elements requires that independent variables be independent of each other, avoiding problems such as "collinearity" and testing false correlations. Most scholars' regression analysis often focuses on the test of a single element, ignoring the synergistic effects of socio-economic, environmental impact, and technological factors, while the QAP method can identify driving forces with "relationship" data as the research object, Breaking through conventional statistical techniques (such as OLS), this method solves the problem of collinearity or false correlation testing that may be caused by multiple regression estimation through permutation matrix data.
QAP analysis can reveal the overall characteristics, individual centrality, and formation mechanism of the group structure of the spatial correlation network of agricultural eco-efficiency in the HRB and characterize the driving factors of homogeneous development or heterogeneity gaps within the basin. First, the study needs to conduct a collinearity test on the correlation driving factors of the spatial correlation network of agricultural eco-efficiency in the HRB from 2010 to 2020. See Table 5 for the collinearity test results of the driving factors of the agricultural eco-efficiency-related network structure in the HRB. Table 5 describes the Pearson correlation coefficient between the difference matrix of agricultural eco-efficiency between cities i and j in the HRB, and the nine independent variables of water resource endowment, water use structure, and planting structure. Generally, if the coefficient is less than 0.8, it is considered that there is no high correlation between the dependent variable and the independent variable, and the multicollinearity problem is avoided among the variables. Meanwhile, the correlation coefficients between variables are all greater than 0, and core explanatory variables such as rice, corn, and agricultural water use have passed the significance level test, indicating that the above variables have a correlation impact on the agricultural eco-efficiency correlation network. The QAP regression coefficient, indicating the driving factors of spatially correlated network structure in the agricultural ecological efficiency of the HRB, is 0.511 and statistically significant at the 1% level (see Table 6). The regression analysis results demonstrate a significant network correlation between rice, maize, agricultural water usage, total water usage, and agricultural ecological efficiency. Specifically, at a 95% confidence level, the area under rice cultivation inhibits the development of agricultural ecological efficiency in the HRB. Similar conclusions were drawn by Deng in his analysis of the influencing factors of inter-provincial agricultural ecological efficiency in China [50], suggesting that the negative impact may be attributed to a higher proportion of grain crop cultivation area compared with the total sown area and the excessive use of nitrogen fertilizer. On the other hand, at a 99% confidence level, an increase in maize cultivation area significantly promotes agricultural ecological efficiency in the HRB, with a 1% increase in maize cultivation area corresponding to a 0.49% increase in ecological efficiency. Therefore, it can be inferred that rational adjustments to crop planting structure, balancing the types and scales of cultivation, starting from emission reduction goals, may contribute to improving agricultural ecological efficiency [51,52]. Additionally, in terms of water usage structure, total water usage significantly enhances agricultural ecological efficiency in the HRB at a 99% confidence level, with a 1% increase in total water usage corresponding to a 0.43% improvement in ecological efficiency. This indicates a synergistic development stage between basin-wide water usage and ecological efficiency. However, agricultural water usage hinders ecological efficiency at a 90% confidence level, suggesting that the efficiency of agricultural water usage needs to be improved through irrigation techniques and water-saving devices specific to agricultural purposes [53] to alleviate the contradiction between agricultural water usage and ecological efficiency in the HRB. Table 6. QAP analysis of the driving factors of spatial correlation network for agricultural ecoefficiency in HRB.

Conclusions and Policy Implications
From the above analysis, it can be concluded that: • In general, there was a decreasing trend in the agricultural eco-efficiency values in the HRB from 2010 to 2020. The average efficiency value from 2010 to 2012 was about 0.98, which was at a high level; and from 2013 to 2020 was about 0.79, which was fluctuating and decreasing. The spatial distribution of efficiency is: upstream > middlestream > downstream, with average efficiency values of 12.15, 9.40, and 6.67, respectively.

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The spatial density of agricultural eco-efficiency in the HRB is 0.17, and the network efficiency is 0.89, indicating that the overall interconnection among the units in the basin exists, but the degree is low; the spatial distribution is uneven and highly unstable. The structural role of the network has a small impact on individuals in each city because the subjects in the basin have not formed a complex network and cannot play reciprocity among individuals.

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The egocentric network index shows the individual capacity of agricultural ecoefficiency network space. Baoji City ranks high in degree centrality with a value of 37.5, and the city has strong agroecological efficiency spatial transactivity and high spillover absorption capacity, while lower Han River urban efficiency spatial transactivity is poor. The mean value of intermediate centrality is 36.13. Among them, Baoji, Ankang, and Xiangyang cities rank high in intermediate centrality, indicating that they have the ability to dominate the flow direction of agricultural eco-efficiency in other provinces and cities.

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In terms of the influencing factors, it is concluded that rice area and agricultural water consumption have a negative influence on the spatial correlation network of agricultural eco-efficiency in the HRB; corn and total water consumption have a positive influence on the spatial correlation network of agricultural eco-efficiency in the HRB. • First, there are currently no laws and policies to address carbon sequestration through agricultural emission reduction [54]. Therefore, the government needs to fill the policy gap. Second, the study concludes that areas with high agricultural eco-efficiency in the Han River basin can play a leading role. Baoji, Ankang, and Xiangyang are key points in the Han River basin where the government can guide the flow of factors between provinces and cities through favorable policies. In addition, this paper suggests that in order to increase economic income, improve water use efficiency, reduce the negative impact of food production on the environment, and ensure the basic needs of food production, the HRB should reduce the area of rice cultivation and increase the area of corn and other economic crops [55,56]. Finally, in terms of water use structure, a water price increase can effectively reduce agricultural irrigation water. The government can regulate the total amount of water used in agriculture in the HRB mainly through water pricing policies, supplemented by agricultural subsidy policies [57,58].