Towards a Sustainable Structure of an Urban Water–Energy–Food Nexus: Based on Network and Hierarchy Analysis

Abstract

Water, energy, and food (WEF) are critical resources to sustain urban development, which requires a sustainable structure of the urban WEF nexus to address trade-offs and achieve synergies. Although interactions in the WEF nexus are widely explored, its sustainable structure has largely been ignored. This study constructs a framework of WEF nexus sustainability factors. Based on a literature review and expert opinions, 21 factors influencing urban WEF nexus sustainability were extracted and their interrelationships determined. We used social network analysis (SNA) and interpretive structural modeling (ISM) to analyze the structure of the urban WEF network. The results indicate that technological investment and industrial added-value energy consumption are the most critical and fundamental factors for promoting the sustainable development of the urban WEF nexus. Additionally, the balance of water supply and demand and the comprehensive management of waste pollutants are also driving and supporting factors for the sustainability of the urban WEF nexus. The results of this study complement the interaction mechanism research of the urban WEF nexus and provide practical references for sustainable decision-making in urban WEF nexus practices.

1. Introduction

Water, energy, food, and urban are core components of 17 sustainable development goals (SDGs) aimed at fostering the harmonious coexistence between humanity and nature [1]. Both human society and the natural environment exert influences on WEF and urban security. For instance, the 2022 drought in Sichuan, China, resulted in various risks, including forest fires, food crises, and energy shortages. Thus, sustainable urban development requires an accurate understanding of urban resource sustainability since urban WEF resources heavily rely on external inputs. Water, energy, and food, as fundamental material resources, constitute the lifeline for ensuring the sustainable development of cities [2]. The “Global Risks Report” by the World Economic Forum comprehensively summarized the relationship among water, energy, and food and referred to it as the “Water–Energy–Food nexus” (WEF nexus) for the first time [3]. This nexus aims to enhance cooperation among the three essential resources (water, energy, and food) by reducing trade-offs and strengthening synergies, thereby achieving WEF nexus sustainability [4,5]. In the context of accelerating global population growth and intensifying global environmental changes, various resource challenges continue to emerge. The competition among water, energy, and food has evolved into a series of unforeseen risks, including increased greenhouse gas emissions, exacerbated climate and land-use changes, and limitations on Earth’s carrying capacity [6,7]. This evolution has widespread implications for the relationships among these three elements, thus, increasing the demand for research that addresses challenges, preserves global natural resources, and provides reliable data for decision-making and policy planning [8]. Therefore, systematically analyzing the factors influencing WEF nexus sustainability is crucial in the field of WEF research. The harmonious development of resources and the ecological environment under the guidance of sustainable development is of great academic value and practical significance for promoting the coordinated and stable development of future cities. To address this, our study focuses on urban WEF systems, investigating the interactions of sustainability factors within the WEF nexus. We place particular emphasis on derivative pathways and hierarchical relationships among key elements to enhance decision-makers’ awareness and facilitate the coordinated development of water, energy, and food resources in urban areas.

Since the inaugural presentation of the WEF nexus at the Bonn Conference, extensive scholarly attention has been devoted to the investigation of interrelationships, particularly concerning conceptual nuances [2], associative structures [9], and influencing factors [10,11]. For instance, some scholars define the nexus as interdependencies among water, energy, and food [12,13], highlighting their coupling in supply, processing, distribution, and utilization [14]. Zhang et al. [2], on the other hand, view the nexus as an analytical method to quantify the connections between nodes (namely water, energy, and food). Despite differences in the definition of the nexus, the research objectives aim to achieve comprehensive management across the three departments through inter-sectoral coordination, fostering the sustainable development of each department [15]. Numerous scholars focus on the opportunities and challenges faced by WEF, analyzing the internal interaction of WEF and the influence of external factors (society, economy, environment, etc.) on the WEF nexus, and putting forward three collaborative resource management measures [2,4]. Conway et al. [16] used South Africa as an example to describe the impact of climate change on the water–energy–food system. Zhang et al. [17] explored the correlation among water, energy, and food and developed a method based on causal loop diagrams. This method serves as a prototype to describe the WEF nexus characteristics, elucidate its issues, explore their causes and consequences, and identify effective measures and policies to mitigate conflicts. Rasul et al. [18] proposed that effective management of the three major resources—water, energy, and food—requires an interdisciplinary management approach. In addition, coordinated management of WEF resources can promote urban sustainable development and future resource security [19,20].

With the increasing severity of environmental and resource constraints and the formal adoption of sustainable development goals, it is particularly important to study the sustainability of the WEF nexus. Wang et al. [21], drawing on the pressure–state–response (PSR) model, constructed a sustainability assessment indicator system for the WEF nexus. They approached the issue from social, economic, and environmental perspectives, employing a combined weighting method and a matter–element extension model to assess the sustainability of China’s water, energy, and food relationships. In response to the multiple uncertainties arising from climate and socio-economic changes, Zeng et al. [22] utilized a simulation fuzzy stochastic grey method (SFSG) based on green criteria to address WEF issues, aiming to achieve sustainability in human development and WEF resource management. Li et al. [23] proposed a subject analysis framework for urban WEF consumption, and based on an Agent-NetLogo combined simulation model, explored effective resource allocation within urban sustainable development. However, despite the progress made in studying WEF nexus relationships, there are still shortcomings in identifying influencing factors for the overall sustainability of the WEF nexus and analyzing the mechanisms at the urban–regional level. The translation of theoretical concepts of the WEF nexus into practical methods to promote sustainable coordination among water, energy, and food resources remains a significant challenge. Sustainability stands as the primary task for the development of the WEF nexus, impacting the current and future state of the three major resources and influencing the prospects and fate of urban development. Elevating the sustainability level of the WEF nexus holds the potential to provide favorable material conditions for the future development of cities. Therefore, investigating the influencing factors and the mechanisms underlying the sustainability of the urban WEF nexus holds great practical significance.

In the realm of WEF research methods and models, numerous scholars have employed various methods such as input–output analysis [24], system dynamics [5,25], multi-objective optimization models [26,27], data envelopment analysis [28], and econometric analysis and game theory [29]. These methods have been applied across various scales (global, national, provincial, urban, etc.) to evaluate, simulate, predict, and optimize the WEF systems. The outcomes of these studies provide scientific guidance for subsequent research. Urban WEF systems are highly open and exhibit intricate interrelationships. Social network analysis, as a quantitative analytical method combining graph theory and sociometrics, calculates network structural characteristics to analyze key factors and inherent connections. The interpretative structural modeling method, through matrix operations, determines the hierarchical influence of factors, offering the advantage of transforming complex systems into a more concise and clear multi-layered hierarchical structure model.

This study aims to provide an analytical framework by applying the SNA-ISM method to WEF nexus research, attempting to establish a hierarchical structure of the urban WEF nexus sustainability factors by identifying representative factors and their interconnections. To achieve the research objectives, this paper introduces the methodology in Section 2. Subsequently, Section 3 identifies intrinsic factors influencing the sustainability of the urban WEF nexus. In Section 4, the interconnections of these factors are determined, and the mechanisms of their effects are analyzed based on the SNA-ISM model. Finally, conclusions and suggestions are provided in Section 5.

2. Methodology

2.1. The Sustainability of the Urban WEF Nexus

The WEF nexus emphasizes the interdependence, interaction, and coordinated development of water, energy, and food. Sustainability refers to meeting current needs without compromising the ability of future generations to meet their needs [30]. WEF nexus sustainability is a holistic concept that advocates for comprehensive planning and interdisciplinary collaboration to achieve the synergistic management of water, energy, and food within the context of limited resources, creating a long-term stable, healthy, and prosperous system. Achieving nexus sustainability at the urban scale contributes to overall urban sustainable development. This study explores factors influencing urban WEF nexus sustainability, and a comprehensive examination is conducted across four key aspects of WEF resources—namely, the supply quantities, the demand quantities, utilization efficiency, and sustainability [31,32,33]. Firstly, the importance of establishing a balanced and sustainable system is emphasized by considering resource supply and demand quantities. In this context, it is crucial to delve into the production and consumption patterns of resources to ensure sustainability based on a foundation of balanced supply and demand. Secondly, the focus is placed on resource utilization efficiency, addressing whether maximum output can be achieved during resource utilization to ensure more efficient economic development and lifestyles within the constraints of limited resources. Lastly, attention is directed towards resource sustainability, evaluating whether resource use and management align with long-term sustainable development goals. This includes a comprehensive assessment of aspects such as resource consumption rates, recycling, ecological impacts, and social responsibility, ensuring that the urban WEF nexus system achieves balanced resource utilization both currently and in the future.

The study initially compiles a list of all possible factors related to WEF nexus sustainability by reviewing the literature on the subject in knowledge databases such as Web of Science and Scopus. Subsequently, experts in the relevant research field are invited to contribute, and representative factors are selected based on the four sustainability principles, considering the characteristics of urban systems that are highly open and reliant on external resource inputs. Finally, through a combination of existing literature research and expert revisions, the study systematically examined each factor’s direct impact on other factors, ultimately establishing the interrelationships between these factors.

2.2. SNA-ISM Model

To achieve the research objectives, this paper constructs an SNA-ISM model to elucidate the mechanisms of factors affecting the sustainability of the WEF nexus. Firstly, the causal attributes of factors are clarified based on the social network model, followed by an analysis of the degree of mutual influence among these factors within the network. Subsequently, the ISM model is applied to structurally process the explanatory and hierarchical relationships among factors, elucidating the derived pathways of sustainability influencing factors. The specific analysis process of influencing factors is illustrated in Figure 1.

Social network analysis (SNA) is a social science research method that describes the structure of group relations by establishing a model of interaction between actors and analyzing a single actor’s influence on group functions or other individuals within a group. SNA can analyze social networks from various perspectives. In this study, we primarily utilized centrality analysis to identify key factors and intrinsic connections. Centrality measures assess the extent to which a node in a social network is central to the entire network and serves as an indicator to judge the importance or influence of a node in the network. Various centrality measures include degree centrality, closeness centrality, and betweenness centrality, among others. Degree centrality ($C_{deg}$) represents the sum of direct connections a node has with other nodes in the network. A higher value indicates that the factor is closer to the center of the network. Closeness centrality ($C_{close}$) reflects how close a node is to other nodes in the network. If a node has small shortest distances to all other nodes in the graph, it has high closeness centrality, and it is closer to the geometric center. In comparison to betweenness centrality, closeness centrality is more geometrically centered. Betweenness centrality ($C_{btw}$) refers to the ratio of the number of shortest paths passing through a node and connecting two other nodes to the total number of shortest paths between those two nodes. A higher value indicates a higher likelihood that the node connects two other nodes, exerting stronger control in the network relationship graph. The calculation formula is as follows:

$$C_{deg}\left(v\right)={\displaystyle \frac{d_v}{\left|N\right|-1}}$$

(1)

where $d_v$ is the number of neighbors of node $v$, $N$ is the set of all nodes in the network, and $\left|N\right|$ is the number of nodes in the network.

$$b_{jk}\left(i\right)={\displaystyle \frac{g_{jk}\left(i\right)}{g_{jk}}}$$

(2)

$$C_{btw}\left(i\right)=\sum _j^n\sum _k^n{b}_{jk}\left(i\right),\left(j\ne i,j<k\right)$$

(3)

where ${\mathrm{b}}_{\mathrm{j}\mathrm{k}}\left(\mathrm{i}\right)$ indicates the ability of point i to control the communication between point j and point k, the number of paths between points j and k is indicated by ${\mathrm{g}}_{\mathrm{j}\mathrm{k}}$, and the number of paths connecting points j and k, through point I, is indicated by ${\mathrm{g}}_{\mathrm{j}\mathrm{k}}\left(\mathrm{i}\right)$.

The interpretative structural modeling method (ISM) is a complex systems analysis approach introduced by Professor Warfield in the United States. It is capable of breaking down systems with complex interrelationships and unclear structures into intuitive and hierarchical multi-layered structures. The results are visualized through tree diagrams, directed graphs, and other methods, revealing the influence pathways among system factors. Currently, the ISM method has been widely applied in various fields, including energy, water resources, and the WEF domain [9,34]. It holds significant reference value in supporting decision-making, optimizing goals, and conducting causal analyses. The main process of the ISM method is as follows:

(1)

Establish a factor set. Clarify the research problem, determine the research object, and establish the factor set $\mathrm{S}=\left\{{\mathrm{S}}_1,{\mathrm{S}}_2,{\mathrm{S}}_3,\cdots {\mathrm{S}}_{\mathrm{n}}\right\}$.

(2)

Construct an adjacency matrix. An adjacency matrix is a Boolean matrix containing only 0 and 1. It describes the direct influence relationship between every two factors in the factor set and is called adjacency matrix $\mathrm{A}={\left({\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)}_{\mathrm{n}\ast \mathrm{n}}$. The specific definition rules are as follows:

$${\mathrm{a}}_{\mathrm{i}\mathrm{j}}=\left\{\begin{array}{c}1,{\mathrm{S}}_{\mathrm{i}} \mathrm{has} \mathrm{a} \mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{on} {\mathrm{S}}_{\mathrm{j}}\\ 0,{\mathrm{S}}_{\mathrm{i}} \mathrm{has} \mathrm{n}\mathrm{o} \mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{i}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{on} {\mathrm{S}}_{\mathrm{j}}\end{array}\right.$$

(4)

(3)

Calculate the reachable matrix M. The reachability matrix is obtained from the adjacency matrix through Boolean operation, and the influence paths among factors other than the adjacency matrix can be obtained. The specific calculation rules are shown in Formula (5):

$$(\mathrm{A}+\mathrm{I})\ne {(\mathrm{A}+\mathrm{I})}^2\ne \cdots \ne {(\mathrm{A}+\mathrm{I})}^{\mathrm{k}}={(\mathrm{A}+\mathrm{I})}^{\mathrm{k}}+\mathrm{I}=\mathrm{M}$$

(5)

where I is the identity matrix, and (A + I) is constantly squared until the values in the matrix no longer change, indicating that the influence relationship among factors is saturated, and no new influence paths are generated and the reachable matrix can be obtained.

(4)

Divide the hierarchical structure. The reachable matrix is divided into different sets, and the result of dividing factors, step by step, can be obtained through set operation. The reachable matrix division rules are as follows:

➀

Reachability set $\mathrm{R}\left({\mathrm{S}}_{\mathrm{i}}\right)=\left\{{\mathrm{S}}_{\mathrm{i}}|{\mathrm{M}}_{\mathrm{i}\mathrm{j}}=1\right\}$, which means the set of factors corresponding to the value 1 in the row of the factor ${\mathrm{S}}_{\mathrm{i}}$ in the reachability matrix M.

➁

Preceding set $\mathrm{A}\left({\mathrm{S}}_{\mathrm{j}}\right)=\left\{{\mathrm{S}}_{\mathrm{j}}|{\mathrm{M}}_{\mathrm{i}\mathrm{j}}=1\right\}$, which means the set of factors corresponding to the value 1 in the column of the factor ${\mathrm{S}}_{\mathrm{j}}$ in the reachable matrix M.

➂

Common factor set $\mathrm{C}\left({\mathrm{S}}_{\mathrm{i}}\right)=\mathrm{R}\left({\mathrm{S}}_{\mathrm{i}}\right)\cap \mathrm{A}\left({\mathrm{S}}_{\mathrm{i}}\right)$, which represents the intersection of the reachable set and the preceding set for factor ${\mathrm{S}}_{\mathrm{i}}$.

➃

If $\mathrm{R}\left({\mathrm{S}}_{\mathrm{i}}\right)=\mathrm{C}\left({\mathrm{S}}_{\mathrm{i}}\right)$, the factor belongs to a hierarchy, and it is divided into rows and columns corresponding to the reachable matrix. The factor set of the next hierarchy is obtained by iteration according to the above rules until all the factors are divided.

(5)

Drawing an analytical structural model. According to the identified factors at all levels, combined with the influence relationship of accessible matrix factors, the influence relationship is represented by a directed graph, and finally, the explanatory structure model diagram is drawn.

2.3. Data Sources and Processing

This study aims to focus on the research theme by inviting one expert from each of the fields of water resources, energy, and food to assist in the research. Their research areas include water resource management, renewable energy development, and agricultural resources and environment. Additionally, three experts specifically focusing on urban water–energy–food research were invited. Their research directions encompass the life cycle of water–energy–food, water–energy–food coupled systems, and water–energy–food sustainability. To identify the interrelationships between influencing factors more scientifically and accurately, we requested the experts to revise the correlation matrix. If the expert agreed, no modification was needed; if they did not, modifications were made. For three or more experts who agreed, the revision suggestion was accepted, ultimately forming a comprehensive and systematic adjacency matrix. Based on this adjacency matrix of WEF nexus sustainability influencing factors, we employed social network analysis software such as Ucinet and Netdraw to construct a visual network. Finally, Matlab code was written to calculate the hierarchical relationships.

3. WEF Nexus Sustainability Factor Identification

The research object of this paper is WEF nexus sustainability, and the literature search is mainly based on the core collection of Web of Science and Scopus. In this study, “Sustainable”, “Food Water Energy Nexus” and “WEF nexus” are used as keywords, and the article category is set to “Article”. Based on their relevance to the research theme and citation frequency, literature with low relevance and citation frequency was excluded. After organizing and screening the collected literature, we conducted focused reading to identify potential factors influencing the sustainability of WEF nexus, and applied coding procedures. In this study, we collected a total of 25 articles and summarized the identified influencing factors in

Table 1. List of WEF nexus sustainability impact factors based on literature review.

Number	Factors	References	Frequency
1	Water supply	[11,21,35,36,37]	23.08%
2	Water demand	[35,36,37,38,39,40,41]	30.77%
3	Water resource utilization rate	[4,35,37,42,43]	19.23%
4	Water consumption per unit GDP	[4,35,37,41,44]	19.23%
5	Industrial added value water consumption	[4,35,37]	11.54%
6	Industrial wastewater discharge	[21,37]	7.70%
7	Total wastewater discharge	[4,21,35,36]	15.38%
8	Sewage treatment rate	[11,37,41,45,46]	19.23%
9	Water production modulus	[4,35,38]	11.54%
10	Proportion of domestic water consumption	[35,36,46]	11.54%
11	Proportion of agricultural water consumption	[35,36,38,41,47]	19.23%
12	Proportion of ecological water consumption	[35,36]	7.70%
13	Proportion of groundwater supply	[35,41,47,48]	15.38%
14	Primary energy production	[35,38]	7.70%
15	Energy supply	[4,35,37,38,39,41,49]	26.92%
16	Degree of electrification	[4,37]	7.70%
17	Energy consumption per unit of GDP	[4,35,37,38,41,50,51,52]	30.77%
18	Energy self-sufficiency rate	[4,35]	7.70%
19	Proportion of coal consumption	[4,41]	7.70%
20	Proportion of natural gas consumption	[4]	3.85%
21	Carbon emissions per unit of GDP	[37,41,53]	11.54%
22	Industrial SO2 emissions	[21,37]	7.70%
23	The amount of industrial solid waste generated	[21,37,46]	11.54%
24	Technology investment as a percentage of GDP	[11,37,40]	11.54%
25	Industrial added value energy consumption	[4,36]	7.70%
26	Proportion of hydropower	[4,35]	7.70%
27	Investment Completed in industrial pollution treatment	[4]	3.85%
28	Investment in energy industry	[35]	7.70%
29	Grain crop sown area	[37,51]	7.70%
30	Proportion of grain crop sown area	[4,35,36,37]	15.38%
31	Per capita output of grain	[4,36,37,38,44,49]	23.08%
32	Grain output per unit area	[4,35,36,37,41,43]	23.08%
33	Burden of chemical fertilizers	[4,35,37,39,41,46,47,54]	30.77%
34	Burden of pesticides	[4]	3.85%
35	Mechanization level of agriculture	[4,21,35,43]	15.38%
36	Proportion of agricultural output value	[37,55]	7.70%
37	Proportion of rural electricity consumption	[37,56]	7.70%
38	Proportion of effective irrigation area	[4,35,36]	11.54%
39	Proportion of water-saving irrigation area	[4,38]	7.70%
40	Turnover cost of food	[4,35]	7.70%
41	Total output value of first industry	[4]	3.85%

.

Constructing a system for identifying factors influencing the sustainability of the WEF nexus enables a clear understanding of the composition and structure of sustainability factors. It also forms the basis for studying the interaction mechanisms among sustainability factors and analyzing the dynamic processes of sustainability factor changes. In this study, experts were invited to combine their insights with an analysis of current urban resource characteristics. After excluding factors with low occurrence frequencies (<7.70%), we identified factors that are scientifically sound, reasonable, and effective in promoting sustainability following the principles of comprehensiveness, applicability, systematicity, and independence. The factors were categorized into three aspects corresponding to water, energy, and food systems, totaling 21 sustainability factors. This paper analyzes the sustainability of each subsystem using selected factors from aspects such as urban resource supply, demand, utilization efficiency, and sustainability. The chosen factors not only impact the supply and consumption of the three nexus resources but also reflect the interdependent status among the three subsystems, emphasizing the interconnected nature of the nexus. The composition of factors is illustrated in Figure 2.

4. Mechanism Analysis of WEF Nexus Sustainability Factors

4.1. Causality Identification

Firstly, this paper initially establishes an adjacency matrix $A={\left(S_{ij}\right)}_{21\ast 21}$, where $S_{ij}=1$ indicates that factor i has a direct influence on factor j, otherwise it is 0. After expert revision, the final adjacency matrix A of WEF nexus sustainability impact factors is presented in

Table 2. WEF Nexus sustainability impact factors’ adjacency matrix A.

		W1	W2	W3	W4	W5	W6	W7	E1	E2	E3	E4	E5	E6	E7	F1	F2	F3	F4	F5	F6	F7
A=	W1	0	0	1	0	1	0	0	0	0	0	0	0	0	0	1	0	1	1	0	0	0
	W2	1	0	1	1	1	0	1	1	0	0	0	0	0	0	1	0	0	1	0	0	0
	W3	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	W4	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	W5	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
	W6	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	W7	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
	E1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
	E2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	E3	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
	E4	0	0	0	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0	0
	E5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	E6	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
	E7	0	0	1	0	0	0	1	1	1	0	0	1	1	0	0	0	0	0	0	1	0
	F1	0	1	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
	F2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
	F3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
	F4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
	F5	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
	F6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	1
	F7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0

.

4.2. Construction of a Social Network Model

4.2.1. Visualization of Social Network Models

The Water–energy–food system is a dynamic system characterized by high correlation, complexity, and openness. To illustrate the interwoven state of the 21 factors, this study utilized the social network analysis software Ucinet to create a visual network based on the adjacency matrix of WEF nexus sustainability influencing factors. This approach visually represents the relationships among the influencing factors of WEF nexus sustainability using a network diagram, allowing for a preliminary analysis of the causal relationships among the factors (Figure 3). In the figure, nodes represent individual influencing factors, and the size of the squares represents the centrality, with larger squares indicating higher centrality. The numbers in the figure represent the centrality level, reflecting the degree to which the corresponding node influences other nodes in the network. The colors blue, green, and orange represent the influencing factors of the water, energy, and food subsystems, respectively. The connections between nodes represent the influence relationships among factors, with the direction of the arrows indicating the direction of influence transmission.

4.2.2. Calculation of Social Network Model Indicators

To further identify key influencing factors and the relationships among them, this study conducted a quantitative analysis of sustainability influencing factors by calculating centrality indicators. The sustainability network in this paper is a directed network. Based on the results obtained from social network analysis software, the specific centrality indicators are presented in

Table 3. Descriptive statistics of the WEF nexus sustainability network model indicators.

Number	Factors	Degree Centrality	Closeness Centrality	Betweenness Centrality
W1	Water supply	40.00	52.63	11.74
W2	Water demand	40.00	48.78	14.06
W3	Water resource utilization rate	20.00	48.78	7.08
W4	Water consumption per unit GDP	10.00	37.74	0.00
W5	Proportion of agricultural water consumption	20.00	45.46	1.56
W6	Total wastewater discharge	20.00	45.46	5.55
W7	Sewage treatment rate	25.00	51.28	6.48
E1	Energy supply	20.00	47.62	4.62
E2	Energy self-sufficiency rate	10.00	38.46	0.00
E3	Energy consumption per unit of GDP	10.00	31.25	0.53
E4	Industrial added value energy consumption	10.00	35.71	4.18
E5	Carbon emissions per unit of GDP	10.00	37.04	5.29
E6	The amount of industrial solid waste generated	20.00	50.00	16.39
E7	Technology investment as a percentage of GDP	35.00	52.63	28.94
F1	Proportion of grain crop sown area	20.00	41.67	4.27
F2	Per capita output of grain	15.00	40.00	4.28
F3	Grain output per unit area	35.00	52.63	21.61
F4	Proportion of effective irrigation area	15.00	44.44	0.79
F5	Burden of chemical fertilizers	10.00	37.74	0.53
F6	Mechanization level of agriculture	15.00	46.51	8.59
F7	Proportion of agricultural output value	10.00	35.09	0.88
	Total	410.00	920.91	147.37
	Maximum value	40.00	52.63	28.94
	Minimum value	10.00	31.25	0.00
	Standard deviation	9.87	6.44	7.49

.

4.2.3. Analysis of SNA Results

From Figure 3, it can be observed that there is a close interconnection of factors within and among the three major systems of water, energy, and food. A disturbance or change in one factor often triggers a cascading reaction throughout the entire system. The feedback loops among the three subsystems further intensify the complexity of WEF relationships. Only by considering the three subsystems as an integrated whole and paying close attention to their interactions can we realize the sustainable and coordinated development of water, energy, and food.

Table 3 describes the structural characteristics of the WEF nexus sustainability spatial network. Based on the analysis of various basic indicators, W1 (water supply), W2 (water demand), E7 (technology investment as a percentage of GDP), and F3 (grain output per unit area) exhibit the highest centrality. This indicates that these factors are situated at the center of the network diagram, making them more susceptible to influencing other factors or being influenced by others. They have the potential to disrupt the sustainability network and are, therefore, deemed important influencing factors in the WEF nexus sustainability network. W1 (water supply), E7 (technology investment as a percentage of GDP), F3 (grain output per unit area), W7 (sewage treatment rate), and E6 (the amount of industrial solid waste generated) possess the highest closeness centrality, indicating that these factors can control other factors more effectively. Improving and adjusting these factors is of paramount significance for the stable control of sustainability in the WEF nexus. In contrast, E3 (energy consumption per unit GDP) and F7 (proportion of agricultural output value) exhibit lower closeness centrality, suggesting their relative independence within the network. The factor with the highest betweenness centrality is E7 (technology investment as a percentage of GDP), indicating that this node serves as a crucial stopping point in the WEF nexus sustainability network, playing a bridging role.

From the comprehensive analysis of the above indicators, it can be concluded that six factors, namely W1 (water supply), W2 (water demand), W7 (sewage treatment rate), F3 (grain output per unit area), E7 (technology investment as a percentage of GDP), and E6 (the amount of industrial solid waste generated), exhibit high values across various indicators, classifying them as key influencing factors.

The directed graph clearly illustrates the interactions among factors, while centrality indicators reveal the closeness and control relationships among these factors. However, the hierarchical structure of these factors is not yet clear, making it challenging to determine which of these sustainability factors are deep-seated fundamental and which are superficial. Therefore, this study uses the ISM method to construct a multi-level hierarchical explanatory structure model of sustainability factors. This method intuitively reveals the hierarchical relationship of influencing factors and identifies the underlying fundamental factors, thus providing constructive suggestions for promoting the sustainable development of the urban WEF nexus.

4.3. ISM Analysis

4.3.1. Calculate the Reachability Matrix

The reachability matrix is obtained from the adjacency matrix through Boolean operations, allowing for the identification of influence paths between factors beyond the adjacency matrix. Following the computational rules [57], the number of iterations in this study is set to 5, resulting in the reachability matrix M, as shown in

Table 4. WEF nexus sustainability impact factors’ reachability matrix M (n = 5).

		W1	W2	W3	W4	W5	W6	W7	E1	E2	E3	E4	E5	E6	E7	F1	F2	F3	F4	F5	F6	F7
M=	W1	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W2	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W3	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W4	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W5	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W6	1	1	1	1	1	1	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	W7	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	E1	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0
	E2	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
	E3	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0
	E4	1	1	1	1	1	1	1	1	1	1	1	1	1	0	1	1	1	1	0	0	0
	E5	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
	E6	1	1	1	1	1	1	1	1	1	0	0	0	1	0	1	1	1	1	0	0	0
	E7	1	1	1	1	1	1	1	1	1	0	0	1	1	1	1	1	1	1	0	1	1
	F1	1	1	1	1	1	0	1	1	1	0	0	0	0	0	1	1	1	1	0	0	0
	F2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
	F3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0
	F4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	0	0	0
	F5	1	1	1	1	1	1	1	1	1	0	0	0	0	0	1	1	1	1	1	0	0
	F6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0	1	1
	F7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1

.

4.3.2. Hierarchical Division

In accordance with the ISM method for rule computation, the reachable set, antecedent set, and common set of each influencing factor are determined. During the process of hierarchical division, factors with identical reachable and intersection sets are identified as belonging to the same level. The already classified factors are then discarded, and the further division process is conducted solely based on the remaining factors until all factors are correctly categorized. Through the associative relationships among factors in the reachable matrix, a strong correlation is identified among W1, W2, W3, W4, W5, W7, and F1. Therefore, this study consolidates W1, W2, W3, W4, W5, and W7 into water supply and demand structure and water environment. Finally, a hierarchical structural model of the influencing factors related to urban WEF nexus sustainability is obtained, where L indicates the level in the figure (Figure 4).

4.3.3. Analysis of ISM Results

From Figure 2, it is evident that the urban WEF nexus sustainability influencing factors form a hierarchical structure with seven levels. The process of sustainable development in the WEF nexus is influenced by various factors, and there are direct or indirect relationships among these factors. These relationships not only have a direct impact on the sustainability outcomes but also result in mutual influences through cascading effects. Such interplay forms a network structure of factors, exerting long-term effects on the sustainability of the WEF nexus.

L1 and L2 represent surface-level factors (E1-E3, E5, F2, F3, and F7), which are the foundational elements in the network, typically manifesting as the first indicators of fluctuations in the sustainability network. As observed in Figure 4, surface-level factors primarily manifest in the energy and food subsystems. For instance, E1 (energy supply) and E2 (energy self-sufficiency rate) are critical for energy security. Increasing the energy supply and improving the self-sufficiency rate can reduce dependence on external energy sources, thereby ensuring the sustainability of the urban energy system. Moreover, water treatment, irrigation, and grain processing all depend on the stable supply of energy, so energy security directly affects the effective utilization of water resources and the sustainability of grain production. E3 (energy consumption per unit of GDP) and E5 (carbon emissions per unit of GDP) reflect not only a city’s resource efficiency and environmental friendliness. High energy consumption and carbon emissions signify excessive resource depletion and environmental pollution, and hence, reducing energy consumption per unit GDP is also a key goal of sustainable development. Surface-level factors in the food subsystem primarily concern a city’s food production capacity. Take, for example, F2 (per capita output of grain) and F3 (grain output per unit area), which are crucial for food security and agricultural production efficiency, playing a vital role in meeting food demand. F7 (proportion of agricultural output value) reflects the importance of agriculture in the overall economy of the city, directly related to food production. A higher share of agriculture indicates a greater emphasis on agricultural development by the government, favoring the sustainability of the food supply.

L3–L6 represent intermediate-level factors (W1–W7, E6, F1, and F4–F6), which are influenced by both the bottom-level factors and, in turn, influence the surface-level factors. There are also interactions among these intermediate-level factors. First, consider W1 (water supply), W2 (water demand), W3 (water resource utilization rate), W4 (water consumption per unit GDP), and W5 (proportion of agricultural water consumption) reflect the management and efficiency of water resources. Rational resource utilization can alleviate competition pressure for water resources in energy and food production, while an irrational supply-demand structure can lead to excessive resource consumption or waste. Secondly, F1 (proportion of grain crop sown area), F4 (proportion of effective irrigation area), and F6 (mechanization level of agriculture) are critical factors in the agricultural sector and serve as driving and supporting factors for WEF nexus sustainability. The proportion of grain crop sown area and proportion of effective irrigation area determine the scale and quality of food production, sustaining the sustainability of food supply. The level of agricultural mechanization represents the modernization of agricultural production, which can reduce labor burden and enhance production efficiency but also requires moderate energy consumption, necessitating a balance under sustainability considerations. Next, W6 (total wastewater discharge) and W7 (sewage treatment rate) are related to wastewater treatment and management. High wastewater discharge can lead to the overuse of water resources and water quality degradation, posing threats to agricultural water use and energy production. A high sewage treatment rate helps reduce water pollution, improve the quality of irrigation water in farmlands, and simultaneously reduce environmental burdens, favoring the sustainability of energy production and food security. Finally, E6 (the amount of industrial solid waste generated) and F5 (the burden of chemical fertilizers) primarily impact nexus sustainability in an environmental context. On the one hand, the substantial generation of industrial solid waste threatens water quality and accessibility, increasing the burden of water resource treatment and purification. On the other hand, excessive use of fertilizers can lead to water pollution and ecosystem damage, further threatening the sustainability of water resources and imparting negative impacts on energy production and usage.

L7 represents the bottom factors (S11, S14), which are the most fundamental elements in the network and often have a pervasive impact on overall sustainability. To enhance the overall sustainability of the network, efforts should be directed towards the bottom factors. The results indicate that E4 (industrial added value energy consumption) and E7 (technology investment as a percentage of GDP) are fundamental factors for measuring WEF nexus sustainability. High industrial value-added energy consumption typically implies the extensive use of energy and water resources in the production process, ultimately leading to environmental pollution and resource depletion, exerting negative impacts on sustainability. However, technology investment determines the mode of technological progress, supporting the development of clean and efficient production technologies in cities, which can reduce resource consumption and environmental burdens, promoting the sustainability of the WEF nexus. Therefore, the performance of these two factors lies in their collective influence on shaping a city’s sustainability efforts in resource utilization and environmental protection, playing a crucial role in balancing dependencies on water, energy, and food resources.

4.4. Comprehensive Analysis of SNA-ISM

Through the comprehensive analysis of SNA-ISM, it is evident that the fundamental driving factor identified by ISM, E7 (technology investment as a percentage of GDP), is also a crucial factor computed by SNA. The intermediate factors obtained through ISM analysis exhibit relatively high measures of closeness centrality and intermediary centrality, indicating susceptibility to influence from other factors and simultaneous regulatory effects on direct factors. Among them, W1 (water supply), W2 (water demand), W7 (sewage treatment rate), and E6 (the amount of industrial solid waste generated) are identified as pivotal factors. The internal closeness centrality indicators for surface-level influencing factors, as derived from ISM, are higher compared to the external closeness centrality indicators. This suggests susceptibility to influence from other factors while exhibiting weaker regulatory capabilities over other factors. Notably, F3 (grain output per unit area) emerges as a critical factor in this regard.

5. Discussion and Suggestions

Factor identification and analysis are crucial for explaining and quantifying the interactive relationships of WEF nexus sustainability factors, which is significant for the advancement of WEF nexus research. Based on the conceptual framework of urban WEF nexus sustainability, this paper follows the steps of the SNA and ISM processes to identify representative factors and their interconnections, establishing a hierarchical structure of factors influencing urban WEF nexus sustainability through matrix decomposition. To this end, identifying influencing factors and recruiting system science experts are key to exploring WEF nexus sustainability issues. This paper identifies 21 factors influencing urban WEF nexus sustainability based on a literature review and expert opinions, and analyzes the mechanisms of influence among these factors. It concludes that the most fundamental and critical elements affecting urban WEF nexus sustainability are technology investment as a percentage of GDP and industrial-added value energy consumption. Following this, the amount of industrial solid waste generated, total wastewater discharge, sewage treatment rate, water supply, and water demand are also highlighted as significant factors. Lastly, the rest of the factors need to be improved on the basis of key factors to make progress and breakthrough.

In Figure 4, L7 is the underlying factor highlighting the priority order and actions to be taken in urban nexus governance among the 21 interwoven factors [9]. E4 (industrial added value energy consumption) is one of the fundamental factors affecting urban WEF nexus sustainability. Energy is an indispensable resource in the supply, distribution, and waste treatment processes of urban resources [58], and the energy consumption of industrial added value indicates the dependency of industrial production on energy and also reflects energy efficiency. The sustainability of the energy subsystem mainly depends on energy resource endowment and self-sufficiency rate, energy structure, and efficiency [4]. Nevertheless, energy issues are not on par with technological investment, which can promote technological innovation and system integration and is widely regarded as a key step for cities to achieve future sustainable development [59]. Additionally, W1 (water supply), W2 (water demand), W7 (sewage treatment rate), and E6 (the amount of industrial solid waste generated) are considered key factors. Water resource sustainability is crucial for ensuring residents’ livelihoods, agricultural irrigation, and industrial production. Given the increasing water demand, wastewater management needs to shift from “treatment and disposal” to “reduction, reuse, recycling, and resource recovery” [60].

Based on the research findings, this paper proposes the following recommendations, aiming to provide a theoretical basis for promoting the sustainable development of urban water, energy, and food.

As a crucial engine for economic development, cities possess a special strategic importance regarding technological investment. For instance, by leveraging big data, the Internet of Things (IoT), and artificial intelligence (AI) technologies, cities can develop an integrated smart system that encompasses functions for managing water resources, energy, and food. This system would enable real-time monitoring and analysis of the urban water–energy–food (WEF) nexus usage, prediction of demand changes, and optimization of resource allocation. Through such a smart system, governments and businesses can formulate policies and management strategies with greater precision, thereby enhancing resource efficiency and reducing waste. Moreover, establishing a green financial system could provide funding support for sustainable WEF development projects. This might involve introducing financial instruments such as green bonds and green funds to attract social capital investment in sustainable development areas. Governments could incentivize financial institutions to increase their investment in green projects by offering tax breaks, guarantees, and other policy supports. Lastly, interdisciplinary research should be encouraged to integrate advanced technologies in the fields of water resources, energy, and food, thereby developing more efficient and environmentally friendly comprehensive solutions to drive technological innovation and integration.

(1)

Optimizing energy efficiency and reducing energy consumption in industrial processes are of crucial importance for achieving sustainable development of urban resources and the environment. Firstly, the government should actively guide businesses to adopt more efficient and cleaner production technologies, such as smart manufacturing, energy-saving equipment, and clean production processes. Financial incentive measures can be provided to support this process, encouraging businesses to invest in the research and application of energy-saving and environmentally friendly technologies. Secondly, although countries around the world have made some progress in the field of renewable energy, there is still a reliance on coal as a primary energy source. The high pollution and carbon emissions from coal have many adverse effects on the environment and climate change. To address this, the government should support the development of renewable energy, such as solar, wind, and hydropower, and strengthen the construction of energy storage and distribution systems to ensure a stable supply of renewable energy. Finally, the government should establish a strict energy management system, monitor the energy usage of businesses, and set energy efficiency standards and guidelines. Incentives can be given to businesses that meet the standards, while penalties can be imposed on those that do not to encourage businesses to pay more attention to energy conservation and emission reduction.

(2)

Promoting the circular economy model in the WEF domain involves viewing waste as a resource and utilizing technological innovation to achieve waste reduction, resource utilization, and harmlessness. For instance, agricultural waste can be converted into biomass energy by harnessing agricultural residues (such as straw, animal manure, etc.) for biomass energy development and utilization, such as biomass power generation and biomass gasification. This approach not only reduces agricultural waste emissions but also provides clean energy for rural areas. Similarly, industrial wastewater can be treated and reused for agricultural irrigation. Through advanced treatment processes to remove harmful substances, industrial wastewater can meet agricultural irrigation water quality standards before being used for irrigation. This practice not only reduces water consumption but also mitigates the environmental impact of wastewater discharge. Overall, this circular economy model can reduce dependence on primary resources and mitigate environmental pollution.

(3)

Each city should optimize resource allocation according to its specific circumstances to achieve a balance between water supply and demand. For cities with a high level of coordinated development, we should optimize the industrial layout to give full play to their resource advantages. This involves upgrading and transforming high-energy and high-water-consuming industries while actively promoting the development of low-energy consumption and environmentally friendly industries. In contrast, cities with a lower level of coordinated development should expedite the implementation of land fallowing policies, intensify research and development of agricultural water-saving technologies, promote efficient water-saving irrigation, and restrict or reduce high-water-consuming energy projects. Additionally, cities should diversify their water resource supply, such as rainwater collection, wastewater treatment and reuse, groundwater and river water sources, so as to reduce the dependence on a single water source. Simultaneously, establishing a scientific water resource management system, including water resource planning, water use permit systems, and emergency water resource dispatch mechanisms, is crucial to ensure the sustainable supply of water resources.

6. Conclusions and Perspective

Research on tracking the sustainability of the WEF nexus at the urban level is of paramount significance for constructing sustainable cities. This study comprehensively analyzed the critical influencing factors and hierarchical relationships of urban WEF nexus sustainability based on the SNA-ISM model, enriching the relevant research on nexus relationships. The research results show that optimizing technological investment and energy consumption of industrial-added value are core strategies for promoting the sustainable development of urban WEF nexus. Additionally, balancing water supply and demand and comprehensive management of waste pollutants are also driving and supporting factors influencing the sustainability of urban WEF nexus. Drawing from the research results, this paper proposes corresponding strategies and recommendations, providing a reference for promoting the sustainable development of urban WEF systems. The suggestions in this study aim to facilitate sustainable development in urban water, energy, and food through technological innovation and efficient resource utilization, thereby reducing environmental pressure and enhancing the quality and sustainability of economic growth. Successful implementation requires collaboration and efforts from the government, businesses, and various sectors of society to ensure the achievement of urban water–energy–food sustainable development goals while safeguarding the environment and maintaining ecological balance.

However, there are also limitations and deficiencies. Firstly, the study selected major factors influencing urban WEF nexus sustainability but overlooked the impact of socio-economic development, resident income, and government regulation on the sustainable development of urban WEF nexus. Future research should delve deeper into these aspects. Secondly, building upon the findings of this study, future research could combine SNA and ISM with system dynamics models or multi-equations models to quantitatively present the interactive behavior of the system. Alternatively, further exploration of the sustainable development levels of urban WEF systems under different development scenarios, such as environmental and resource scenarios, would help propose targeted improvement measures. Finally, this study focuses on the sustainable linkage structure between urban water, energy, and food (WEF) systems, but its methodology, analytical framework, and findings have wide applicability. For example, the WEF nexus sustainability factor framework and analytical methods (such as SNA and ISM) proposed in this study can be applied to other environmental resource management systems, such as urban waste treatment, air quality management, and biodiversity conservation. By identifying the key influencing factors and interactions in these systems, more comprehensive and effective environmental management strategies can be developed. In addition, this study focuses only on urban WEF systems, but expanding the research scale to cross-regional levels in the future may yield new findings. By adopting the WEF nexus analytical framework, policymakers can more systematically consider the trade-offs and synergies between different resource sectors and formulate more scientifically sound sustainable development plans.