Dynamics and Determinants of China’s Inter-Provincial Staple Food Flow Resilience: A Network Perspective

Abstract

Global climate change results in increasing challenges to the structural security of China’s food system, while pronounced spatial heterogeneities in provincial production and consumption intensify the risk of supply-demand imbalance. This study examines the resilience of China’s inter-provincial staple food flow network from a systemic perspective and identifies its key drivers. Inter-provincial food flows are first inferred using a cost-minimization optimization model. Network resilience is then evaluated by integrating complex network analysis with ecological network resilience theory. Finally, econometric analysis is applied to quantify the relative contributions of multiple structural factors to resilience dynamics. The results reveal an overall decline in the resilience of aggregated staple food, alongside persistently low resilience in soybeans network, indicating heightened structural vulnerability. Substantial heterogeneity is observed across staples in both resilience levels and underlying mechanisms. In general, greater connectivity and diversity of flow paths enhance system resilience, although this effect is markedly weaker for soybeans due to concentrated and import-dependent supply structures. By explicitly linking flow, network structure, and resilience, this study provides system-level insights into the functioning of inter-provincial food flow networks. The proposed analytical framework offers a transferable tool for assessing interregional food flow resilience and supports evidence-based strategies for validating system robustness under uncertainties.

1. Introduction

Food security has become an increasingly critical challenge under the pressures of global environmental and socio-economic change. According to the State of Food Security and Nutrition in the World 2024, global hunger has remained high for three consecutive years. In 2023, about 733 million people, roughly one in every eleven individuals, were undernourished, posing a serious obstacle to achieving the United Nations’ Sustainable Development Goal 2 (SDG, Zero Hunger) [1]. Historically, the vulnerability of the global food system has been repeatedly exposed by crises. In the 1970s, the oil crisis and natural disasters triggered a global food crisis as major exporters such as the United States reduced grain exports, causing severe supply fluctuations [2]. In the 21st century, global food security remains vulnerable. The COVID-19 pandemic in 2020 disrupted supply chains, pushing nearly 12 percent of the world’s population into severe food insecurity, an increase of 148 million people from 2019 [3]. In 2022, the Russia-Ukraine conflict further disrupted grain exports, prompting 23 countries to implement export restrictions, including 12 with wheat export bans [4].

Inter-provincial food flow faces challenges in many countries, and spatial mismatches between food supply and demand exert significant pressure on food security [5]. First, disruptions in inter-provincial food flows are a widespread phenomenon. Second, the spatial distribution of food production capacity and consumption demand varies considerably across provinces. As a result, structural mismatches have emerged between major producing and consuming regions, with some areas experiencing long-term surpluses while others remain persistently dependent on external supply. Such inefficiencies in inter-provincial flow mechanisms can easily cause localized or regional food crises [6]. In addition, inadequate logistics infrastructure further constrains the efficiency of food flows. In many developing countries and regions, transportation and storage systems exhibit evident limitations. Long transport distances increase losses, while food waste along supply chains remains severe, undermining the stability and security of food supply [7].

Despite China’s relatively limited natural resource endowment, the total food production has continued to rise in recent years, helping maintain the overall stability of national food security. However, as the center of gravity of food production continues to shift northward, China increasingly faces pronounced challenges related to regional vulnerability and sustainability [6,8]. On the one hand, major food production areas are concentrated in northern regions where the environmental carrying capacity is relatively weak, thereby intensifying pressures on water and soil resources and heightening ecological risks [8]. On the other hand, the growing frequency of extreme weather events has substantially increased the vulnerability and uncertainty of agricultural production systems [9]. Facing the complex and evolving environment, inter-provincial food flows face structural imbalances and multiple potential risks, posing new challenges to safeguarding national food security. Strengthening infrastructure development and improving the efficiency of inter-provincial food flow have therefore become urgent priorities. These measures are essential for reinforcing the country’s internal food redistribution mechanisms and enhancing the resilience of the food flow system.

A growing literature has focused on inter-provincial food flows in China. Dalin et al. [10] provided an early analysis of the role of international and inter-provincial food trade in shaping China’s agricultural water use and food supply. Zhuo et al. [11] investigated virtual water flows associated with inter-provincial maize and pork trade, while Zhai et al. [12] further analyzed the flow patterns of inter-provincial grain-related virtual water and their associated environmental impacts. Zuo et al. [13] estimated the carbon emissions associated with inter-provincial grain transportation in China between 1990 and 2015. In addition, Ji et al. [14] examined the impact of inter-provincial trade on economic growth using a two-way fixed-effects model, and Wang et al. [15] compared the comprehensive benefits of virtual water flows in grain trade from resource, economic, and environmental perspectives. More recently, Luo et al. [16] developed a comprehensive dataset of inter-provincial physical food flows in mainland China covering the period 2000–2022, encompassing 15 key plant-based and animal-based food products. Despite these advances, research explicitly focusing on the resilience of inter-provincial staple food flows in China remains relatively limited.

Resilience assessment methods in existing research primarily include ecological network resilience, statistical indicator methods, and recovery-curve analysis. Ulanowicz et al. [17] introduced an information theory approach that evaluates overall system resilience by quantifying two core attributes: efficiency and redundancy. Kummu et al. [18] identified two key principles through which global trade enhances food system resilience: maintaining diversity and managing connectivity. Blessley and Mudambi [19] employed a statistical indicator approach to systematically assess the stability of food supply chains during the trade war and the COVID-19 pandemic. From a food security perspective, Béné et al. [20] developed a comprehensive indicator framework for food system resilience and examined strategies for data acquisition. Bruneau et al. [21] proposed a conceptual framework for assessing community resilience, defining robustness and rapidity as outcome dimensions and redundancy as enabling capacities. They introduced recovery-curve analysis as a unified quantitative tool applicable to a wide range of socio-ecological systems. Building on the Pressure-State-Response framework, Wu et al. [22] incorporated recovery-curve analysis to identify critical thresholds in land use change and developed a resilience assessment model that captures the nonlinear effects of multiple driving factors.

Ecological network resilience, as a key approach for assessing a system’s capacity to withstand external shocks, has made substantial progress in both theoretical foundation and empirical application. Rooted in Holling’s seminal concept of ecological resilience, this approach emphasizes a system’s ability to preserve its structure and function in the face of disturbances [23]. Tendall et al. [24] were the first to introduce the notion of food system resilience, defining it as the capacity of food systems and their multi-level components to ensure the sufficient, appropriate and accessible of food for all people. In China, ecological network resilience has also continued to deepen, with research gradually shifting from qualitative assessments to multi-indicator quantitative evaluation. Zeng et al. [25] developed a coupled model that integrates a physical network with an information and decision risk network, enabling the assessment of system robustness and resilience dynamics under various failure scenarios. Drawing on the concept of ecological security patterns, Yang et al. [26] constructed a multi-factor evaluation framework and developed an ecological network for the Loess Plateau using a gravity-model approach. Through network robustness simulations across multiple scenarios, they examined resilience evolution processes and identified the influence intensity and spatial reach of core nodes.

This paper develops a resilience assessment framework for China’s inter-provincial staple food flow network (CISFN) and identifies its resilience dynamics and key determinants. First, a cost-minimizing mathematical programming model is employed to derive the flow relationships of various staples among provinces and municipalities (hereafter collectively referred to as “provinces”). Second, the CISFN is constructed for the period 1998–2022, and its resilience evolution is examined using complex network analysis combined with ecological network resilience theory. Third, key drivers of resilience are identified through econometric approaches, and the relative contributions of major components to resilience changes are quantified. The proposed model provides a rigorous quantitative framework for analyzing and evaluating the resilience of different staples within China’s inter-provincial food flow system under external shocks. It also plays an important foundation for understanding the regional characteristics and spatial heterogeneity of food system resilience in China.

Based on the above analysis, the main novelty and contribution of this paper can be summarized as follows. (1) Incorporation of international import in staple-specific flow estimation. Due to the lack of publicly available inter-provincial food flow data in China, this study employs a mathematical programming approach to estimate provincial flows. During this process, imports and exports of each staple are incorporated, ensuring more accurate and realistic flow estimations. (2) Network-based assessment of CISFN resilience. This study evaluates the resilience of the CISFN from the systemic perspective. By adopting a network-oriented resilience framework, it provides a comprehensive and systematic understanding of inter-provincial food flow, thereby filling a research gap in resilience assessment within China’s domestic food flow system. (3) Identification and quantification of resilience determinants across staples. The study empirically identifies the key driving factors of CISFN resilience and reveals heterogeneity across staples. Using econometric techniques, it further quantifies the relative contributions of these determinants, offering deeper insights into the resilience mechanisms of various staples.

The remainder of this paper is organized as follows. Section 2 introduces the study area and data sources, and describes the current status of staple food production and consumption across Chinese provinces. Section 3 presents the materials and research methods. Section 4 reports the main results, including the evolution of network structure and resilience, as well as the identification of key driving factors. Section 5 discusses the findings and provides policy recommendations. Finally, the conclusions of the study are summarized in Section 6.

2. Study Area and Data

2.1. Research Framework

The research framework for investigating the resilience dynamics and determinants of the CISFN is illustrated in Figure 1. First, this study reconstructs inter-provincial staple food flows by assuming that staple foods are transported from surplus provinces, where production exceeds consumption, to deficit provinces, where consumption exceeds production. Provincial production and consumption are linked through an optimization-based cost-minimization model, yielding a set of inter-provincial flow matrices that capture the spatial organization of staple food flow. Second, network resilience is quantified by integrating complex network analysis with ecological network resilience theory. Provinces are represented as nodes and food flows as weighted edges to construct the CISFN. Resilience is characterized through key structural properties, including interdependence, concentration, and independence of nodes and flows, which are further synthesized into efficiency and redundancy components. Together, these dimensions provide a systemic measure of network resilience. Finally, resilience dynamics and determinants are examined. Temporal variations in resilience are analyzed to identify long-term trends and crop-specific patterns, while econometric analysis is applied to quantify the relative contributions of multiple network topology indicators. In addition, model validation and sensitivity analysis are conducted using alternative friction scenarios to assess robustness. This integrated framework enables a comprehensive assessment of CISFN resilience under structural and external uncertainties.

2.2. Study Area

This section provides an overview of the production and consumption patterns of five staple foods across China’s provinces. As one of the world’s largest agricultural producers, China has long faced enormous pressure to ensure the security of staple food structure. The coordination among production capacity, consumption patterns, and interprovincial flow plays a critical role in shaping the resilience of the national food system.

According to data from the National Bureau of Statistics, China’s major staple-producing and consuming provinces exhibit a pronounced spatial imbalance between supply and demand. Figure 2 presents the production patterns and composition of five staple foods across provinces in 2000, 2010, 2015, and 2020. The background color of the map represents the total production of aggregated staple foods. Spatially, the core production regions are concentrated in Northeast China, the North China Plain, and the middle and lower reaches of the Yangtze River, where rice and maize dominate in the northeast, wheat and maize in the north, and rice in the south. Over time, production capacity has expanded in the northern regions but declined in several southern provinces, reflecting pronounced regional heterogeneity. Northeast and North China have gradually become the main food outflow regions, whereas the economically developed southern coastal provinces increasingly rely on inflows from other regions. This spatial mismatch between production and consumption has increased the complexity of inter-provincial food circulation and deepened dependence on long-distance transportation, raising both logistics costs and systemic vulnerability [6]. Any disruption in production or transport may severely affect the stability of the national food supply. Furthermore, the trend toward monoculture in several provinces has exacerbated systemic risks [8]. It reduces agro-ecosystem resilience and amplifies the impacts of pests, diseases, and extreme weather events, potentially triggering regional shortages and threatening overall food security.

The spatial heterogeneity of food production and consumption increases the complexity of inter-provincial circulation in China. Figure 3 illustrates the consumption and composition of five staple foods across provinces in 2000, 2010, 2015, and 2020. In general, urban agglomerations in the eastern coastal regions, such as the Yangtze River Delta and the Pearl River Delta, exhibit consumption levels that substantially exceed their local production capacities. These regions also show increasingly diversified consumption structures. In contrast, the central and western regions, despite their abundant production, display relatively lower consumption, reflecting their role as primary staple-supplying areas. The economically developed coastal provinces depend heavily on inflows from other regions [14]. Combined with the production patterns shown in Figure 2, a pronounced spatial mismatch between production and consumption emerges, forming a complex inter-provincial staple flow network between outflow and inflow regions. The efficient functioning of this network depends on a stable logistics system, disruptions in either production or logistics pose serious challenges to inter-provincial food flow [5]. Moreover, the rapid increase in demand for specific staple such as soybeans and maize has further deepened reliance on inflow, heightening food supply risks. Significant differences in consumption structures among provinces also reflect the diversity of dietary habits, economic levels, and cultural preferences across regions. Such heterogeneous demand imposes stricter requirements on flow paths and storage conditions, thereby increasing the coordination difficulty and operational complexity of inter-provincial food flow.

2.3. Data Sources

This section focuses on the inter-provincial flows of staple foods in China. However, data on staple flows between provinces are not publicly available. Therefore, this study indirectly infers the inter-provincial flow patterns based on provincial production and consumption data [11]. All data were obtained from authoritative and publicly available sources. The provincial production and consumption data were derived from the China Statistical Yearbook, while the FAO Statistical Database and China Customs Statistics were used to verify the national import and export volumes of staple foods. Considering data availability and consistency, the study covers the period from 1998 to 2022. Furthermore, to facilitate comparison among different staples, all fresh potatoes were converted into standard grain equivalents using the conventional conversion ratio of five kilograms of fresh potatoes to one kilogram of standard grain production [27].

This study focuses on rice, wheat, maize, soybeans, and potatoes as the research objects, given their representativeness and complementarity in both global and Chinese food security systems [28]. Together, these five staples form a comprehensive nutritional foundation, providing carbohydrates, proteins, and various micronutrients [29]. Spatially, they are distributed across diverse climatic and ecological zones, reflecting distinct geographical characteristics and environmental adaptability. In terms of consumption, their functions vary considerably, ranging from staple food and feed to industrial processing. Therefore, analyzing these five staples allows for a systematic examination of the structural characteristics and resilience differences across CISFNs.

3. Materials and Methods

3.1. Construction of the CISFN

This section describes the construction method of the CISFN. Due to the limited availability of inter-provincial flow data for different staples, such information is often not directly accessible. Consequently, inter-provincial food flow patterns are commonly inferred through mathematical programming models based on provincial production and consumption data [10]. The core idea is to balance supply and demand across provinces and, by incorporating factors such as transportation costs and spatial distance, to reasonably estimate inter-provincial food transfer volumes.

Considering that transportation cost is a primary factor influencing inter-provincial staple food flows [12,30], this study sets the minimization of total transportation costs between provinces as the objective function [11,15]. Based on provincial-level production and consumption data, the mathematical programming model for inter-provincial staple flow is formulated as follows:

$$\begin{array}{c}\mathit{min}{\displaystyle \sum _{i=1}^{N^m\left(t\right)}}{\displaystyle \sum _{j=1}^{31-N^m\left(t\right)}}{c}_{i,j}^m\left(t\right)·w_{i,j}^m\left(t\right),\\ s.t.\left\{\begin{array}{c}{\displaystyle \sum _{j=1}^{31-N^m\left(t\right)}}{w}_{i,j}^m\left(t\right)\le s_i^m\left(t\right),\\ {\displaystyle \sum _{i=1}^{N^m\left(t\right)}}{w}_{i,j}^m\left(t\right)={{(1+\theta }_{i,j}^m)·d}_j^m\left(t\right),\\ w_{i,j}^m\left(t\right)\ge 0.\end{array}\right.\end{array}$$

(1)

Here, $i$ denotes a surplus province, $m$ represents the staple type, and $N^m\left(t\right)$ indicates the number of surplus provinces for staple $m$ in year $t$. $j$ refers to a deficit province, and $31-N^m\left(t\right)$ represents the number of deficit provinces for staple $m$ in year $t$. $w_{i,j}^m\left(t\right)$ denotes the flow volume of staple $m$ from surplus province $i$ to deficit province $j$ in year $t$, while $c_{i,j}^m\left(t\right)$ represents the basic transportation cost per unit volume (yuan/ton). ${\theta }_{i,j}^m$ denotes the logistical friction coefficient induced by infrastructure conditions, capacity constraints, and transportation time, indicating that higher effective demand is required to meet a given level of need. $s_i^m\left(t\right)$ indicates the total surplus of surplus province $i$ for staple $m$ in year $t$, and $d_j^m\left(t\right)$ denotes the total deficit of deficit province $j$ for the same year.

Furthermore, this study assumes that inter-provincial staple flows occur through provincial capital cities, and the minimum unit transportation cost between these capitals is adopted as the transport cost [11,12]. Consequently, the inter-provincial flow results represent an optimal, cost-minimizing outcome rather than an empirically observed logistics system. The choice to model flows between provincial capitals is because this abstraction reflects a theoretical network rather than the full complexity of real logistics [10]. Provincial capitals serve as representative provincial hubs due to their administrative and logistical centrality, as well as the availability of consistent province-level data [12]. This simplified optimal network enables us to focus on the structural characteristics and resilience patterns of the CISFN. The provinces and their corresponding capital cities involved in inter-provincial staple flows are listed in

Table A1. The serial numbers and names of China’s 31 provinces and municipalities in this study.

Number	Province	Provincial Capital
1	Beijing	Beijing
2	Tianjin	Tianjin
3	Hebei Province	Shijiazhuang
4	Shanxi Province	Taiyuan
5	Inner Mongolia Autonomous Region	Hohhot
6	Liaoning Province	Shenyang
7	Jilin Province	Changchun
8	Heilongjiang Province	Harbin
9	Shanghai	Shanghai
10	Jiangsu Province	Nanjing
11	Zhejiang Province	Hangzhou
12	Anhui Province	Hefei
13	Fujian Province	Fuzhou
14	Jiangxi Province	Nanchang
15	Shandong Province	Jinan
16	Henan Province	Zhengzhou
17	Hubei Province	Wuhan
18	Hunan Province	Changsha
19	Guangdong Province	Guangzhou
20	Guangxi Zhuang Autonomous Region	Nanning
21	Hainan Province	Haikou
22	Chongqing	Chongqing
23	Sichuan Province	Chengdu
24	Guizhou Province	Guiyang
25	Yunnan Province	Kunming
26	Tibet Autonomous Region	Lhasa
27	Shaanxi Province	Xi’an
28	Gansu Province	Lanzhou
29	Qinghai Province	Xining
30	Ningxia Hui Autonomous Region	Yinchuan
31	Xinjiang Uygur Autonomous Region	Urumqi

. The minimum unit transportation costs between provinces are derived from Gao et al. [31], providing the fundamental data support for constructing the CISFN in subsequent analyses.

Finally, by using China’s 31 provinces as nodes and the inter-provincial staple food flows as edges, the CISFNs can be constructed as follows:

$$G^m\left(t\right)=\left(V^m\left(t\right),E^m\left(t\right)\right),$$

(2)

where $G^m\left(t\right)$ refers to the CISFN of staple $m$ in year $t$, $V^m\left(t\right)$ denotes the set of provinces participating in the flows of staple $m$ in year $t$, and $E^m\left(t\right)$ represents the set of directed flows of staple $m$ in the same year. In the CISFN, the total number of nodes participating in inter-provincial staple flows is denoted by $n^m\left(t\right)$, and the total number of edges by $e^m\left(t\right)$.

Accordingly, the adjacency matrix of staple $m$ in year $t$ is defined as $A^m\left(t\right)$, where the element $a_{i,j}^m\left(t\right)$ equals 1 if there exists a directed flow from province $i$ to province $j$ in year $t$, and 0 otherwise. Since the flows are weighted, a directed weighted matrix $W^m\left(t\right)$ is further defined, where the element $w_{i,j}^m\left(t\right)$ in Equation (1) represents the actual flow (in 10⁴ tons) of staple $m$ from province $i$ to $j$ in year $t$.

To examine the robustness of inter-provincial flow patterns under varying logistical conditions, we construct four transportation friction scenarios representing progressively increasing levels of network disruption (

Table 1. Transportation friction scenario design.

Scenario	Friction Value	Interpretation
S0: Baseline	${\theta }_{i,j}^m=0$	Idealized case with only basic transportation costs and no additional logistical frictions
S1: Low friction	${\theta }_{i,j}^m=0.1$	Well-developed transportation infrastructure with minor logistical frictions, close to baseline costs
S2: Medium friction	${\theta }_{i,j}^m=0.2$	Degraded road conditions and constrained transport capacity, leading to moderate logistical frictions
S3: High friction	${\theta }_{i,j}^m=0.3$	Severe disruptions such as major disasters or extreme congestion, resulting in substantial logistical frictions

). For each scenario, the optimization model is solved independently, yielding a set of friction-adjusted flow matrices that allow systematic comparison of flow reallocation and route deviations across assumptions. Unless otherwise noted, all main results presented in this paper are based on the baseline scenario, while the alternative scenarios are used to assess the stability and sensitivity of the inferred flow patterns.

3.2. Topological Structure of CISFNs

This section focuses on identifying and quantifying the internal structural determinants of the CISFNs. Ten fundamental topological indicators are employed to systematically characterize the network structure across three dimensions: node, edge, and overall network levels [32]. These indicators provide a comprehensive framework for examining the relationship between network topology and system resilience.

3.2.1. Degree and Weighted Degree

The in-degree $k_i^{m,in}\left(t\right)$ and out-degree $k_i^{m,out}\left(t\right)$ of province $i$ in year $t$ represent the number of provinces connected to it as inflow and outflow partners for staple $m$, respectively. The specific formulas are:

$$\left\{\begin{array}{c}{k}_i^{m,in}\left(t\right)={\displaystyle \sum _{j=1}^{n^m\left(t\right)}}{a}_{j,i}^m\left(t\right)\\ k_i^{m,out}\left(t\right)={\displaystyle \sum _{j=1}^{n^m\left(t\right)}}{a}_{i,j}^m\left(t\right)\end{array}\right..$$

(3)

The total degree $k_i^m\left(t\right)$ of node $i$ in year $t$ is defined as the sum of its in-degree and out-degree, reflecting the diversity of its flow partners [33]. The average degree ${\stackrel{-}{k}}^m\left(t\right)$ of CISFNs in year $t$ represents the average number of flow partners across all provinces and is calculated as:

$${\overline{k}}^m\left(t\right)={\displaystyle \frac{1}{n^m\left(t\right)}}\sum _{i=1}^{n^m\left(t\right)}{k}_i^m\left(t\right),$$

(4)

where $n^m\left(t\right)$ denotes the number of provinces participating in the inter-provincial flow of staple $m$ in year $t$.

The inflow strength $S_i^{m,in}\left(t\right)$ of CISFNs represents the total inflow volume of province $i$ in year $t$, while the outflow strength $S_i^{m,out}\left(t\right)$ denotes its total outflow. They are given by:

$$\left\{\begin{array}{c}{S}_i^{m,in}\left(t\right)={\displaystyle \sum _{j=1}^{n^m\left(t\right)}}{w}_{j,i}^m\left(t\right)\\ S_i^{m,out}\left(t\right)={\displaystyle \sum _{j=1}^{n^m\left(t\right)}}{w}_{i,j}^m\left(t\right)\end{array}\right.,$$

(5)

where $w_{j,i}^m(t)$ and $w_{i,j}^m(t)$ denote the quantity of staple $m$ flowing from province $j$ to $i$ and from $i$ to $j$ in year $t$ respectively. The total strength $S_i^m(t)$ of node $i$ in year $t$ is defined as the sum of its inflow and outflow strengths, representing the total volume of staple flow passing through node $i$ [34], as shown in Figure 4.

Furthermore, the average weighted degree ${\stackrel{-}{S}}^m\left(t\right)$ represents the mean flow volume per province in CISFNs, calculated as:

$${\overline{S}}^m\left(t\right)={\displaystyle \frac{1}{n^m\left(t\right)}}\sum _{i=1}^{n^m\left(t\right)}{S}_i^m\left(t\right).$$

(6)

3.2.2. Clustering Coefficient and Network Density

The clustering coefficient measures whether provinces participating in inter-provincial food flows tend to form groups or communities within the network, reflecting the local interconnectivity among their neighboring nodes [35]. For a given province $i$ in year $t$, the clustering coefficient $C_i^m\left(t\right)$ is defined as the degree of interconnection among its flow partners, represented by the actual number of links $E_i^m\left(t\right)$ between them [32]. The mathematical expression is as follows:

$$C_i^m\left(t\right)={\displaystyle \frac{E_i^m\left(t\right)}{k_i^{m,in}\left(t\right)·\left(k_i^{m,in}\left(t\right)-1\right)+k_i^{m,out}\left(t\right)·\left(k_i^{m,out}\left(t\right)-1\right)}},$$

(7)

where $E_i^m\left(t\right)$ denotes the actual number of links among all flow partners of province $i$, and $k_i^{m,in}\left(t\right)$ and $k_i^{m,out}\left(t\right)$ represent its in-degree and out-degree, respectively.

The average clustering coefficient ${\stackrel{-}{C}}_i^m\left(t\right)$ is defined as the mean of all provinces’ clustering coefficients, serving as an important indicator of the network’s overall cohesiveness [36]. A higher average clustering coefficient generally indicates that provinces in the CISFN tend to form more tightly connected groups or communities, exhibiting stronger internal connectivity. It is calculated as:

$${\overline{C}}_i^m\left(t\right)={\displaystyle \frac{1}{n^m\left(t\right)}}\sum _{i=1}^{n^m\left(t\right)}{C}_i^m\left(t\right).$$

(8)

The network density represents the degree of interconnectedness among provinces participating in the CISFN [37]. It is defined as the ratio of the actual number of links to the maximum possible number of links. For the CISFN of staple $m$ in year $t$, the network density is calculated as:

$${\mathrm{∆}}^m\left(t\right)={\displaystyle \frac{2l^m\left(t\right)}{n^m\left(t\right)\left(n^m\left(t\right)-1\right)}},$$

(9)

where $l^m\left(t\right)$ denotes the actual number of links in the CISFN of staple $m$ in year $t$, reflecting the diversity of flow paths. The value of network density ranges from 0 to 1, where 0 indicates the absence of any connections in the network, and 1 indicates a fully connected system.

3.2.3. Average Path Length and Network Diameter

In the CISFN, the path length measures the degree of separation between provinces and serves as an important indicator of the network’s overall structural characteristics [35]. For a given year $t$, the path length between provinces $i$ and $j$ is defined as the minimum number of links required to connect them, i.e., their shortest distance.

The average path length of the CISFN represents the mean distance between any two provinces and is calculated as follows:

$$L^m\left(t\right)={\displaystyle \frac{1}{2n^m\left(t\right)(n^m\left(t\right)-1)}}\sum _{1\le i<j\le n^m\left(t\right)}{d^m}_{i,j}\left(t\right),$$

(10)

where $d_{i,j}^m(t)$ denotes the shortest path length between provinces $i$ and $j$.

The network diameter describes the longest of all shortest paths between any two provinces in the CISFN [38] and is defined as:

$$D^m\left(t\right)=\underset{1\le i<j\le n^m\left(t\right)}{\mathit{max}}{d^m}_{i,j}\left(t\right).$$

(11)

Both the average path length and network diameter characterize the overall connectivity of the network and help identify provinces that play critical intermediary roles within the CISFN. Generally, shorter average path lengths and diameters indicate a more efficient flow system, reflecting stronger adaptability and resilience in response to external shocks.

3.2.4. Community Structure and Modularity

Exploring the relationship between community structure and resilience in the CISFN is of great importance. When the network is exposed to external shocks, its community structure can significantly influence the propagation path, scope, and speed of the disturbance, thereby directly affecting the overall resilience [39]. Networks characterized by node heterogeneity and incomplete connectivity often exhibit modular structures that naturally form communities [40]. Therefore, both the quality and quantity of community partitions are closely related to the resilience level of the CISFN.

In the CISFN, a community is defined as a group of provinces that are closely interconnected through staple-flow relationships. To identify community structures, this study employs the fast modularity optimization algorithm proposed by Blondel et al. [41]. Modularity serves as a key indicator for evaluating the quality of community divisions: the higher the modularity, the clearer and more distinct the community structure. Following Newman and Girvan [42], the modularity of the CISFN is defined as:

$$Q^m\left(t\right)={\displaystyle \frac{1}{2T^m\left(t\right)}}\sum _{i=1}^{n^m\left(t\right)}\sum _{j=1}^{n^m\left(t\right)}\left[\left(w_{i,j}^m\left(t\right)-{\displaystyle \frac{S_i^{m,in}\left(t\right)·S_i^{m,out}\left(t\right)}{2T^m\left(t\right)}}\right)\delta \left(c_i^m\left(t\right),c_j^m\left(t\right)\right)\right].$$

(12)

where $c_i^m(t)$ denotes the community to which province $i$ belongs in year $t$, and the indicator function $\delta (\cdot ,\cdot )$ equals 1 if $c_i^m(t)=c_j^m(t)$ and 0 otherwise. The value of $Q^m\left(t\right)$ ranges from –1 to 1; generally, a modularity value between 0.3 and 0.7 indicates a reasonable community partition.

3.3. Resilience Quantification of the CISFN

This section introduces the quantitative framework used to evaluate the resilience of CISFN. Building on Holling’s seminal concept of ecological resilience, the approach emphasizes a system’s capacity to maintain its structure and function in the face of disturbances [23]. The resilience index used in this study is based on complex network analysis and the ecological network resilience theory proposed by Ulanowicz et al. [17]. This method is primarily used to reveal and compare system structure and functionality, and it has been widely applied in research on food systems [38,43].

In this study, resilience is defined as the system’s capacity to resist, adapt to, and recover from external shocks, with its optimal state characterized by a balanced relationship between efficiency and redundancy [17,44]. The resilience indicator is derived from complex network analysis and ecological network resilience theory, and its theoretical foundations lie in thermodynamics, information theory, and ecosystem ecology [45,46]. For a detailed explanation of the theoretical basis, please refer to Appendix C.

The efficiency of the CISFN reflects its ability to facilitate the concentration of staple flows [43]. Generally, more direct flow paths correspond to higher network efficiency. For instance, provinces may pursue preferential interactions in inter-provincial flows, which can enhance overall productivity but potentially reduce the diversity of flow partners and staple flow paths [43]. This outcome aligns with the development of an integrated national market and modern logistics infrastructure. Within the CISFN, efficiency is primarily determined by the concentration of flow paths (CD) and their mutual interdependence (PMI). For staple $m$ in year $t$, efficiency is defined as:

$${Eff}^m\left(t\right)={\sum }_{i=1}^{n^m\left(t\right)}{\sum }_{j=1}^{n^m\left(t\right)}{CD}_{i,j}^m\left(t\right)·\mathit{ln}\left({PMI}_{i,j}^m\left(t\right)\right),$$

(13)

where

$$\left\{\begin{array}{c}{CD}_{i,j}^m\left(t\right)=w_{i,j}^m\left(t\right)/T^m\left(t\right),\\ {PMI}_{i,j}^m\left(t\right)=w_{i,j}^m\left(t\right)·T^m\left(t\right)/{(S}_i^{m,in}\left(t\right)·S_i^{m,out}\left(t\right)).\end{array}\right.$$

(14)

Here, $w_{i,j}^m\left(t\right)$ denotes the flow volume of staple $m$ from province $i$ to $j$ in year $t$; $T^m\left(t\right)$ is the total flow volume of staple $m$; and $S_i^{m,in}\left(t\right)$ and $S_i^{m,out}\left(t\right)$ represent the inflow and outflow of province $i$ and $j$, respectively.

Specifically, ${CD}_{i,j}^m\left(t\right)$ represents the proportion of flow from province $i$ to $j$ relative to the total volume, while ${PMI}_{i,j}^m\left(t\right)$ measures the degree of dependence between the two provinces $i$ and $j$, a higher value implies a stronger bilateral connection [47]. The total flow volume $T^m\left(t\right)$ is defined as:

$$T^m\left(t\right)=\sum _{i=1}^{n^m\left(t\right)}\sum _{j=1}^{n^m\left(t\right)}{w}_{i,j}^m\left(t\right).$$

(15)

The redundancy of the CISFN reflects the diversity of flow paths, playing a critical role in mitigating the effects of external disturbances. Redundancy also functions as a strategic buffer embedded within China’s multi-level reserve system [47]. In inter-provincial staple food flows, the ability to choose among multiple supply and demand partners is fundamental to market flexibility and enhances the system’s capacity to adapt to changing conditions. Similarly to efficiency, redundancy is jointly determined by concentration (CD) and mutual independence (PMR). For staple $m$ in year $t$, the redundancy can be expressed as:

$${Red}^m\left(t\right)={\sum }_{i=1}^{n^m\left(t\right)}{\sum }_{j=1}^{n^m\left(t\right)}{CD}_{i,j}^m\left(t\right)·\mathit{ln}\left({PMR}_{i,j}^m\left(t\right)\right),$$

(16)

where

$$\left\{\begin{array}{c}{CD}_{i,j}^m\left(t\right)=w_{i,j}^m\left(t\right)/T^m\left(t\right),\\ {PMR}_{i,j}^m\left(t\right)=\mathit{ln}\left(\left({S_i^{m,in}\left(t\right)·S}_i^{m,out}\left(t\right)\right)/{\left(T^m\left(t\right)\right)}^2\right).\end{array}\right.$$

(17)

The mutual independence ${PMR}_{i,j}^m\left(t\right)$ forms a matrix that measures the degree of freedom between provinces $i$ and $j$. A higher PMR value indicates a greater number of potential alternative flow paths between the two provinces.

The resilience of the CISFN ultimately arises from the balance between its efficiency and redundancy [33,43]. For staple $m$ in year $t$, the network resilience is defined as:

$${Res}^m\left(t\right)=-{\alpha }^m\left(t\right)·\mathit{ln}\left({\alpha }^m\left(t\right)\right),$$

(18)

where ${\alpha }^m\left(t\right)$ represents the system’s order parameter:

$${\alpha }^m\left(t\right)={\displaystyle \frac{{Eff}^m\left(t\right)}{{Eff}^m\left(t\right)+{Red}^m\left(t\right)}},0\le {\alpha }^m\left(t\right)\le 1.$$

(19)

This resilience metric captures the optimal trade-off between efficiency and redundancy, providing deeper insights into the stability and adaptability of the CISFN under external shocks such as global climate change and geopolitical tensions. Figure 5 presents a numerical example illustrating the relationship among efficiency, redundancy, and resilience. As shown, resilience achieves its maximum value. We can find that the resilience achieves its maximum value (${Res}^{*}=1/e\approx 0.3679$) when the order parameter reaches its optimal value (${\alpha }^{*}=1/e\approx 0.3679$) [33,43]. Both excessive efficiency and excessive redundancy could weaken resilience, confirming that resilience emerges from an optimal balance between the two.

3.4. Determinant Identification of the CISFN

To explore the complex mechanisms shaping the resilience of CISFN, this section employs multiple statistical methods, including the Pearson correlation coefficient and multivariate regression analysis. These methods comprehensively evaluate how various structural and systemic drivers influence network resilience.

The Pearson correlation coefficient is used to assess the strength and direction of the linear association between resilience and its potential drivers [38], while multivariate regression quantifies their independent effects after accounting for interactions among variables [48]. However, due to the substantial multicollinearity among network topological indicators, this study first applies a multiple stepwise regression model to identify a parsimonious set of explanatory variables, followed by diagnostic testing using variance inflation factors (VIFs). Finally, a fixed-effects model is employed to evaluate the robustness of the stepwise regression results.

By integrating multiple potential determinants of CISFN resilience, the following multiple linear regression model is constructed:

$$\begin{array}{cc}{Res}_t^m\hfill & =b_0^m+b_1^m·n_t^m+b_2^m·e_t^m+b_3^m·{\overline{k}}_t^m+b_4^m·{\overline{S}}_t^m+b_5^m·{\overline{C}}_t^m\hfill \\ \hfill & +b_6^m·{\mathrm{∆}}_t^m+b_7^m·L_t^m+b_8^m·D_t^m+b_9^m·Q_t^m+b_{10}^m·{NOC}_t^m+e_t^m,\hfill \end{array}$$

(20)

where $m$ and $t$ denote the staple type and year, respectively. The dependent variable is the resilience of the CISFN, and the 10 explanatory variables include: number of nodes (n), number of edges (e), average degree ($\stackrel{-}{k}$), average weighted degree ($\stackrel{-}{S}$), average clustering coefficient ($\stackrel{-}{C}$), network density (Δ), average path length (L), and network diameter (D), modularity (Q), and number of communities (NOC). Here, $b_0^m$ denotes the intercept and $e_t^m$ the random error term.

To avoid scale effects, improve numerical stability, and ensure comparability of coefficients across variables, all independent variables were standardized using min-max normalization prior to the multiple regression analysis [49]. This normalization step helps reduce the influence of heterogeneous units of measurement, enhances model convergence, and allows the fixed-effects estimation to better capture the underlying relationships among the variables.

Beyond network topology, identifying the fundamental components of network resilience is crucial for effective analysis and policy formulation in the context of inter-provincial food security. To this end, the Structural Decomposition Analysis (SDA) approach is adopted to quantify how efficiency and redundancy contribute to temporal changes in resilience from 1998 to 2022 [50]. SDA also facilitates the evaluation of how inter-provincial food flow dynamics shape resilience patterns over time.

The contributions of efficiency and redundancy to changes in CISFN resilience are defined as:

$$\begin{array}{cc}\mathrm{∆}{Res}^m\left(t^{\prime }\right)\hfill & =\mathrm{∆}{Eff}^m\left(t^{\prime }\right)·1/2\left({Red}^m\left(t\right)+{Red}^m\left(t^{\prime }\right)\right)\hfill \\ \hfill & +\mathrm{∆}{Red}^m\left(t^{\prime }\right)·1/2\left({Eff}^m\left(t\right)+{Eff}^m\left(t^{\prime }\right)\right),\hfill \\ \hfill & ={\mathrm{∆}}_{Eff}{Res}^m\left(t^{\prime }\right)+{\mathrm{∆}}_{Red}{Res}^m\left(t^{\prime }\right),\hfill \end{array}$$

(21)

where ${\mathrm{∆}}_{Eff}{Res}^m\left(t^{\prime }\right)$ and ${\mathrm{∆}}_{Red}{Res}^m\left(t^{\prime }\right)$ denote the respective contributions of changes in efficiency and redundancy to the variation in resilience between years t to t′.

Similarly, the cumulative contributions of all inflow and outflow variations to changes in network resilience are expressed as:

$$\left\{\begin{array}{c}\mathrm{∆}{Res}_{·,j}^m\left(t^{\prime }\right)={\displaystyle \sum _{i=1}^n}\mathrm{∆}{Res}_{i,j}^m\left(t^{\prime }\right),\\ \mathrm{∆}{Res}_{i,·}^m\left(t^{\prime }\right)={\displaystyle \sum _{j=1}^n}\mathrm{∆}{Res}_{i,j}\left(t^{\prime }\right).\end{array}\right.$$

(22)

A detailed derivation of Equations (21) and (22) is provided in Appendix B.

4. Results

This section first analyzes the spatiotemporal evolution of inter-provincial staple food flows in China, then interprets the structural and resilience evolution of the flow network, and finally investigates the primary driving factors governing its resilience.

4.1. Spatiotemporal Evolution of the CISFN

As one of the world’s largest agricultural producers, China has long faced considerable pressure in maintaining the structural security of its staple foods. The coordination among staple food production capacity, consumption structure, and inter-provincial flow patterns directly influences the stability and resilience of the national food system. This subsection aims to systematically examine the spatiotemporal evolution of inter-provincial staple food flows in China.

Figure 6 illustrates the inter-provincial flows of five staple foods and aggregated staple food in China in 2020. The black lines represent the directions of inter-provincial food flows, with line thickness indicating flow magnitude, thicker lines correspond to larger flow volumes. To ensure data stability, a five-year average (2018–2022) was used to represent the food flow volume in 2020. The background color shows the difference between production and consumption in each province, where red indicates surplus and blue indicates deficit. Overall, the southeastern coastal provinces and other densely populated regions appear predominantly in blue, reflecting a strong dependence on external food supplies. Red dots denote outflowing provinces, while blue dots represent inflowing provinces. Notably, some provinces appear as outflowing regions even though they are net consumers. This occurs because such provinces often function as transshipment or redistribution hubs in the inter-provincial food flow network. For example, centrally located provinces may receive food from upstream production regions and subsequently transport it downstream to major consumption centers, thereby exhibiting outflowing characteristics [38]. This phenomenon underscores the structural complexity of food flow, which is shaped not only by supply-demand imbalances but also by geographic location and logistics system. Among the five staple foods, rice, wheat, maize, and potatoes exhibit substantial inter-provincial flows, while inter-provincial soybean flows remain limited, as domestic consumption depends heavily on international imports [51]. Overall, China’s inter-provincial food flow exhibits a fundamental “north-to-south” spatial structure, characterized by multi-path network linkages. While the spatial mismatch between production and consumption defines the necessity of food flows, the inter-provincial food flow network effectively mitigates regional supply-demand imbalances.

Figure 7 illustrates the evolution of China’s inter-provincial aggregated staple food flows in 2000, 2010, 2015, and 2020, clearly revealing the spatial distribution and structural characteristics of food flow across different periods. Overall, with socioeconomic development and the improvement of transportation infrastructure, the inter-provincial food flow paths in China have continuously increased, the spatial coverage has expanded, and the overall network structure has become more complex and interconnected. In 2000, the inter-provincial food flow network was relatively sparse, with limited flow paths concentrated between major production regions in Northeast and North China and key consumption regions such as the Yangtze River Delta and the Pearl River Delta. The overall flow pattern exhibited a simple “point-to-point” and unidirectional structure. By 2010, with enhanced transportation capacity, the number of flow paths had increased substantially, and large quantities of food were being transported to East, South, and Southwest China, indicating stronger inter-provincial linkages and higher network complexity. By 2015, the network structure had further evolved, forming multiple interactive flow paths between production and consumption regions and resulting in tighter regional connectivity. By 2020, both the scale and spatial scope of food flow had expanded even further. The dominant roles of Northeast and North China as core production bases became more pronounced, with a significant increase in food flows directed toward East and South China. Consequently, a highly integrated and well-connected inter-provincial food flow network had been established nationwide [11]. From a supply-demand perspective, the southeastern coastal provinces and densely populated central-western regions have long depended on external food inflows, whereas the Northeast and the North China Plain have consistently served as the primary food-outflowing areas.

4.2. Network Structure Evolution of the CISFN

This section examines the evolution of the topological structure of the CISFN for six types of staple foods, comprising five individual staples and their aggregated staple food, during the period from 1998 to 2022. The analysis of topological evolution focuses on the temporal dynamics of eight key structural indicators and the changes in the community structure of the networks.

Figure 8 presents the evolution of ten topological indicators for the CISFN, revealing an overall trend of expanding network scale and improving operational efficiency. For aggregated staple food, the number of nodes remains consistently around 27, indicating extensive and stable provincial participation. Correspondingly, the number of edges increases from approximately 60 in 2000 to nearly 130 in 2022, suggesting that inter-provincial flows have grown substantially and spatial linkages have continuously strengthened. The average degree rises from 4.5 to about 8, indicating gradually denser flows among provinces. Meanwhile, the average weighted degree grows from 1.8 × 10⁶ to nearly 7 × 10⁶, reflecting a marked increase in total flow volume and enhanced network carrying capacity. The fluctuations in the average clustering coefficient imply instability in regional coordination within the flow network, yet they also highlight the system’s overall regulatory capacity [52]. Network density increases from below 0.1 to 0.3, signifying improved efficiency in resource allocation. Despite the expansion of the network, both the average path length (approximately 2) and the network diameter (around 4) remain stable, indicating that overall flow efficiency has been maintained. Overall, the aggregated staple food exhibits steady structural optimization, indicating its enhanced ability to improve resource allocation and respond to increasingly complex demand dynamics.

From a comparative perspective, Figure 8 reveals clear structural heterogeneity across the different staple food. Rice demonstrates the most stable and efficient network, whereas soybeans and potatoes appear more sensitive to market dynamics and policy changes. In terms of nodes and edges, rice, wheat, and maize exhibit consistently high and gradually increasing numbers, indicating relatively robust flow structures. By contrast, soybeans involve fewer participating provinces but maintain a relatively large number of edges, suggesting limited spatial participation yet intensive flow linkages. The considerable fluctuations in soybean edges likely reflect the influence of international markets and import-related policies [6]. Regarding average degree and weighted degree, soybeans show the most pronounced increase, approaching an average degree of 2 by 2022 and displaying a sharp rise in weighted degree. This pattern implies a more complex network structure and an expanding flow volume. The average clustering coefficient shows the highest values for rice and aggregated staple food, rising rapidly to around 0.4 after 2015. This indicates the formation of more highly clustered substructures. Other staples exhibit lower clustering coefficients, suggesting weaker inter-provincial linkages. Soybeans also display the highest network density, highlighting their relatively intensive flows. The average path length and network diameter are shortest for rice and aggregated staple food, while potatoes show substantial fluctuations, with the diameter at times exceeding 5. This indicates more fragmented flow patterns and longer transport distances.

Figure 9 illustrates the evolution of community structures within the CISFN. Using wheat as an example, the figure presents community partitions for the years 2000, 2010, 2015, and 2020. Different colors indicate clear communities, where provinces within the same community are more closely connected. Provinces shown in blank represent those not participating in inter-provincial wheat flows in that year. Overall, the CISFN has evolved from a relatively fragmented pattern toward greater integration, underscoring the strengthening and optimization of China’s inter-provincial food flow system. In 2000, the wheat network already exhibited clear regional characteristics. Major wheat-producing provinces in northern China and key consumption areas along the eastern coast belonged to the same community, indicating robust inter-provincial linkages [8]. By 2010, previously separate communities had gradually merged into larger clusters. Connections between several northeastern and northern provinces intensified, reflecting more frequent flows from production bases to major consumption regions. By 2015, the community structure became more complex. Communities in the eastern coastal region and the middle-lower Yangtze River area remained relatively stable, likely due to their advanced economic development and well-established transportation infrastructure. By 2020, the community distribution had become more distinct, with multiple provinces forming tighter clusters. Overall, the observed evolution highlights not only the shifting geography of food production and consumption in China but also the crucial roles of public policy and logistics infrastructure in shaping inter-provincial food flow.

Figure 10 presents the community distribution of five individual staple foods and the aggregated staple food within the CISFN in 2020, revealing the functional roles and connectivity patterns of different staples in inter-provincial flows. Rice exhibits obvious regional characteristics. Adjacent producing and consuming regions form a closely connected community, implying predominantly inter-provincial rice flows. Wheat is centered in northern China, with Henan and Shandong forming the primary communities, reflecting their leading production roles. Maize shows two major community clusters: one in the north (Inner Mongolia and Hebei) and another extending across Sichuan, Guizhou, and Hunan, suggesting relatively frequent inter-provincial flows. Soybeans communities are concentrated in the Northeast, where Jilin and Liaoning form the core flow region, consistent with the area’s role as China’s primary soybean production base. Connectivity in other regions is weaker, and several provinces do not participate in inter-provincial soybean flows. Potatoes flows appear more fragmented, with northwestern provinces such as Qinghai and Ningxia forming the main communities, indicating that its flow structure is largely production driven and exhibits relatively low overall connectivity. The aggregated staple food network integrates the flow relationships of all staple types, producing a more intricate community structure. Larger and more cohesive communities emerge in North, Northeast, and Southwest China, reflecting the combined flow advantages of multiple staple foods. Meanwhile, certain provinces remain outside the network, indicating relatively low participation in the overall inter-provincial food flow system.

4.3. Resilience Dynamics Evolution of the CISFN

This section examines the evolutionary characteristics of resilience in the CISFN. It further analyzes the dynamics of its two key components, efficiency and redundancy, and discusses how the balance between them influences overall network resilience.

Figure 11 presents the evolution of resilience, efficiency, and redundancy in the CISFN for five staple foods and the aggregated staple food from 1998 to 2022. Overall, maize and wheat display the strongest resilience, demonstrating substantial capacity to withstand external disturbances. Soybeans resilience fluctuates considerably, with a pronounced decline around 2010, reflecting its vulnerability to policy adjustments and shifts in the economic environment. Potatoes exhibit a pattern of continuous improvement, with resilience and efficiency increasing in parallel, indicating that CISFN has gradually moved toward greater stability and diversification [5]. Figure 11b illustrates network efficiency, which reflects the effectiveness of resource allocation. Wheat and maize maintain relatively high efficiency throughout the study period, implying that their inter-provincial flows are more resource-efficient and flexible. Rice and potatoes also demonstrate high efficiency, but with greater volatility. In contrast, soybeans efficiency declines sharply around 2010, further underscoring its sensitivity and structural fragility to external shocks. Figure 11c depicts network redundancy, which captures the availability of alternative flow paths and the degree of structural diversity. Soybeans exhibit relatively high redundancy, enhancing the network’s capacity to absorb localized disruptions. The redundancy of the aggregated staple food increases steadily, indicating continuous diversification of flow paths. Rice, however, shows comparatively low redundancy, reflecting weaker substitutability and limited flexibility in its flow structure.

Figure 12 illustrates the relationships among resilience, efficiency, and redundancy in the CISFN, revealing heterogeneity across staple foods. Rice, wheat, and maize demonstrate relatively high resilience and strong resource-use efficiency, whereas soybeans and potatoes exhibit greater potential for improving the balance between resilience and efficiency. Specifically, rice, wheat, maize, and potatoes cluster primarily in the region characterized by high efficiency (above 1) and low redundancy (0–1.5), indicating that these staples achieve efficient resource utilization while maintaining moderate flexibility. Larger bubbles correspond to higher resilience, reflecting a stronger capacity to withstand external shocks such as natural disasters, policy adjustments, or market fluctuations. In contrast, soybeans resilience is more widely dispersed, with many observations located in the region of low efficiency and high redundancy. This pattern reflects China’s strong depend on international markets for soybean supply [38]. Most imports enter through a small number of coastal provinces that also host the majority of the domestic crushing industry, creating highly concentrated processing and redistribution hubs. Although this structure increases redundancy by providing multiple redistribution pathways, it simultaneously reduces network efficiency because inter-provincial flows must pass through these clustered coastal ports [53]. China’s import-oriented strategy and the geographic concentration of its crushing industry therefore shape the configuration of the domestic soybeans flow network, generating structural vulnerabilities that ultimately weaken its overall resilience performance. The aggregated staple food (abbreviated as aggregated in Figure 12) exhibits bubbles concentrated in the region of high efficiency and high redundancy, indicating a structurally stable network. This stability may arise from complementary interactions among different staples, whereby fluctuations in certain crops are compensated by the relative stability of others.

4.4. Multiple Determinants of the CISFN Resilience

This section examines both the direction and relative contributions of multiple determinants to resilience. Pearson correlation coefficients are employed to assess the strength and direction between each driver and resilience. A multivariate regression model is applied to determine the relative contribution of multiple determinants to resilience.

Figure 13 presents the Pearson correlation coefficients between CISFN resilience and the multiple determinants. Overall, average path length and network diameter exhibit a consistently significant positive correlation with resilience, whereas the remaining eight indicators may weaken resilience under certain staple- or network-specific conditions. Except for soybeans and aggregated staple food, the number of edges, average degree, and average weighted degree are generally positively associated with resilience. For example, the correlation between resilience and the number of edges reaches 0.64 for rice and 0.72 for potatoes, indicating that stronger network connectivity plays a crucial role in enhancing resilience. Similarly, increases in average degree and average weighted degree, which reflect the intensity of inter-provincial flows, substantially strengthen resilience. Wheat exhibits comparatively weaker correlations, with most coefficients below 0.5 and statistically insignificant. Notably, the number of nodes is significantly negatively correlated with maize resilience, suggesting that resilience declines when additional provinces participate in inter-provincial flow. Soybeans show distinct patterns: resilience is significantly related to network density, average path length, and network diameter. In particular, the strong negative correlation between network density and resilience indicates that soybeans resilience depends on a relatively concentrated and low-density flow structure. For aggregated staple food, resilience patterns differ markedly from those of individual staples. The number of edges, average degree, average weighted degree, and network density are all significantly negatively correlated with resilience, implying that expanding network size or increasing flow volume does not necessarily improve resilience. Instead, excessive concentration and cascading dependencies may undermine it. The heterogeneous signs across indicators and crops reflect genuine structural and functional differences within the CISFN. By contrast, average path length and network diameter consistently exhibit positive correlations with resilience, suggesting that moderate levels of intermediation may help prevent the rapid propagation of systemic risks.

Table 2. The stepwise regression estimation results between the CISFN resilience and multiple determinants.

	Rice	Wheat	Maize	Soybeans	Potatoes	Aggregated Staple Food
Intercept	0.142 *** (0.028)	0.327 *** (0.008)	0.395 *** (0.037)	0.176 *** (0.025)	0.205 *** (0.017)	0.345 *** (0.004)
Number of nodes	/	−0.025 ** (0.012)	−0.152 *** (0.048)	/	/	/
Number of edges	0.235 *** (0.067)	0.026 ** (0.011)	/	/	0.122 *** (0.024)	/
Average degree	/	/	/	/	/	/
Average weighted degree	0.365 (0.237)	/	0.079 ** (0.032)	/	/	/
Average clustering coefficient	/	/	/	/	/	/
Network density	/	/	/	−0.147 *** (0.034)	/	0.014 *** (0.005)
Average path length	/	/	0.041 ** (0.014)	/	/	/
Network diameter	/	0.027 *** (0.009)	/	0.202 *** (0.051)	/	0.017 *** (0.003)
Modularity	/	/	/	/	/	/
Number of communities	/	/	/	/	/	/
Max VIF	3.541	1.221	2.254	1.716	1	5.472
Mean VIF	3.541	1.148	1.820	1.716	1	5.472
F-value	10.895	6.351	11.877	34.467	25.255	34.788
p-value	0.000	0.003	0.000	0.000	0.000	0.000
R2	0.609	0.476	0.704	0.831	0.523	0.760
Adjusted R2	0.553	0.401	0.644	0.807	0.503	0.738
RMSE	0.039	0.013	0.016	0.042	0.030	0.003

Note: Parentheses report standard errors. RMSE refers to the root mean square error. “/” denotes variables excluded due to multicollinearity. ** p < 0.05, *** p < 0.01.

reports the stepwise regression results linking CISFN resilience to key topological indicators across staples, with multicollinearity mitigated through variable selection [54]. Together with the fixed-effects robustness checks (

Table A2. The fixed effect regression estimation results between the CISFN resilience and multiple determinants.

	Rice	Wheat	Maize	Soybeans	Potatoes	Aggregated Staple Food
Number of nodes	/	−0.025 ** (0.010)	−0.043 * (0.026)	/	/	/
Number of edges	0.235 *** (0.081)	0.026 *** (0.008)	/	/	0.122 *** (0.023)	/
Average degree	/	/	/	/	/	/
Average weighted degree	0.365 (0.247)	/	0.016 (0.023)	/	/	/
Average clustering coefficient	/	/	/	/	/	/
Network density	/	/	/	−0.147 *** (0.029)	/	0.014 *** (0.004)
Average path length	/	0.027 *** (0.009)	0.041 ** (0.019)	/	/	/
Network diameter	/	/	/	0.202 *** (0.064)	/	0.017 *** (0.002)
Modularity	/	/	/	/	/	/
Number of communities	/	/	/	/	/	/
Max VIF	3.541	1.221	2.254	1.716	1	5.472
Mean VIF	3.541	1.148	1.820	1.716	1	5.472
F-value	11.413	6.654	11.838	36.108	26.353	36.369
p-value	0.000	0.002	0.000	0.000	0.000	0.000
R2	0.609	0.476	0.617	0.831	0.523	0.760
Adjusted R2	0.573	0.428	0.583	0.816	0.523	0.749
RMSE	0.042	0.014	0.020	0.045	0.030	0.003

Note: Parentheses report standard errors. RMSE refers to the root mean square error. “/” denotes variables excluded due to multicollinearity. * p < 0.1, ** p < 0.05, *** p < 0.01.

), the results reveal pronounced staple-specific heterogeneity in the structural determinants of resilience [55]. First, network connectivity exhibits markedly different effects across staples. The number of edges is positively and significantly associated with resilience for rice, wheat, and potatoes, indicating that denser inter-provincial linkages enhance the capacity of these systems to absorb shocks. In contrast, the number of nodes shows significantly negative coefficients for wheat and maize, suggesting that excessive network expansion may introduce coordination costs or structural inefficiencies that weaken resilience. Second, network density displays clear staple-specific patterns. While density is positively related to resilience in the aggregated staple food network, it is significantly negatively associated with soybeans resilience. This finding is consistent with the strong import dependence and hub-concentrated structure of soybean flows, where higher density may amplify systemic exposure to disruptions [53]. Third, path-based indicators play an important role in shaping resilience. The network diameter of soybeans is positively and significantly related to resilience, implying that a broader spatial reach and the involvement of intermediate provinces can enhance system resilience. This pattern reflects the endogenous dependence of China’s soybean system on international markets, arising from high import reliance and the spatial concentration of port-based crushing industries along the coast [6]. Average path length also exhibits a positive effect for maize, suggesting that longer flow paths may contribute to adaptive flexibility under certain conditions. Finally, the overall model performance is satisfactory across all staples. The regression models yield statistically significant F-values and acceptable multicollinearity diagnostics.

5. Discussion

This section provides an in-depth discussion of the results. First, it examines the cumulative contributions of efficiency and redundancy to changes in resilience, focusing on these two core components. It then analyzes each province contributes to overall resilience change, from the perspectives of inflow, outflow, and total flow. Based on these findings, corresponding policy implications are proposed. Finally, the limitations of this study and potential directions for future research are discussed.

5.1. Contributions of Efficiency and Redundancy to Resilience Changes

Redundancy and efficiency form the two core components of the CISFN resilience. The analysis of resilience evolution focuses on the dynamic of overall resilience, with particular attention to the trade-off between these two fundamental attributes.

Figure 14 illustrates the cumulative contributions of efficiency and redundancy to changes in the CISFN resilience from 1998 to 2022, with their sum equal to one. Overall, the results reveal distinct crop-specific resilience mechanisms that reflect not only network structure but also the political-economic context of China’s food system. Rice resilience is predominantly efficiency driven, wheat and potatoes exhibit higher sensitivity to external shocks, maize displays a relatively balanced contribution from efficiency and redundancy, soybeans show persistent structural vulnerability, and the aggregated staple food still exhibits room for improvement. This result is broadly in line with Wu et al.’s findings on resilience-driven heterogeneity in spatial resilience in the Ili River Valley, China [22]. Specifically, rice resilience is consistent with China’s long-standing policy emphasis on rice self-sufficiency and stable domestic circulation, supported by strong state coordination in production and interregional distribution. Wheat reflects the combined effects of international market volatility, adjustments in domestic supply-side policies, and extreme climate events, all of which interact with policy-driven stabilization mechanisms such as reserve adjustments and cross-regional reallocations, which is consistent with Béné et al.’s results [20]. Maize reflects the coordinated development of maize production regions and relatively diversified flow paths under national food security strategies. In contrast, soybeans resilience highlights the political-economic vulnerability associated with China’s heavy reliance on imports and the concentration of soybeans supply chains, which limits adaptive capacity under international market shocks and trade risks. Potatoes resilience fluctuates substantially, with efficiency often exceeding redundancy, suggesting that their resilience relies more heavily on redundant paths to mitigate external shocks, in line with findings on the network resilience of phosphorus cycling in China [43]. For the aggregated staple food, resilience changes are relatively moderate, with the contributions of efficiency and redundancy remaining largely stable.

5.2. Contributions of Provinces to Resilience Changes

Figure 15 systematically analyzes provincial contributions to resilience changes in the CISFN from the perspectives of inflow, outflow, and total flow. The results reveal pronounced spatial heterogeneity that reflects not only logistical conditions but also the long-standing governance structure of China’s food system. Specifically: (1) Inflow contributions: Southeastern coastal provinces exhibit substantial positive inflow contributions. Beyond demographic and economic drivers, this pattern is closely linked to China’s food security governance, under which major consumption regions are prioritized for stable supply through coordinated inter-provincial transfers and reserve mechanisms. By contrast, several center provinces exhibit negative inflow contributions, likely due to unstable inflow paths or stronger dependence on external supply, both of which can undermine resilience. This finding corroborates evidence from the global phosphorus trade network, where reliance on external inflows has been shown to weaken systemic resilience [33]. (2) Outflow contributions: Positive outflow contributions are concentrated in major production regions. These provinces have long been particular as grain-producing bases under national food security policies and are closely integrated into state-coordinated storage and redistribution systems [56]. (3) Total flow contributions: By combining inflow and outflow effects, total flow contributions highlight provinces that function as key redistribution and balancing hubs. Provinces such as Henan, Shandong, and Heilongjiang emerge as central nodes for supply-demand balancing [38], reflecting not only their geographic and production advantages but also their institutional roles in cross-regional grain allocation. Their substantial total flow contributions enhance the structural stability and regulatory capacity of the inter-provincial food flow system, underscoring the importance of governance-driven coordination in shaping network resilience.

The comparative analysis across staple foods reveals pronounced regional patterns and spatial heterogeneity. Combined with Figure 6 and Figure 7, several key findings emerge: (1) Rice exhibits strong positive contributions in the southeastern coastal and southern regions. Inflows are concentrated in Guangdong and Zhejiang, while outflows mainly originate from Hunan and Jiangxi, forming the classic “north-to-south” flow pattern. (2) Wheat shows contributions concentrated in central provinces. Henan and Shandong function both as major outflow regions and as critical hubs of total flows, underscoring their central role in national wheat redistribution. (3) Maize displays a more dispersed spatial structure: inflows cluster in the southwest, whereas outflows are dominated by northern provinces such as Inner Mongolia and Jilin, reflecting a broadly connected and highly interlinked flow network. (4) Soybeans rely heavily on inflows. These are concentrated in coastal provinces such as Shandong and Jiangsu, while outflows stem primarily from the northeastern production base, forming a hybrid “import and domestic redistribution” pattern. (5) Potatoes exhibit strong regional dependence. Outflows mainly come from southwestern provinces, whereas inflows are concentrated in southeastern coastal areas such as Jiangsu and Zhejiang, indicating geographically constrained and highly concentrated flow paths. (6) For the aggregated staple food network, total flow contributions are generally positive. Provinces such as Henan, Shandong, and Heilongjiang stand out as essential national hubs, highlighting their indispensable roles in sustaining the resilience of the CISFN.

5.3. Model Validation and Sensitivity Analysis

This subsection presents the validation, sensitivity analysis, and uncertainty assessment of the proposed modeling framework. Model robustness is first examined by constructing alternative inter-provincial staple food flow scenarios and conducting quantitative comparisons with existing studies. We then perform a sensitivity analysis of the resilience model under shock perturbations, followed by a discussion of the main sources of uncertainty and their potential implications for the results.

Figure 16 indicates that transportation frictions can indeed reduce network resilience, as reflected by the generally lower resilience levels observed under higher-friction scenarios for certain staples, such as soybeans. At the same time, the overall temporal patterns of resilience remain largely consistent across scenarios, suggesting that the impact of logistical frictions is mediated by the underlying structure of the food flow network. Crop-specific differences highlight that resilience responses to friction depend on supply-demand configurations and network connectivity, rather than on transportation conditions alone. In particular, structurally concentrated or import-dependent networks appear more sensitive to increased frictions, whereas diversified systems exhibit greater stability. These findings underscore that logistical frictions and network structure jointly shape resilience dynamics, with neither factor acting in isolation. This also provides additional support for the robustness of the resilience results, as they remain qualitatively similar under alternative friction assumptions, in line with Zeng et al.’s finding that such multi-layered structures substantially increase both system complexity and fragility [25]. Uncertainty in the estimated food flows arises from data limitations, parameter assumptions regarding transportation costs and logistical frictions, and structural simplifications in the cost-minimization framework. While these factors may affect absolute flow magnitudes, the main conclusions rely on relative patterns and cross-scenario consistency, indicating that the resilience results are robust within reasonable margins of uncertainty.

Table 3. Comparison of total grain flows between this study and previous studies (10⁴ t).

Indicator	This Study	Ben et al., 2016 [57]	Relative Deviation (%)
Total inter-provincial grain flow	13,110.58	12,474.30	4.85%
Outflow from Northeast China	5496.36	5641.60	2.64%
Outflow from the middle and lower Yangtze River region	1935.77	1976.10	2.08%

provides a further comparison of inter-regional food flows between this study and previous work. Ben et al. [57] employed a cost-minimization optimization framework to simulate inter-provincial grain flows in China, using three-year averages (2010–2012) for major grain crops, including cereals, legumes, and tubers. Following a consistent approach, we calculated the average inter-provincial flows of rice, wheat, maize, soybeans, and potatoes over the same period for comparison. Ben et al. reported national-scale grain flow volumes as well as aggregated outflows from key regions, including Northeast China (Heilongjiang, Jilin, and Liaoning) and the middle and lower reaches of the Yangtze River (Hubei, Hunan, Jiangxi, Anhui, Jiangsu, Zhejiang, and Shanghai). Accordingly, our comparison focuses on these aggregated regional flows. The results show that the differences between the two studies are generally within 5%, indicating a high degree of consistency in overall flow magnitudes and providing quantitative support for the reasonableness of the inferred flow structures used in our resilience analysis.

Figure 17 presents the sensitivity analysis of the resilience of the inter-provincial aggregated staple food flow network under different disturbance scenarios. Four types of simulated shocks are examined: targeted node removal, random node removal, targeted edge removal, and random edge removal. For each scenario, 10%, 30%, 50%, 70%, and 90% of nodes or edges are removed, and the resulting resilience is tracked over the period 1998–2022. Figure 17a,b show the effects of node removal. Targeted node removal leads to substantially greater reductions in resilience compared with random removal, particularly when 70% or 90% of the most important nodes are eliminated. Under these severe targeted-removal scenarios, the network becomes partially or fully fragmented, causing resilience to decline sharply or even collapse entirely. In contrast, random node removal produces relatively smoother variations in resilience, indicating that the system is less sensitive to unstructured disturbances. Figure 17c,d display the effects of edge removal. Similarly to node removal, targeted deletion of high-weighted edges significantly decreases network resilience, especially under the 70% and 90% removal levels. Random removal of edges results in milder fluctuations, with resilience decreasing gradually rather than abruptly. Overall, these results demonstrate that the network is considerably more vulnerable to the loss of structurally important nodes and edges than to random disruptions. They also confirm that the resilience metric is sensitive to meaningful structural perturbations while remaining relatively stable under random noise, supporting the robustness and interpretability of the resilience model.

5.4. Policy Recommendations

Based on these findings, several policy recommendations are proposed to enhance CISFN resilience.

• Strengthen coordination in inter-provincial staples flow. Although the aggregated staple food network exhibits stronger resilience than individual staple networks, several challenges remain, including relatively low efficiency and imbalanced flow structures. Consistent with resilience studies in food, water, and energy systems, strengthening redundancy through a multi-node and multi-path logistics system [5,58], such as dedicated food railway, multimodal transport hubs, and intelligent storage facilities, would enhance network flexibility and promote more efficient internal allocation of staple foods.
• Optimize coordinated allocation across multiple staples. The CISFN resilience depends strongly on the diversity and balance of staple structures [18,38]. Wheat and maize tend to exhibit high efficiency with relatively low redundancy, whereas soybeans display higher redundancy but lower efficiency under certain conditions. These differences highlight the importance of integrated, multi-crop coordination strategies. Policy measures that jointly consider multiple staple crops and promote optimized flow mechanisms can leverage the complementary strengths of different staples and thereby enhance the overall resilience of interprovincial food flows.
• Improve multi-level regulatory mechanisms. Food flows operate across interconnected global, national, and provincial levels, where disruptions can propagate through multiple channels. Similarly to findings in other critical resource systems [33,43], governance limited to a single administrative level is insufficient to manage systemic risks. Strengthening multi-level regulatory frameworks and cross-sector coordination among agricultural, transportation, and trade authorities can significantly improve adaptive capacity. Such governance mechanisms are essential for managing uncertainty and maintaining resilience under increasingly complex logistical and environmental conditions.

Beyond the Chinese context, the policy insights derived from this study are applicable to other countries and regions characterized by large spatial scales and heterogeneous production-consumption patterns. The proposed framework provides a transferable tool for evaluating how network structure shapes food system resilience, offering guidance for resilience-oriented agricultural and logistics planning in diverse institutional settings.

5.5. Limitations and Future Research

There are several limitations to this study. First, the evolving dynamics of global climate change and international food trade highlight the need to incorporate more detailed international trade information. Second, due to data availability, this study relies on annual data at the provincial scale. A monthly, city-level representation of staple food flows would enable a more precise assessment of resilience characteristics. Third, the estimation of inter-provincial food flows is based on static transportation cost data, which may not fully capture real-world variability.

Accordingly, three directions for future research are proposed. The first is to integrate global food trade with China’s inter-provincial flows and develop a cross-scale food flow network capable of addressing the combined risks arising from both global market volatility and domestic structural imbalances. The second is to extend the historical dataset and conduct continuous analyses of resilience evolution, with particular attention to refining temporal and spatial scales to better capture emerging trends and key drivers of resilience dynamics. Finally, future research would benefit from incorporating dynamic, time-varying transportation cost data to more accurately reflect real-world conditions, or from applying gravity models that incorporate relevant social and economic factors as a complementary comparison.

6. Conclusions

This study develops a resilience evaluation framework for China’s inter-provincial staple food flows by integrating mathematical programming with complex network analysis. It further examines resilience dynamics and identifies their key determinants. The main conclusions are summarized as follows. (1) Maize and wheat exhibit the highest levels of resilience, whereas soybeans are the least resilient and are more susceptible to external shocks. (2) Rice, wheat, and maize demonstrate relatively high resilience coupled with strong efficiency, while soybeans and potatoes exhibit greater potential for improving the balance between efficiency and redundancy. (3) Connectivity and diversity of flow paths exert particularly strong positive effects on resilience, with the exception of soybeans. In addition, a higher number of intermediate transfer nodes is associated with enhanced resilience, highlighting the importance of shock-absorbing capacity enabled by network structure. (4) The determinants of resilience display pronounced heterogeneity across staples. Rice resilience is predominantly efficiency driven; wheat and potatoes are more sensitive to external disruptions; maize maintains a well-coordinated balance between efficiency and redundancy; and soybeans exhibit persistent structural vulnerability. (5) Resilience enhancement shows clear spatial heterogeneity. Consumption-oriented provinces primarily contribute through stable inflows, whereas major production regions strengthen resilience through sustained outflows. Moreover, staple food flows exhibit distinct spatial nesting and functional coupling, underscoring the critical role of multi-level policy coordination in reinforcing overall system resilience.