Analysis of the spatial association network of agricultural water use efficiency and its driving factors in China

Regional imbalance exist in agricultural water use efficiency across China. Promoting inter-provincial collaboration to improve the overall efficiency level is crucial for ensuring food security and resource equity. While existing research often focuses more on efficiency improvements within single geographical units, studies on spatial spillover effects and the dynamic evolution of networks are still limited. Therefore, this study measures agricultural water use efficiency in Chinese provinces from 2005 to 2023 based on the SE-SBM model, constructs a spatial association network and applies social network analysis (SNA) and the stochastic actor-oriented model (SAOM) to examine its structural characteristics and driving factors. The results show that: (1) The spatial association of agricultural water use efficiency presents a complex network structure. Provinces like Guangdong, Shanghai and Fujian plays important radiating and bridging roles in the network. Future policy design should place emphasis on strengthening their efficiency spillover effects. (2) As connections between provinces become closer, efficiency is gradually breaking through geographical limitations to form new spatial spillovers. Cross-regional water resource management strategies should take this emerging trend into account. (3) Both network structural effects and exogenous factors significantly drive the evolution of the spatial association network, highlighting the need for targeted policies and inter-provincial cooperation. By exploring the inter-provincial association of agricultural water use efficiency from a network perspective, this study provides critical insights for cross-regional cooperation in agricultural water resource management.

1 Introduction

Water scarcity is one of the most pressing global challenges, threatening to sustainable development, economic growth, and ecological stability. Agriculture is the largest global water-consuming sector, accounting for 80%–90% of total freshwater consumption (Cao et al., 2020). Therefore, improving agricultural water use efficiency is essential to ensuring global food and water security. As a major agricultural country in the world, China has faced severe shortages of agricultural water resources. Water resource per capita in China is far below the global average, while agricultural water consumption constitutes over 60% of national water use (Tian et al., 2023; Kuai et al., 2024). Moreover, climate change, frequent natural disasters, and diffuse agricultural pollution from overuse of fertilizers, pesticides, and plastic mulch have further aggravated the imbalance between water resources and food production (Omer et al., 2020; Dilanchiev et al., 2024; Deng et al., 2025). In this case, Optimizing the use of agricultural water resources has become an important approach to alleviate water scarcity and ensure food security in China and globally (Alharbi et al., 2024).

Numerous researches have explored various approaches to improving agricultural water use efficiency, including upgrading irrigation infrastructure, promoting water-saving irrigation technologies, facilitating water resource recycling and reuse, improving vegetation quality, optimizing basin-level water resource allocation systems, and implementing water rights trading mechanisms (Berbela et al., 2018; Wang et al., 2019; Hatamkhani et al., 2022a; Yan et al., 2024; Naderi and Moridi, 2025; Lu et al., 2025). However, a large number of studies have mainly focused on the resource endowments and functional attributes of spatial units themselves, while research on the external effects generated by the interactions of economic agents is still relatively limited. In fact, in today’s era of economic globalization and increasing regional integration, thanks to the rapid development of transportation and communication technologies, inter-regional connections have become increasingly close, forming a spatial pattern of mutual interaction and influence among regions (Cai et al., 2022; Liu et al., 2024). This means that the corresponding research should not remain focused solely on a single subject but should be extended to the network space (Lüthi et al., 2018).

Moreover, Existing studies suggest that water use efficiency in China exhibits significant spillover effects (Song et al., 2022; Sheng and Qiu, 2022). This means that one region’s water use efficiency can influence that of other regions through efficiency spillovers (Li and Long, 2019; Wang et al., 2019). The efficiency spillover among regions essentially belongs to a technological spillover and is represented by the spatial association of efficiency (Zhi et al., 2022a; Cheng et al., 2024). Scholars measured the strength of spatial association between different regions and constructed a spatial association network of efficiency. For example, Yang et al. (2022) developed a modified gravity model to investigate the strength of spatial association of water use efficiency between 2008 and 2010, while Zhi et al. (2022b) constructed a spatial correlation network based on the vector autoregression (VAR) and highlighted the necessity of managing water resources from a network perspective.

With the deepening of research, the structural characteristics of efficiency spatial association networks and their evolutionary mechanisms have begun to be examined. Recent studies extensively adopted social network analysis (SNA) to examine the spatial structures and connection patterns of regional efficiency networks (Yang et al., 2023; Cheng et al., 2024; Bai and Lin, 2024). For example, Han et al. (2024) employed social network analysis (SNA) to investigate the structural characteristics of the network of intensive water resource use in the Yellow River Basin, finding that spatial linkages among provinces have gradually strengthened alongside the implementation of basin-wide water-saving policies. Zhao et al. (2025) analyzed the spatial association network structure of urban water resource green efficiency in the Yellow River Basin, found a core-periphery structure and emphasized the importance of inter-regional cooperation for enhancing the overall water use efficiency. In terms of the dynamic evolution mechanisms of spatial association network, scholars employed the Quadratic Assignment Procedure (QAP) to analyze the effect of individual attribute factors on the strength of network relationships (Han et al., 2024; Zhou and Wen, 2024; Zhang et al., 2025). Factors such as the level of economic development, resource endowments, and geographical distance have been widely confirmed to be the main determinants influencing network evolution.

In summary, although existing studies emphasized the necessity of agricultural water resources management from a network perspective, there are still two aspects need to be improved. First, measurement of water use efficiency has not taken the role of green water into account. Green water plays a crucial role in irrigated agriculture (Cao et al., 2017). In China, the green water footprint accounts for 65.6% of the total agricultural water footprint, so it is necessary to consider the influence of green water when measuring agricultural water resource efficiency (Geng et al., 2019). Second, research focusing on the dynamic evolution mechanisms of spatial association network of agricultural water use efficiency is still limited. Existing studies suggest that the mechanisms of network evolution not only include the impact of traditional exogenous variables but also the endogenous structural effects (Wu et al., 2024). However, QAP only reflect the strength of relationships in the network and cannot reveal the interdependencies among nodes (Pan et al., 2022; Smith and Sarabi, 2022). The role of inter-regional collaboration patterns in network evolution is still insufficiently considered. To address this limitation, recent studies introduced temporal exponential random graph models (TERGM) and stochastic actor-oriented models (SAOM) to explore the role of structural factors in network evolution (Liu et al., 2024; Ma et al., 2025; Lu and Qin, 2025). Among these, SAOM provides a more robust framework for analyzing dynamic network changes. This method not only relaxes the independence assumptions of traditional econometric models, but also examines the impact of network structural factors and external factors on network evolution, and can analyze the dynamic changes in network structure across different time periods (Snijders, 2017). But its application in the study of water resource efficiency network evolution is still relatively limited.

Therefore, this study measures agricultural water resource efficiency using the SBM model, constructs a spatial association network of agricultural water use efficiency based on the modified gravity model, and analyzes the network structure using Social Network Analysis (SNA) methods. By exploring the efficiency spillover capacity and the capacity to receive efficiency spillovers of key provinces, the study focuses on their roles in agricultural water resource management. Furthermore, the Stochastic Actor-Oriented Model (SAOM) is introduced to explore the driving factors of network evolution and investigate the potential paths for improving agricultural water resource efficiency.

2 Materials and methods

This study explores the structural characteristics and driving factors of the spatial association network of agricultural water resource efficiency using the following methods. First, the Agricultural Water Resource Efficiency of each province in China is measured based on the SBM model. Second, the spatial association intensity of efficiency among provinces is measured based on the Modified Gravity Model, and a network is constructed accordingly. Third, the overall network structural characteristics and individual characteristics are analyzed using the Social Network Analysis (SNA) method. Finally, the network evolution mechanism is analyzed by introducing the Stochastic Actor-Oriented Model (SAOM). The research framework of this study is illustrated in the Figure 1.

Figure 1

Figure 1. Research framework of this paper.

2.1 Super-efficiency slack-based measure (SE-SBM) model

The SE-SBM model was used to estimate agricultural water use efficiency in China. Compared with the radial DEA model, it addresses the problem of input and output slack and compensates for the lack of comparative analysis among effective decision-making units. It is assumed there exist $\mathrm{w}$ decision-making units (DMU), each of which comprises $q_1$ inputs $x$, $q_2$ expected outputs $y$ and $q_3$ non-expected outputs $b$, let $X=\left[x_1,x_2,\cdots ,x_n\right]$, $Y=\left[y_1,y_2,\cdots ,y_n\right]$, $B=\left[b_1,b_2,\cdots ,b_n\right]$, and $X>0$, $Y>0$, $B>0$, then the production set can be expressed as: $P=\left\{\left(x,y,b\right)|x\ge \gamma X,y\ge \gamma Y,b\ge \gamma B\right\}$, where $\gamma$ is the weighting variable. The Equations 1, 2 are used to measure agricultural water use efficiency in China:

$\min eff=\frac{1+\frac{1}{q_1}{\displaystyle {\sum }_{i=1}^{q_1}}{s}_i^{-}/x_{ip}}{1-\frac{1}{q_2+q_3}\left({\displaystyle {\sum }_{m=1}^{q_2}}{s}_m^{+}/y_{mp}+{\displaystyle {\sum }_{r=1}^{q_3}}{s}_r^{z-}/z_{rp}\right)}(1)$

Limits:

$\begin{array}{c}{\displaystyle \sum _{j=1,j\ne p}^w}{x}_{ij}{\gamma }_j-s_i^{-}\le x_{ip}\\ {\displaystyle \sum _{j=1,j\ne p}^w}{y}_{mj}{\gamma }_j+s_m^{+}\ge y_{mp}\\ {\displaystyle \sum _{j=1,j\ne p}^w}{z}_{rj}{\gamma }_j-s_r^{z-}\le z_{rp}\\ 1-\frac{1}{q_2+q_3}\left({\displaystyle \sum _{m=1}^{q_2}}\frac{s_m^{+}}{y_{mp}}+{\displaystyle \sum _{r=1}^{q_3}}\frac{s_r^{z-}}{z_{rp}}\right)>0\\ \gamma ,s^{-},s^{+},s^{z-}\ge 0\\ i=1,2,\dots ,q_1\\ m=1,2,\dots ,q_2\\ r=1,2,\dots ,q_3\\ j=1,2,\dots ,w\left(j\ne p\right)\end{array}(2)$

where $eff$ denotes agricultural water use efficiency, $w$ symbolizes the number of provinces, $x_{ij}$ stands for the $\mathrm{i}$-th input of decision-making unit $\mathrm{j}$, $y_{mj}$ and $z_{rj}$ represent the $m$-th and $r$-th outputs of decision-making unit $\mathrm{j}$, $q_1,q_2,q_3$ represent the number of indicators corresponding to inputs, desirable outputs, and undesirable outputs, respectively. And $s^{-},s^{+},s^{z-}$ are defined as the slack variables associated with inputs, desirable outputs, and undesirable outputs, respectively.

2.2 Modified gravity model

Existing studies use VAR method and modified gravity model to construct the network. Since VAR model is unable to build yearly association matrices, this study uses the modified gravity model to construct the spatial association network year by year. The intensity of the association between provinces is defined as:

$s_{ij}=k_{ij}\frac{\sqrt[3]{E_i{G}_i{P}_i}\sqrt[3]{E_j{G}_j{P}_j}}{d_{ij}^2},\text{Where\hspace{0.17em}}{k}_{ij}=\frac{E_i}{E_i+E_j},d_{ij}=\frac{D_{ij}}{g_i-g_j}(3)$

where $s_{ij}$ denotes the intensity of the association between province $i$ and $j$, $k_{ij}$ denotes the empirical constant, $E,G,P$ respectively denote agricultural water use efficiency, GDP and population, $D_{ij}$ is the geographic distance from province $i$ to $j$, $g$ is GDP per capita.

According to the results of Equation 3, a Gravity Matrix can be obtained, with province $i$ defined as rows and province j defined as columns. Mean of each row reflects the average gravitational interaction between province $i$ and all other provinces in the matrix. When the gravity value between province $i$ and province j exceeds the average gravitational interaction value, province $i$ is considered to have a strong efficiency spillover effect on province j, and the linkage is assigned 1, while it below the mean is assigned a value of 0 (Bai et al., 2020).

2.3 Social network analysis (SNA)

2.3.1 Overall network characteristics

This study uses network density, hierarchy and efficiency to measure the characteristics of the overall network.

Network density is defined as Equation 4:

$Density=T/N\left(N-1\right)(4)$

where $Density$ is the network density, $T$ denotes the total number of existing export and import connections between provinces, and $N$ is defined as the total number of provinces.

Network hierarchy assesses asymmetrical reachability across nodes in a graph. Based on Equation 5, it can be calculated as:

$H=1-T/\max \left(T\right)(5)$

where $T$ denotes the number of symmetrically accessible node pairs, and $\max \left(T\right)$ denotes the maximum possible quantity of symmetrically accessible node pairs.

Network efficiency assesses the level of redundant lines within a graph. Based on Equation 6, it can be calculated as:

$E=1-Q/\max \left(Q\right)(6)$

where $Q$ denotes the number of redundant lines, and $\max \left(Q\right)$ denotes the maximum number of redundant lines.

2.3.2 Individual network characteristics

This study computes outdegree, betweenness and closeness centrality to characterize the individual network structure.

1. Outdegree centrality. To compare the changes in the degree centrality of different provinces across various periods, this study selects relative degree centrality for analysis. Equation 7 for Outdegree centrality is as follows:

${DC}_i=\frac{{\displaystyle {\sum }_j}{t}_{ij}}{N-1}(7)$

where ${DC}_i$ is relative outdegree centrality of province $i$, $t_{ij}$ is the total number of connections that spill over all remaining provinces within the network.

2. Betweenness centrality. It assesses the extent of control each province has over resources in the network. Equation 8 for Betweenness centrality is as follows:

${BC}_i=\frac{2}{\left(N-2\right)\left(N-1\right)}{\displaystyle \sum _{s\ne i\ne t}}{n}_{st}^i/g_{st}(8)$

where ${BC}_i$ is the betweenness centrality of province $i$, $n_{st}^i$ is the number of shortest paths from province $s$ to province $t$ that pass through province $i$, and $g_{st}$ is the total number of shortest paths connecting province $s$ and province $t$.

3. Closeness centrality. Based on Equation 9, it can be calculated as:

${CL}_i=\frac{{\displaystyle {\sum }_{j=1}^n}{\mathrm{d}}_{ij}}{N-1}(9)$

where ${\mathrm{d}}_{\text{ij}}$ is the shortcut distance between the province $\mathrm{i}$ and province $\mathrm{j}$.

2.3.3 Network community analysis

To partition network communities, the modularity index is calculated. Equation 10 for the modularity index is:

$\mathrm{Q}=\frac{1}{2m}{\displaystyle \sum _{ij}}\left[w_{ij}-\frac{s_i{s}_j}{2m}\right]\delta \left(v_i,v_j\right)(10)$

$Q$ represents the modularity index, which is measured by the expected difference between the proportion of edges connecting nodes within a community in the actual network and in a random network, and $s_i$ denotes the total trade flows associated with node $i$ in the network, $s_j$ denotes the total trade flows associated with node j in the network, $m$ is the total sum of all trade volume. $\delta \left(v_i,v_j\right)$ is defined as whether countries i and j belong to the same community in the vegetable trade network. If they belong to the same community, $\delta \left(v_i,v_j\right)$ = 1; otherwise, it is 0.

2.4 Stochastic actor-oriented model (SAOM)

2.4.1 Mechanism analysis

Existing research suggests that the evolution of network relationships are influenced by both exogenous and endogenous mechanisms (Wu et al., 2024). Among them, exogenous mechanisms refer to actors’ attribute selection preferences and external situational factors, while endogenous mechanisms mainly refer to the self-organizing effects of the network (Liu et al., 2024).

Exogenous mechanisms refer to the influence of node and edge attributes outside the internal relationships of the network on network evolution. This study divides them into attribute-related effects and spatial externalities. Network actor attributes include receiver effects, sender effects, and homophily effects (Robins et al., 2007), which refer to different network relationship structures formed due to differences in actor attribute characteristics. Specifically, in the spatial association network of agricultural water use efficiency of this study, receiver effects refer to the probability that provinces with certain specific attributes become recipients of agricultural water use efficiency, whereas sender effects refer to the probability that a certain type of province is more inclined to radiate efficiency outward (Pan et al., 2022). In addition, homophily effects refer to the likelihood of establishing efficiency spillover relationships among provinces with the same attributes (Cai et al., 2022). Spatial externalities refer to the impact of exogenous networks on efficiency-related spatial networks. This study uses a geographic distance matrix between provinces to explore the effect of spatial externalities on network evolution (Htwe et al., 2020). Generally, efficiency spillover effects exhibit spatial proximity. The farther the provinces are from each other, the higher the cost of efficiency interaction (Pan et al., 2022), making it difficult to establish efficiency spillover connections.

Endogenous mechanisms refer to the self-organizing effects of networks. Network relationships can undergo self-organizing processes, where existing connections influence the formation of other relationships, ultimately forming certain network patterns. This process is defined as the self-organizing effect of networks, including reciprocity effects, preferential attachment effects, and transitivity effects (Robins et al., 2007). This study examines the impact of reciprocity and transitivity effects on network evolution. Reciprocity effect refers to the bidirectional interactive relationships of efficiency spillovers among provinces (Lu and Qin, 2025). According to complex network theory, reciprocity helps enhance trust and stability among entities (Shi et al., 2024), thereby facilitating information dissemination and resource flow between provinces. Therefore, an increase in reciprocity within the network may promote the diffusion of efficiency. Transitivity effects include both transitive triples effect and 3-cycles effects. The transitive triples effect refers to the tendency of Province A to establish efficiency spillover links with Province B, while also forming efficiency spillover connections with B’s partner provinces. It is used to measure the likelihood of provinces with shared partners establishing efficiency spillover relationships (Pan et al., 2022). The 3-cycles effect places greater emphasis on the direction of efficiency spillover relationships, reflecting the tendency for several provinces to form a ‘closed-loop’ relationship (Cai et al., 2022). These two types of endogenous structures can test whether regions prefer to cooperate in a ‘group’ pattern during the process of agricultural water resources efficiency diffusion (Liu et al., 2024).

2.4.2 Model construction

SAOM includes a rate function and an objective function. The rate function, denoted as ${\omega }_i\left(x,\alpha \right)$, has a value that is fixed as a constant during model fitting, and the objective function is denoted as $f_i\left(x,\beta \right)$.

The rate function determines the waiting time for changes in the efficiency association relationships between provinces in the network. Let the initial network state of province $i$ be $x^0$. The time variable t is a random variable that follows an exponential distribution with a parameter of ${\displaystyle {\sum }_{n=1}^{31}}{\omega }_n\left(x,\alpha \right)$. Let the network state after a time increment Δt be $x^1$. The probability distribution function for province i to gain an opportunity to change its relationship status is expressed as Equation 11:

${\delta }_i=\frac{{\omega }_i\left(x,\alpha \right)}{{\displaystyle {\sum }_{n=1}^{31}}{\omega }_n\left(x,\alpha \right)}(11)$

For all provinces $\mathrm{j}\ne \mathrm{i}$ in the network, province i will select the next network $x^1$ with a probability ${\epsilon }_{ij}$. And it is shown in Equation 12.

${\epsilon }_{ij}=\frac{\mathit{exp}\left[f_i\left(x^1,\beta \right)-f_i\left(x^0,\beta \right)\right]}{{\displaystyle {\sum }_{n=1}^{31}}\mathit{exp}\left[f_i\left(x^1,\beta \right)-f_i\left(x^0,\beta \right)\right]}(12)$

This paper assumes that the SAOM rate functions ${\omega }_i\left(x,\alpha \right)$ all select province nodes with the same probability ${\epsilon }_i$. The model’s objective function reflects the changes in efficiency association relationships that a province will make after receiving an opportunity to change its relationship status. Specifically, it is expressed as a linear combination of the effects of endogenously generated network structural variables, one-way exogenous control variables, and two-way exogenous control variables (see Equation 13).

$f_i\left(x,\beta \right)=\sum {\beta }_k{S}_{ki}\left(x\right)(13)$

where: $x$ is the given observed values of the longitudinal network, $S_{ki}\left(x\right)$ represents the endogenous structural effects and exogenous influencing factors, β = (β0, …, βl) is the parameter values corresponding to the various effects in the model’s objective function, reflecting the degree to which these effects influence the probability of a change in the efficiency relationship status for province $\mathrm{i}$ in the network. A positive (negative) ${\beta }_k$ indicates that the corresponding network effect $S_{ki}\left(x\right)$ will increase (decrease) the probability of province i forming a corresponding relationship.

2.5 Indicator selection and data sources

Agricultural water use efficiency is evaluated using input, desired output, and undesired output indicators. Detailed variable descriptions are shown in Table 1. Data are drawn mainly from the China Rural Statistical Yearbook and the National Bureau of Statistics of China. Green water footprint data from Meknonnen and Hoekstra (2011).

Table 1

Table 1. Input-output variables for agricultural water use efficiency measurement.

Population, GDP, and related variables used to the modified gravity model come from the China Statistical Yearbook, and GDP is deflated to 2003 prices to control for inflation.

Driving factors comprise 2005–2023 network as the dependent variable and explanatory variables capturing network structural effects and exogenous effects (see Table 2). Structural effects are derived from network metrics. And Description of exogenous variables is shown in Table 3. Data of these is sourced from the China Statistical Yearbook and China Rural Statistical Yearbook.

Table 2

Table 2. Description for network structural and exogenous effects.

Table 3

Table 3. Description for exogenous variables.

3 Results

3.1 Time-series dynamic evolution characteristics of agricultural water use efficiency

This study computes agricultural water use efficiency in 31 provinces using MaxDEA 12.0. Based on the comprehensive average growth rate and mean level (Figure 2), agricultural water use efficiency during 2005–2023 in China can be divided into two development stages. The first stage is from 2005 to 2010, and it is characterized by a low level of agricultural water use efficiency. During this period, the growth rate was slow and even experienced negative growth. While in the second period (2011–2023), the growth rate of agricultural water use efficiency accelerated, and the efficiency level significantly improved compared to the previous period. China began to emphasize water conservation and launched a series of policies starting in the 1990s. These policies include promoting water-saving technologies, developing high-standard farmland, advancing water rights trading, and improving water conservancy infrastructure such as the construction of multi-objective reservoirs and water-saving irrigation equipment (Cheng et al., 2022). The above results indicate that although the initial effects of the policies were not fully realized, China’s agricultural water resource efficiency has significantly improved with the continuous refinement of infrastructure and the popularization of technology.

Figure 2

Figure 2. Mean and average growth rate of agricultural water use efficiency in China, 2005–2023.

From a provincial perspective, there are significant spatial heterogeneity in agricultural water use efficiency (Figure 3A). Agricultural water use efficiency in the major grain-consuming areas is significantly higher than that in major grain-producing areas and the grain production-consumption balance areas (Figure 3B). China’s water resources are not evenly distributed. Southern regions possess nearly 80% of the water resources, but the main grain-producing areas are located in the relatively water-scarce northern regions (Lai et al., 2025). Due to the mismatch between water resource endowment and production structure, main grain-producing areas have borne substantial resource and environmental costs in meeting the food demands of other regions. And the improvement of agricultural water use efficiency in these areas is crucial for alleviating local water scarcity and ensuring equity between regions. However, despite the relatively high cumulative growth rate of water resources in provinces like Shandong, Henan, and Hebei, the overall efficiency level in the main grain-producing areas remains lower than that of the main grain-consuming areas. This indicates that although the main grain-producing areas have made some efforts to improve their own water resource efficiency, further efforts are still needed. When setting water allocation policies, these regions should consider the value of ecosystem services and make greater efforts to increase reservoir storage and promote smart irrigation (Berbela et al., 2018; Hatamkhani et al., 2022b). In addition, some provinces that are both grain-producing and consuming (e.g., Shanxi, Neimenggu and Gansu) exhibit low levels of water resource efficiency. Due to geographical constraints and a lack of intrinsic motivation, their efficiency growth rate is slow. But these regions are located within the Yellow River Basin ecological zone, and improving their water resource efficiency is vital for basin ecological governance and agricultural sustainable development. Therefore, increased policy attention is needed in the future.

Figure 3

Figure 3. Agricultural water use efficiency in China, 2005–2023 (A) Agricultural water use efficiency in different regions. (B) Average and growth rate of agricultural water use efficiency by province. Note: The specific provinces comprising the major grain-producing, major grain-consuming and grain production-consumption balance areas are listed in the appendix.

3.2 Structural characteristics of the spatial association network of agricultural water use efficiency

3.2.1 Analysis of overall network characteristics

This study evaluates the overall structural characteristics of the spatial association network of agricultural water use efficiency from the perspectives of network density, network hierarchy, and network efficiency (Figure 4). The results show that network density exhibits a fluctuating upward trend, stabilizing at 0.26–0.27 after 2010, which is consistent with the findings of Han et al. (2024) and Lai et al. (2025). This indicates that the network structure has become relatively stable. However, the average network density during the sample period is 0.26, suggesting that spatial linkages among provinces remain relatively loose, and further efforts are needed to strengthen interregional links and cooperation. From the perspective of network hierarchy, the index shows a fluctuating downward trend but consistently remains above 0.1, suggesting that the spatial association network has maintained a relatively high level of hierarchy with a clear ordered structure. This is due to the huge differences in resource endowment and socio-economic development levels among provinces and cities (Zhang et al., 2024). Nonetheless, with increasingly close interprovincial linkages, the degree of hierarchy has gradually declined. Network efficiency remains relatively stable, fluctuating around 0.67, indicating that redundant relationships among nodes have been reduced and the efficiency of interprovincial communication and cooperation is relatively high. Overall, the findings suggest that while the spatial spillover effects of agricultural water use efficiency across provinces in China are relatively strong, there remains considerable room for improving the density and stability of the spatial association network.

Figure 4

Figure 4. Overall network characteristics in 2005–2023.

3.2.2 Analysis of individual network characteristics

To reflect the position and role of individual nodes, it is necessary to measure the individual network characteristics of the spatial association network. This study presents the outdegree centrality, betweenness centrality, and closeness centrality of each province in China’s agricultural water use efficiency spatial association network in 2005 and 2023, as shown in the Table 4.

Table 4

Table 4. Centrality analysis of China’s agricultural water use efficiency networks in 2005 and 2023.

Outdegree centrality of each province reflects its efficiency spillover capacity within the network. Over the sample period, outdegree centrality of most provinces have increased, reflecting a growing spillover effect of agricultural water use efficiency. Among them, Guangdong, Shanghai, and Fujian, which have high levels of economic development and relatively convenient transportation, have consistently played a strong efficiency spillover role in the network. As these regions possess higher technological levels and economic strength, they should be encouraged to promote cooperation with their grain trade partner provinces to maximize their efficiency-driving effect. Meanwhile, the rankings of Qinghai, Neimenggu and Xizang increased significantly, indicating an enhanced efficiency spillover effect in the western provinces. With the support of policies such as the Western Development Strategy, the communication between the western provinces and other areas has become increasingly close. However, given the fragile ecological environment, their agricultural water use efficiency should be further improved by enhancing vegetation coverage, strengthening infrastructure development and promoting water-saving technologies. That will ensure the sustainability of their efficiency spillover effect.

Betweenness centrality reflects the capacity of provinces to act as a bridge controlling information flow within the network. The level of betweenness centrality also increased in 2023, indicating that more provinces are beginning to act as “intermediaries” and “bridges” within the network. In 2005, the provinces acting as “bridges” were mainly developed coastal provinces such as Beijing, Shanghai, and Guangdong. They controlled the transmission of information within the network by virtue of their relatively convenient transportation conditions and frequent economic exchanges with surrounding provinces. By 2023, provinces like Neimenggu, Jiangsu, and Fujian joined this group. Most of the provinces with high betweenness are economically developed and geographically important. And they play an important role in controlling the spillover and reception channels related to agricultural water use efficiency (Lai et al., 2025).

Closeness centrality measures the average degree of spatial proximity between a province and all other provinces in the network. The average closeness centrality of all provinces rose from 0.013 in 2005 to 0.015 in 2023. This indicates that the entire spatial association network for agricultural water use efficiency has become more efficient. A higher individual closeness centrality means that the province is more likely to receive efficiency spillovers from other regions. In 2023, 13 provinces had a closeness centrality above the average. Most of these regions are located in the central and western parts of the country. While their economic levels may be lower, their advantageous geographical location along key corridors connecting the coastal and inland areas gives them a potential advantage for improving water resource efficiency.

3.2.3 Evolution of provincial roles in the spatial association network of agricultural water use efficiency

To characterize the role transformation of each province within the network and clarify their future strategies for improving agricultural water use efficiency, this study performs a classification of the provinces. Based on agricultural water use efficiency levels, outdegree centrality, betweenness centrality and closeness centrality, provinces can be categorized into four types: global-core, regional-core, potential and peripheral provinces. Figure 5 shows that, compared with 2005, the roles of most provinces had shifted in 2023. The number of regional core provinces has increased significantly compared to 2005, reflecting the further expansion of the network and the growing spillover effects brought about by improvements in agricultural water use efficiency.

Figure 5

Figure 5. Provincial regional type classification. (A) Provincial regional type classification in 2005. (B) Provincial regional type classification in 2023.

The global core provinces, including Shanghai, Guangdong, Fujian, and Chongqing, should promote multi-channel cooperation with other regions to fully leverage their radiative and driving effects. Moreover, Provinces such as Jilin, Zhejiang, Henan, Guizhou, and Tianjin have transitioned from potential provinces to regional core status, while Qinghai, Shaanxi, Xinjiang, and Guangxi have moved from marginal status to regional core status. Some provinces, including Hebei, Yunnan, Guizhou, and Liaoning remain in a stage of potential growth. In the future, they need to strengthen exchanges and cooperation with neighboring provinces and fully utilize the network connectivity to enhance more efficient use of agricultural water resources.

Additionally, it is worth noting that although the total of peripheral provinces decreased in comparison with 2005, 66.67% of the peripheral provinces are major grain-producing areas in 2023. Such regions still face significant challenges in achieving green agricultural water resource production. This highlights the urgent need to strengthen production-marketing linkages and technological collaboration with more advanced regions, thereby promoting a comprehensive green transformation of agriculture in these grain-producing provinces.

3.2.4 Community evolution characteristics in the spatial association network of agricultural water use efficiency

The dynamics of communities in the spatial association network has undergone significant changes (Figure 6). In 2005, the network could be divided into three communities, while it evolved into four communities in 2023. Moreover, composition of these communities also changed.

Figure 6

Figure 6. Network community evolution in 2005 and 2023. (A) Network community in 2005. (B) Network community in 2023.

Spatial association of agricultural water use efficiency among provinces was relatively unbalanced. The largest community within the network consisted of 18 provinces located in northern and western China, exhibiting extensive interregional and inter-basin linkages. The community’s internal edge density was 0.23, indicating relatively loose interprovincial connections. The second community includes 10 provinces in central and southern China, such as Anhui, Hubei, and Guangdong. Shanghai, Fujian, and Guangdong were the core provinces of this community. The provinces in this community are geographically close, have frequent economic exchanges, and exhibit relatively close ties within the community. In addition, Shandong, Henan, and Gansu formed a smaller community that was isolated within the overall network and had weaker connections with other regions.

The community structure in 2023 exhibits characteristics of multi-centralization and deep integration between the northern and southern regions. Nine provinces in central and western China, together with Shanghai, Fujian, and Hebei, formed the largest community in the network. The community’s density increased to 0.30, indicating that collaboration and connections among the central and western provinces were strengthened. Benefiting from the state’s investment in ecological protection and water resource management, as well as the development of high-value-added agriculture in the central and western areas, the efficiency spillover capacity of western provinces such as Inner Mongolia, Qinghai, and Tibet significantly increased. And they have attracted beneficiaries such as Shanghai and Fujian. Meanwhile, Heilongjiang, Beijing, and Jiangsu joined a community dominated by Anhui and southern provinces, forming the second-largest community in the network. Compared with 2005, the scope of influence of this community has expanded. Among them, Guangdong strengthened its position and absorbed provinces like Heilongjiang, Beijing, and Jiangsu. Guangdong as a major grain consumption area and economic center, has driven the efficiency improvement of the grain-producing regions in the North and Northeast through its demand. Shandong, Shanxi, Henan, and Zhejiang form a small community, with relatively close internal connections within the group. In addition, this community also has close connections with Community 2. This indicates that grain trade and inter-regional water rights trading strengthened the spatial association. Meanwhile, Liaoning and Jilin constitute the smallest community in the network, which suggests that these two provinces are relatively isolated within the network. Although its internal connections were strong, its external linkages with other regions were limited, indicating that this region remained relatively isolated within the overall network.

The evolutionary trend of community structures reveals that, as interprovincial linkages have become increasingly close, agricultural water use efficiency spillovers are gradually breaking through geographical boundaries to form new spatial diffusion patterns. In future regional water management policies, the coordination among provinces should be planned from a holistic network perspective. Furthermore, the central and western provinces are no longer on the network periphery but have become important sources of efficiency spillover through the improvement of water resource efficiency and cross-regional economic ties. This suggests a significant improvement in the regional fairness and synergy of China’s agricultural water resource management.

3.3 Analysis of the driving factors of the spatial association network of agricultural water use efficiency

This study examines the driving factors of the spatial association network of agricultural water use efficiency from the perspectives of both network structure and exogenous influences. All convergence t ratios are all below 0.1, and the overall maximum convergence ratio is within 0.25, indicating that the SAOM specification is appropriate (Ripley et al., 2023). The results show that, in addition to exogenous influencing factors, the network structure effect is an important driving force affecting the formation and evolution of the spatial association network of agricultural water use efficiency (Table 5). In advancing regional collaborative strategies for agricultural water resource management, economic connections and technological cooperation between provinces should be considered, in addition to the provinces’ own development status.

Table 5

Table 5. Regression results of SAOM.

Network structure has a significant impact on network evolution, which is consistent with the findings of Liu et al. (2024), indicating that cooperation patterns between regions play an important role in the spillover relationships of agricultural water resource efficiency among regions. Specifically, reciprocity effect has a significant positive effect on network formation, suggesting that bilateral spillover relationships dominate the spatial association network of agricultural water use efficiency. The two-way interaction between provinces is strong, with noticeable mutual influences and feedback mechanisms in areas such as agricultural water-saving, technology diffusion, and policy learning. In contrast, 3-cycles effect has a significant negative effect, indicating a weak tendency to form stable closed-loop cooperative relations among three nodes and the lacks of multi-party collaborative cooperation. Additionally, transitive triples effect is not significant, indicating a lack of clear “efficiency spillover paths” in the network, and a mechanism where high-efficiency provinces drive medium- and low-efficiency provinces has not yet formed. Therefore, current inter-regional efficiency spillovers are primarily bilateral interactions, and pattern of collective cooperation has not yet emerged. This suggests that agricultural water resource management in China is still largely province-driven, and cross-regional cooperation systems still need to be improved.

Among exogenous influencing factors, economic development level, geographical distance, industrial structure, resource endowment, and local fiscal support all have a significant impact. Specifically, economic development and resource endowment play important roles in network evolution. The sender and receiver effects of regional economic development levels are significantly positive, indicating that provinces with higher levels of economic development are more likely to generate spatial efficiency spillovers within the network. However, the homophily effect of economic development is negative, suggesting that efficiency spillovers are more likely to form between regions with larger economic disparities. In future policy design, attention should be paid to cooperation and support between economically developed regions and less-developed regions. In terms of resource endowment, the homogeneity effects of water resource and labor endowment are significantly positive, indicating that provinces with similar water resource and labor endowments are more inclined to establish efficiency spillover relationships. Therefore, regional cooperation alliances based on “resource endowment similarity” can be promoted to ensure that regions with high homogeneity can smoothly learn from and replicate each other’s best practices and management experience. The sender effects of industrial structure and local government support are significantly positive, suggesting that provinces with a higher proportion of agricultural output generally have higher agricultural water resource use efficiency, thereby possessing stronger efficiency spillover capabilities. These advantageous regions should be encouraged to develop high-value-added, water-saving agriculture, improving efficiency through industrial upgrading itself, and in turn driving neighboring regions to follow suit. And local fiscal support in each province also plays a positive role in improving agricultural water resource efficiency and facilitating spatial spillovers. Government should establish incentive mechanisms linked to water-saving performance to ensure that funds are truly used to improve agricultural water use efficiency and promote technology spillovers.

To explore the relative importance of various driving factors in the evolution of the network, this study adopted the method of Indlekofer and Brandes (2013) to calculate the contribution of each factor). Figure 7 presents the results of the average relative importance of the factors. The results indicate that GDP, distance and resource endowment are the key factors influencing the efficiency spillover network. However, network structural effects also have a relatively significant impact on the evolution of the efficiency network, indicating that network structural factors are important drivers that cannot be ignored (Lu and Qin, 2025). Therefore, emphasis should be placed on the coordinated governance and structural optimization of agricultural water resources across regions. Establishing cross-regional cooperation platforms, improving the inter-regional technology diffusion mechanism and implementing ecological compensation policies will help enhance the overall agricultural water resource efficiency nationwide and achieve spatial balance.

Figure 7

Figure 7. Average relative importance of driving factors.

4 Discussion

Clarifying the spatial association of agricultural water use efficiency and its driving mechanisms is crucial for regional water resource management and sustainable agricultural development. Based on Social Network Analysis (SNA) and the Stochastic Actor-Oriented Model (SAOM), this study investigates the structural characteristics and dynamic drivers of the spatial association network of agricultural water use efficiency in China.

First, the analysis reveals significant regional heterogeneity in China’s agricultural water use efficiency. Although existing studies have reported variations in quantitative results due to differences in measurement frameworks and methods, a general consensus persists that substantial interprovincial disparities in agricultural water use efficiency remain (Cao et al., 2020; Ji et al., 2025; Wang et al., 2025). Therefore, adopting region-specific water management policy is necessary. For example, Grain demand in eastern coastal regions mainly depends on major grain-producing areas, so these regions should reduce food and water waste and invest more in developing water-saving technologies. As a key agricultural base, Northeast areas should balance ecological protection and agricultural development to ensure the sustainable use of agricultural water resources (Lu et al., 2025). Moreover, such heterogeneity hinders the overall improvement of national water use efficiency, underscoring the necessity of exploring cross-regional cooperation from a network perspective (Zhi et al., 2022b; Zhao et al., 2025).

Second, this study finds that as interprovincial connections have become increasingly close, a spatially associated agricultural water use efficiency network has gradually formed, with growing complexity in relational structures. It indicates that there are stronger interdependencies among provinces. This finding aligns with existing research (Yang et al., 2022; Lai et al., 2025; Chang et al., 2025), which suggests that under the context of regional integration and agricultural modernization, spatial linkages in agricultural water use efficiency are becoming more evident. Therefore, exploring efficiency enhancement from a network-based perspective offers new insights for regional coordination in agricultural water resource management (Han et al., 2024). Moreover, the results of centrality analysis and community evolution indicate that the structure of efficiency spillover relationships has undergone significant changes over time, yet the core provinces remain concentrated in the economically developed eastern coastal regions. In the future, attention should be given to strengthening the spillover effects of these core provinces to promote the coordinated improvement of agricultural water use efficiency across regions (Zhi et al., 2022b).

Third, the application of the SAOM model demonstrates that the network structure itself is a critical driver shaping the formation and evolution of the agricultural water use efficiency network. This finding is similarly confirmed in air pollution transition and energy efficiency networks (Liu et al., 2024; Lu and Qin, 2025). Specifically, the increasing reciprocity within the network indicates stronger bilateral efficiency spillovers among provinces, reflecting enhanced mutual learning and policy diffusion in agricultural water use. However, the negative effect of 3-cycles suggests that multilateral cooperation across provinces remains weak, and collective coordination mechanisms have yet to be established. But this finding contrasts with the recent pattern of growing cooperation and integration observed in China’s grain virtual water trade network (Huang et al., 2025; Shen et al., 2025). This discrepancy implies that while interregional collaboration in agricultural product exchange has intensified, cooperation in technological innovation and joint efficiency enhancement has lagged behind. This mismatch reflects that grain-consuming regions benefit from the water and ecological resources of major grain-producing areas without providing adequate compensation or feedback, which may intensify regional ecological inequality (Gao et al., 2020; Xu et al., 2025). Hence, strengthening interregional technological cooperation and institutional coordination is crucial for the coordinated development of regional water resources (Zhao et al., 2024; Xu et al., 2025). Policies should encourage the establishment of cross-regional collaboration platforms, promote joint R&D in water-saving technologies, and reinforce ecological compensation mechanisms between grain-producing and consuming areas. By fostering cooperative governance and network-based policy design, China can better balance agricultural productivity with sustainable water resource management.

5 Conclusion

Due to differences in geographical conditions and industrial structures across provinces, the level of green development of agricultural water resources is uneven in China (Shi and Zhu, 2025). Therefore, how to enhance regional cooperation to promote the agricultural water use efficiency nationwide is a concern for the government. With the growing interconnections among provinces, it is insufficient to explore the improvement of agricultural water use efficiency only from the perspective of traditional location theory. Latest research is paying more attention to the role of network externalities (Shi et al., 2022). Therefore, this study constructed a spatial association network of agricultural water use efficiency and analyzed the structural evolution characteristics and driving factors of the network.

Results show that the spatial correlation network of agricultural water use efficiency in China exhibits a relatively complex network structure. But the overall network is still relatively loose, and the hierarchical characteristics are evident, which means that he current network structure has a limited effect on information dissemination and efficiency spillover. And promoting inter-provincial cooperation to strengthen spatial connections among provinces is necessary. At the individual level, provinces such as Guangdong, Shanghai and Fujian act as radiation sources of efficiency spillovers, playing important intermediary and bridging roles in the network. In the future, attention should be paid to continuously optimizing water resource management in these regions, making full use of their efficiency spillover effects to help improve agricultural water use efficiency in other provinces.

As interprovincial linkages have become increasingly close, agricultural water use efficiency spillovers are gradually breaking through geographical boundaries to form new spatial diffusion patterns. This provides insights for future agricultural water resource management policies. Policymakers should integrate spatial correlation characteristics with functional area planning, and coordinate cross-regional policies to promote the dissemination and improvement of agricultural water use efficiency. The southern and coastal regions have formed a high-efficiency collaborative community, the western region has closer internal connections, while the northeastern region shows a trend of marginalization.

Moreover, spatial association of agricultural water use efficiency among provinces is mainly based on pairwise connections, and a multi-regional collaboration model has not yet formed. This highlights that, in the future advancement of national agricultural water resource management policies, a network perspective should be emphasized. Furthermore, it is important to actively promote cross-regional cooperation and coordination mechanisms. By establishing water resource technology exchange centers and cross-regional collaboration platforms, provinces can work together in agricultural production, marketing and technology. This will ensure coordinated advancement of the green development of agricultural water resources nationwide. Meanwhile, improving economic development and providing fiscal support for local technology research and development promotion will be helpful. Especially in water-scarce areas in western and northern China, governments should spend more on water infrastructure, practical technologies, and the control of agricultural pollution. This will help increase water storage capacity and irrigation efficiency, and support the sustainable use of agricultural water resources.

Although this study provides some insights for future agricultural water resource management policies, there are still some limitations. The directions for future research are as follows:

First, the impact of specific regional cooperation mechanisms on water resource efficiency has not yet been considered. Future research needs to conduct detailed policy effect evaluations for concrete regional cooperation policies, such as cross-regional water pollution control. Second, the study has not assessed the specific promotion effect of strengthening the spillover effects of water resource efficiency in core network provinces on overall water resource efficiency. Future research should combine methods from network dynamics to simulate the specific impact of the improvement in agricultural water resource efficiency and the strengthening of spillover effects from core provinces on the overall efficiency.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

YX: Conceptualization, Methodology, Writing – original draft, Writing – review and editing, Software. DW: Data curation, Funding acquisition, Methodology, Resources, Software, Supervision, Writing – review and editing. YZ: Software, Validation, Writing – original draft.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This research was funded by National Natural Science Foundation of China (Grant No. 72373111), 2025 Annual Project of the Dual-Carbon Industry Research Institute in Shanxi University of Finance and Economics (Project No. SCST 2025N13), Shanxi Provincial Philosophy and Social Science Planning Project (Project No. 2024QN099) and Research Project of Philosophy and Social Sciences in Higher Education Institutions of Shanxi Province (Project No. 2024W078).

Acknowledgements

We are grateful to the reviewers and the editor for their valuable time and constructive feedback on the article. And we thank all the institutions for supporting this work.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenvs.2025.1730331/full#supplementary-material

Abbreviations

SAOM, Stochastic actor-oriented model; GDP per, Per-capita GDP; dis, Geographic distance; AL, Agricultural land endowments; AW, Agricultural water endowments; ALE, agricultural labor force; ALQ, Agricultural human capital; FI, Fiscal support for agriculture; IND, Agricultural industrial structure.

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