An Analysis of the Structural Traits and Drivers of Virtual Land Trade Networks Within the G20 Countries

Abstract

With the deepening of international trade and the increasing shortage of land resources, the importance of virtual soil trade in grain has become increasingly prominent. Based on FAO data, this study constructs the virtual soil trade network of wheat, rice, corn and soybean in the major G20 grain trading countries in 2013 and 2023, measures its network characteristics, and uses the exponential random graph model to explore its influencing factors from three dimensions of economic scale, geographical characteristics and resource endowment. The results show that: (1) virtual land trade is essentially a redistribution mechanism of land use pressure, rather than a simple grain flow; (2) the formation of network is driven by exogenous economic factors and endogenous relations; and (3) the role of each country in the network varies with the grain and food category and the development stage, showing a systematic differentiation. It is suggested that the allocation of land resources should be optimized according to the differences in virtual land flows in different countries and food categories. Since the export of virtual land is accompanied by ecological costs (such as deforestation, soil degradation, and water consumption), sustainability must be integrated into trade policies. Rations involve national security strategy, and it is necessary to strengthen domestic productivity and strategic reserves. Feed grain can use the market mechanism to promote trade liberalization and diversification, and reduce the risk of supply chain concentration while giving full play to the global comparative advantage.

1. Introduction

With the development of the world economy and the increase in population, the demand for land is increasing, and the shortage of land resources has become an important factor restricting the economic and social development of countries all over the world. According to the global food and agriculture statistical yearbook 2023 released by the FAO [1], the total area of cultivated land in the world is about 1.667 billion hectares, accounting for 11% of the land area. However, the regional distribution is extremely uneven, with most cultivated land resources being concentrated in countries in North America, South America, Europe and Asia (such as India, the United States, and Russia). Countries such as Japan and Saudi Arabia face natural constraints, with limited arable land availability. From the per capita level, the global average cultivated land area is 0.217 hectares, while the per capita cultivated land in countries such as Australia and Argentina is more than 0.8 hectares, which has significant grain export potential. In contrast, China’s per capita agricultural land amounts to merely 0.09 hectares, less than 1/3 of the global average. Although India’s arable land area is similar to China’s, its per unit yield is low, with per capita arable land of about 0.1 hectares. With the continuous growth of the global population, the reduction in per capita cultivated land resources and land degradation (such as pollution, salinization, and desertification) are superimposed, which aggravates the pressure on food security. The fixity of land resources limits the flow and cross-regional transfer of land resources among regions. Virtual land can embed land resources into products and realize the circulation of land resources among regions through transactions. In this context, the flow of virtual cultivated land resources with grain trade as the carrier has become a new way to alleviate the constraints of land resources. Virtual land provides a resource centric perspective to directly solve the problems of land scarcity and sustainability, while the monetary value is affected by price fluctuations and market distortions, which may mask the actual resource consumption pattern. The virtual land framework conforms to the ecological footprint paradigm, allowing researchers to track the geographical displacement of land use and determine the teleconnection between the consumption of one region and the land development of another region. This is particularly important for understanding how countries with limited land use indirectly occupy land through trade to meet their food needs. Therefore, modeling the trade network through virtual land can provide a deeper understanding of the structural dynamics of resource security, environmental sustainability and global land resource governance. Economically developed regions with scarce land resources can indirectly use cultivated land resources in other regions by importing land intensive agricultural products, so as to optimize the allocation efficiency of global land resources [2]. Scholars generally believe that virtual soil flow has reconstructed the spatial allocation of global land resources through the food trade network, and its scale and structural evolution have a profound impact on national food security and ecological sustainability [3,4,5]. This concept has developed from single-product accounting to multi-scale network analysis. Early research focused on the driving mechanism of virtual water trade [6], while more recently scholars have revealed the geographical displacement of virtual soil [7]. Existing studies can be classified into the following three categories according to different thematic dimensions. The first category focuses on the temporal and spatial evolution of multi-scale network patterns at the following three different scales: global [8,9], national, and industrial sector [5,10,11,12,13]. One view is that the global virtual land trade network presents a “core edge” structure, and China, as the core node, has significantly reshaped the hierarchical relationship of global land resource allocation [3]. In contrast, another view emphasizes the centralized characteristics of the soybean trade network, whose topology is dominated by the supply chain of multinational enterprises [14]. Thus, a basic consensus revealed by global-scale research is that the networked characteristics of virtual soil flow determine the efficiency and vulnerability of resource redistribution. In the context of trade globalization, national-scale research focuses on the one-way flow from resource-rich areas to core consumption areas. The externalization of consumption-driven land demand in the EU shows that developed countries transfer ecological pressure to developing countries through trade [5], while the unbalanced structure of China’s global virtual cultivated land flow reflects the mismatch between trade policy and resource endowment [10].

The second type of research deeply explores the driving mechanism of economic and social motivation and is subdivided into the following three perspectives: consumer side, trade side, and policy side. One view is that income growth and dietary structure transformation are the core driving forces of virtual soil flow, and rich countries externalize the demand for biological capacity through trade [9]. Another view emphasizes the interaction between economic variables in trade, such as distance, market size, and resource endowment [15,16]; the “belt and road” initiative reshapes the transnational flow path through trade facilitation [17]. The third type of research focuses on deepening the evaluation of resource risk policy effect, with the core aim of revealing the multidimensional impact of virtual soil flow. Unlike the spatial description of the first category and the mechanistic analysis of the second, the third type of research pays more attention to the sustainability consequences of the flow pattern. The resource saving effect shows that trade-driven specialized production improves global land use efficiency [18], but the shift in ecological pressure reveals the paradox of efficiency and fairness [2]. Policy application, ecological compensation mechanism design [19], and import structure optimization [20] are also frequently studied.

Although the above three types of research have deepened our understanding of virtual land trade from different dimensions, several gaps remain. First, in global-scale network analyses, most existing studies construct networks based on physical trade volumes, failing to account for cross-country differences in agricultural productivity and their impact on virtual land flows, thereby providing an imprecise depiction of “land-use pressure redistribution.” Second, in terms of driving factor analysis, conventional studies predominantly employ gravity models that assume independent trade relationships, neglecting the endogenous structural effects (e.g., reciprocity) that shape network formation. Third, few studies have conducted interactive analyses combining country heterogeneity (developed vs. developing countries) and grain type heterogeneity (food grains vs. feed grains), making it difficult to reveal the differentiated roles of various countries and grain types within the network.

This research endeavors to furnish an empirical foundation for refining international virtual land trade configurations and advancing the sustainable management of global land resources. The main innovations are as follows: (1) scholars examining the dynamics of virtual land commerce within grain markets have traditionally approached the subject through the lens of individual trade routes or the geographical distribution of arable resources among participating countries, lacking a comprehensive analysis of the virtual land trade network for grain products. Consequently, this study conceptualizes the virtual land trade of grain commodities within G20 countries as a complex network, thereby enabling analysis of its central nodes while elucidating the structural positions and interrelationships among participating countries. We demonstrate that virtual land weighting reorders the importance of countries based on agroecological efficiency (e.g., Argentina rises in the corn network due to its lower yields). This reveals a hidden dimension of land-use pressure redistribution that physical trade analysis cannot capture. (2) The application of exponential random graph model (ERGM) to uncover endogenous network mechanisms. Although ERGM has been used in trade network studies, its application to virtual land trade is novel. Unlike conventional gravity models that assume independent trade relationships, ERGM allows us to test for network self-organization—specifically, whether the existence of a trade link from country A to B increases the likelihood of a reverse link (reciprocity). Our results show that it is not merely driven by exogenous factors like GDP and distance, but also by endogenous relational dynamics that shape the redistribution of land pressure. This provides a deeper understanding of how trust, logistics efficiency, and institutional ties co-evolve with resource flows.

2. Materials and Methods

2.1. Research Method

2.1.1. Virtual Land Accounting Method

At present, the quantification of virtual cultivated land resources is mainly carried out from the perspective of producers and consumers. In order to truly calculate the implied virtual cultivated land resources in the trade of major agricultural products among G20 countries, the main agricultural exports are quantified from the perspective of producers, and the main imports are quantified from the perspective of consumers. The specific accounting formula is as follows:

$${VLC}_{i,c,t}={\displaystyle \frac{Y_{i,c,t}}{W_{i,c,t}}},$$

(1)

where VLC_i,c,t is the unit of virtual land area (m²/kg) of grain products c in year t of country i; Y_i,c,t is the harvest area of grain products c in year t of country i (m²); and W_i,c,t is the output (kg) of grain products c in year t of country i.

Analyzing virtual land trade imports and exports of grain products is another necessary step in the study of virtual land trade flow. The formula for calculating the virtual land export area VLE_i,c,t of grain products c in year t of country i is shown in Equation (2):

$${VLE}_{i,c,t}={VLC}_{i,c,t}\times {EX}_{i,c,t},$$

(2)

where EX_i,c,t is the total export output (kg) of grain products c in year t of country i.

Similarly, the formula for calculating the virtual land import area VLI_i,c,t of grain products c in year t of country i is

$${VLI}_{i,c,t}={VLC}_{i,c,t}\times {IM}_{i,c,t},$$

(3)

where IM_i,c,t is the total import output (kg) of grain products c in year t of country i.

Similarly, the formula for calculating the virtual land net flow VLN_i,c,t of grain products c in year t of country i is

$${VIN}_{i,c,t}={VLE}_{i,c,t}-{VLI}_{i,c,t},$$

(4)

If the value of VIN_i,c,t is positive, it means that country i is the virtual net exporter of grain products c in year t; otherwise, it is a net importer.

It needs to be clarified that weighting trade flows with virtual land area is not just scaling of physical volume but fundamentally changes the interpretation of network structure. Due to the differences in yield per unit area among countries, the virtual land content per unit crop is significantly different. Therefore, the virtual land contained in a ton of grain exported by a high-yield country is far less than that exported by a low-yield country. This means that the virtual land trade network puts more emphasis on the mobility of countries that originate from extensive land (low per unit area yield) production, while the physical trade network treats all tons equally. In this study, this difference is particularly obvious in soybean and corn. Although the United States and Brazil dominate the two networks, the centrality changes in some countries (such as Argentina in the corn trade and Russia in the wheat trade) in the virtual land network precisely reflect the differences in their agricultural productivity. Therefore, the virtual land analysis captures the redistribution of land resource pressure, which cannot be revealed by pure physical trade volume.

2.1.2. Virtual Land Trade Network for Grain Products

Social network analysis (SNA) is a quantitative tool for examining actor relationships within networks grounded in social network theory. From an SNA perspective, global grain trade can be represented as a network comprising vertices and their connecting arcs. This acknowledges the differences in grain output and virtual land flows among countries and that trade flow of virtual land is directional. In this study, we built a weighted directed network to analyze virtual land trade in wheat, rice, corn, and soybean products among 19 G20 countries in 2013 and 2023. Network node V represents the 19 countries that participate in the virtual land trade of grain products, V = {v_z:z = 1, 2, …, n₁}, where n₁ is the number of nodes. Side E indicates trade relations between countries, E = {e_z:z = 1, 2, …, n₂}, n₂ is the number of sides, and the strength of the relationship between exporting and importing countries is quantified by virtual land trade area, which serves as the network weight.

2.1.3. Network Structural Indicators for Virtual Land Trade in Grain Products

Drawing on Guan and Wasserman [21,22], this study quantitatively analyzes the global characteristics of the virtual land trade network for four agricultural commodities through five structural metrics: network density, degree centrality, average degree, average clustering coefficient, and average path length. The precise rationalization of these indicators, including their theoretical definitions and mathematical formulations, is presented in

Table 1. Definition of the global characterization metric.

Category	Network Indicators	Explanation
Overall network indicators	Network density	The ratio of the actual number of edges in the network to the upper limit of the number of edges that can be accommodated
	Degree center potential	Ratio of maximum degree to average degree in network
	Average degree	Average degree of all nodes in the network
	Average clustering coefficient	Usually the average of the clustering coefficients of all nodes
	Average path length	The average length of the minimal path between any two nodes

.

For the individual characteristics of the network, the centrality of nodes in the network is taken as the dominant measure, which is embodied in the relative centrality, intermediary centrality and feature vector centrality. The most basic measure for evaluating node centrality in a network is degree centrality. The degree centrality of a node directly reflects its structural importance within the network. In practice, relative degree centrality serves as a standardized measure for comparing node centrality across networks of varying scales. In directed networks, it is calculated as the ratio of a node’s actual degree relative to the network’s maximum degree, the relative in-degree centrality C_dc-in (i) and out-degree centrality C_dc-out (i) are expressed by Equations (5) and (6), respectively:

$$C_{dc-in}\left(i\right)={\sum }_{j=1}^n{x}_{ij}\left(in\right),$$

(5)

$$C_{dc-out}\left(i\right)={\sum }_{j=1}^n{x}_{ij}\left(out\right),$$

(6)

where $\sum _{j=1}^n{x}_{ij}\left(in\right)$ is the number of relationships between i node and other n-1 j nodes, $\sum _{j=1}^n{x}_{ij}\left(out\right)$ is the number of direct relationships between i node and other n-1 j nodes, and n is the number of nodes.

Mediation centrality $g\left(v\right)$ g calculates the shortest path through the node, reflecting the mediation role of the node in the network. Betweenness centrality is interpreted as a measure of resource control. A country with high betweenness lies on the shortest paths between many other countries, acting as a critical conduit for virtual land flows. Its removal would disrupt numerous trade routes, reflecting its power to facilitate or impede resource transfers. A node’s centrality and mediating function increase with shorter path lengths through it, as computed by Equation (7):

$$g\left(v\right)={\sum }_{s\ne v\ne t}{\displaystyle \frac{{\sigma }_{st}\left(v\right)}{{\sigma }_{st}}},$$

(7)

where ${\sigma }_{st}\left(\mathrm{v}\right)$ represents the count of all shortest paths between node s and node t that pass through node v, and ${\sigma }_{st}$ is the number of all the shortest paths from node s to node t.

Eigenvector centrality quantifies a node’s significance based on its degree and the importance of its neighboring nodes. A sparse but strategically important network of connectors results in high eigenvector centrality. Eigenvector centrality goes beyond direct connections by measuring a node’s importance based on the importance of its neighbors. A country with high eigenvector centrality is connected to other highly central countries, placing it at the core of the trade network. This reflects structural influence: such countries are not just well-connected but are strategically positioned within the most influential trading circles. Shifts in their trade policies or production capacity would ripple through the network, affecting many other nodes. High centrality of eigenvectors does not mean high degree centrality. The calculation formula of the centrality of the eigenvector is

$$C_e\left(vi\right)={\displaystyle \frac{1}{\lambda }}{\sum }_{j=1}^n{A}_{j,i}{C}_e\left(v_{ij}\right),$$

(8)

where λ is a constant, and $C_e={\left\{C_e\left(v_1\right),C_e\left(v_2,\dots ,C_e\left(v_n\right)\right)\right\}}^T$ is the center vector of all nodes.

2.1.4. Exponential Random Graph Model

The exponential random graph model (ERGM) is commonly employed to investigate the mechanisms of relationship formation in networks. The core premise of this approach is that the probability of network link formation depends on the presence of existing link within the system. It emphasizes the interdependence of network relationships. Compared with traditional regression analysis, a key methodological advantage is its capacity to simultaneously analyze both endogenous and exogenous drivers of static network formation [23]. ERGM framework captures endogenous structures, such as reciprocity, that cannot be identified by traditional gravity models. Gravity model assumes that trade relations are independent; ERGM reveals that virtual land trade is self-organized—the link from A to B will increase the possibility of reverse link. This confirms that virtual land analysis is a unique framework, revealing the redistribution of land use pressure and its driving mechanism. According to the definition in Herman [24], this paper selects this model to explore the evolution mechanism of virtual land trade network, and sets it as follows:

$$Pr\left(Y=y│\theta \right)\equiv P_{\theta }\left(y\right)={\displaystyle \frac{exp\left({\theta }^{\tau }{g}_{\alpha }\left(y\right)+{\theta }^{\tau }{g}_{\beta }\left(y,x\right)+{\theta }^{\tau }{g}_{\gamma }\left(y,\overline{g}\right)\right)}{k\left(\theta \right)}}$$

(9)

The above formula signifies the probability of the explained variable y being included in the feasible set Y given parameter θ, and $K\left(\theta \right)$ represents a standardized constant. Suppose that the influencing factors of the network are divided into endogenous structural factor α, actor attribute β, and influencing factor γ of other networks related to the network, and $\alpha , \beta , \gamma \in \mathrm{H}$. $g_{\alpha }\left(y\right)$ is the “endogenous network structure statistic” that may affect the formation of the network itself, such as reciprocity. Such variables emphasize that the formation of network relations stems from the evolution of the internal organization of network relations. $g_{\beta }(y,x)$ is a network statistic reflecting the attribute $\left(x\right)$ of network nodes, such as the impact of attribute variables “carried” by nodes (actors) such as economic strength and population size on network relations. $g_{\gamma }\left(y,\overline{g}\right)$ is the network statistics of external environmental factors $\left(\overline{g}\right)$. ${\theta }_{\alpha }^T{\theta }_{\beta }^T{\theta }_{\gamma }^T$ represents the parameter to be estimated, and its significance and symbol indicate the extent to which the corresponding network statistics influence network formation [25,26].

The selection of actor attribute variables in this study is guided by the theoretical framework of virtual land trade drivers, which can be categorized into supply capacity, demand pressure, and resource endowment, as shown in

Table 2. Main variables and meanings of exponential random graph model of virtual land trade network.

Variable Name	Variable Properties	Meaning
edges	Edge	The number of edges in the network reflects the network density
mutual	Reciprocity	Tendency of network nodes to link with each other
nodeicov.gdp	Sender	The impact of economic strength of nodes on the sending relationship in the network
nodeicov.pop		The influence of node population size on the outgoing relationship in the network
nodeicov.cal		Influence of arable land area of nodes on emission relationship in network
nodeicov.pcal		The impact of per capita arable land area of nodes on the emission relationship in the network
nodeicov.work		The impact of labor resources of nodes on the outgoing relationship in the network
nodeocov.gdp	Receiver	The impact of economic strength of nodes on the receiving relationship in the network
nodeocov.pop		Influence of node population size on receiving relationship in network
nodeocov.cal		Influence of arable land area of node on receiving relationship in network
nodeocov.pcal		Influence of per capita arable land area of node on receiving relationship in network
nodeocov.work		The impact of labor resources of nodes on the receiving relationship in the network
edgecov.NN1	Language proximity	The influence of language proximity on the formation of virtual land trade network
edgecov.NN2	Distance between countries	The influence of the distance between national capitals on the formation of virtual land trade network

. Economic strength (GDP) and population size (POP) are included to capture both supply and demand sides of virtual land trade. On the supply side, countries with higher GDP possess greater capital for agricultural technology and infrastructure, enhancing their capacity to export land-intensive crops. On the demand side, larger populations and higher incomes drive food consumption, increasing the need for virtual land imports. These variables are standard in trade gravity models and have been empirically validated in previous virtual land studies [15,16]. Cultivated land scale (CAL) and per capita arable land area (PCAL) represent a country’s physical land endowment. Countries with abundant land (high CAL) are more likely to be net exporters of virtual land, as they can produce surplus grain. However, CAL alone may be misleading—large countries with extensive but low-yield farmland may export less than smaller countries with intensive agriculture. Therefore, PCAL is included to capture land abundance relative to population, which better reflects a country’s potential to externalize land use through trade. This distinction is critical because a country with large CAL but high population density (e.g., India) may still be a net importer. Labor resources (WORK) are included to account for agricultural labor intensity. Countries with abundant labor may engage in labor-intensive, high-yield farming, reducing the virtual land content per ton of output. Conversely, labor-scarce countries may rely on extensive farming, increasing their virtual land footprint per unit of production. Thus, labor availability influences both export capacity and the ecological efficiency of land use.

2.2. Data and Sources

The trade data for grain products in this study are sourced from the Food and Agriculture Organization of the United Countries (FAO), which provides the food statistics of 245 countries and regions from 1961 to 2023 and a detailed matrix of food product trade among countries. Endogenous variables include side effects and reciprocity, and their data are derived from the spatial structure extraction index of the virtual land trade network. Attribute variables include economic development level, population size, arable land area, cultivable land per person, and workforce availability; the data are from the world bank database. Exogenous variables include common language and geographical distance, and their data are taken from the CEPII database. We selected four kinds of food products—wheat, rice, corn and soybean—from 2013 to 2023 to study the virtual land trade of major food products among G20 countries. Based on FAO data, 19 major grain-producing countries with significant virtual land trade areas were analyzed (excluding G20 countries in the European Union). The 19 countries are Argentina (ARG), Australia (AUS), Brazil (BRA), Canada (CAN), China (CHN), Germany (DEU), France (FRA), Indonesia (IDN), India (IND), Italy (ITA), Japan (JPN), South Korea (KOR), Mexico (MEX), Russia (RUS), Saudi Arabia (SAU), Turkey (TUR), the United Kingdom (UKR), the United States (USA), and South Africa (ZAF).

3. Results

3.1. Analysis of Virtual Land Area in the Grain Trade

3.1.1. Analysis of Annual Average Virtual Land Area in the Grain Trade

We begin our structural analysis by examining the area and direction of virtual land flows. An annual average of 4.13 × 10³ km² of virtual land was exported through wheat trade by the selected 19 countries during 2013–2023. The annual average import area is 4.87 × 10³ km², the average annual export area of virtual land for rice is 2.36 × 10³ km², and the average annual import area is 1.35 × 10³ km². The average annual export area of virtual land for corn is 69.48 × 10³ km², and the average annual import area is 137.25 × 10³ km². The average annual export area of virtual land for soybeans is 338.79 × 10³ km², and the average annual import area is 559.18 × 10³ km². While wheat trade exhibited a net virtual land average annual inflow, rice, corn, and soybean trade collectively showed a net virtual land outflow during the study period.

Table 3. Mean yearly net virtual land area of grain products among G20 countries (10³ km²).

Wheat virtual land exporter	Net exports	Wheat virtual land importer	Net imports
ARG	0.92	BRA	2.10
ITA	0.43	MEX	0.26
IND	0.29	FRA	0.20
TUR	0.23	IDN	0.17
Rice virtual land exporter	Net exports	Rice virtual land importer	Net imports
ZAF	1.28	MEX	1.07
USA	0.80	TUR	0.12
RUS	0.10	SAU	0.07
BRA	0.10	DEU	0.01
Corn virtual land exporter	Net exports	Corn virtual land importer	Net imports
USA	32.15	JPN	55.78
BRA	17.72	MEX	38.22
ARG	8.55	KOR	16.63
RUS	3.95	CHN	9.32
Exporter of soybean virtual land	Net exports	Soybean virtual land importer	Net imports
BRA	182.04	CHN	453.37
USA	119.72	MEX	25.06
ARG	17.15	JPN	19.69
CAN	7.04	IDN	15.33

illustrates the yearly average net virtual land trade area for primary grain-producing nations from 2013 to 2023. In the wheat virtual soil trade network, Argentina, Italy, India and Turkey are the main net exporters, and Argentina’s net export area is the highest, reaching 0.92 × 10³ km²; Brazil has become the largest importer of virtual soil with a net import area of 2.10 × 10³ km², and Mexico, France and Indonesia are also among the net importers, reflecting the hidden flow of land resources based on wheat between South America, Europe and Asia. In the rice virtual soil trade network, South Africa is the core net exporter, with a net export area of 1.28 × 10³ km², far exceeding other exporters such as the United States, Russia and Brazil; Mexico is the largest net importer of rice virtual soil, with a net import area of 1.07 × 10³ km². Turkey, Saudi Arabia and Germany also show varying degrees of net import dependence, indicating that the flow direction of rice virtual soil trade is highly concentrated in a few nodes. In the corn virtual soil trade network, the United States, Brazil and Argentina constitute a solid supply side camp, with net exports of 32.15 × 10³ km², 17.72 × 10³ km² and 8.55 × 10³ km² respectively, while Japan has become the world’s largest inflow country of corn virtual soil with a net import of 55.78 × 10³ km². Mexico, South Korea and China are also the main importers, reflecting the deep land resource output of the American corn belt to the markets of East Asia and North America. In the soybean virtual soil trade network, the flow direction of virtual soil presents the characteristics of extreme one-way agglomeration. Brazil and the United States are absolutely dominant net exporters, with net exports of 182.04 × 10³ km² and 119.72 × 10³ km², respectively. Argentina and Canada also contribute considerable net outflows. With a net import area of 453.37 × 10³ km², China has become the world’s largest inflow country of soybean virtual soil, far surpassing other importers such as Mexico, Japan and Indonesia, highlighting China’s external dependence on land resources driven by soybean imports. In general, the United States occupies the core supply position in the virtual soil trade of corn and soybean, while Brazil ranks first in the virtual soil export of soybean. The differentiation of the roles of countries in different crop networks clearly reflects the reallocation pattern of land resources behind the global food trade.

3.1.2. Analysis of Virtual Land Trading Pattern of Grain Products

We selected four kinds of grain products in 2013 and 2023 to compare the net flow pattern of virtual land between countries and analyze the changing trends.

The net virtual land flow patterns of wheat in 2013 and 2023 are presented in Figure 1. In 2013, the export area of wheat virtual land between Argentina and Brazil was the largest, at up to 0.41 × 10³ km², followed by 0.25 × 10³ km² of wheat virtual land exported from Turkey to Indonesia. From the perspective of wheat import virtual land area, Brazil was the largest importer of wheat virtual land from Argentina, at 0.44 × 20³ km², followed by 0.19 × 10³ km² of wheat virtual land imported from Turkey by Indonesia. In 2023, Argentina was the top virtual land exporter of wheat to Brazil, at 0.98 × 10³ km², followed by Germany, which exported 0.29 × 10³ km² to France. In terms of wheat virtual land imports, Brazil and Argentina had the largest trade area (1.04 × 10³ km²), followed by the United States and Canada (0.41 × 10³ km²). From 2013 to 2023, the role of Argentina and Brazil as major wheat trading countries remained unchanged. The export area of wheat virtual land in 2023 increased compared with that in 2013, while the import demand of France, Canada, and other countries increased significantly.

The net virtual land flow patterns of rice in 2013 and 2023 are presented in Figure 2. The United States was the primary net exporter of virtual land incorporated in rice trade in 2013 based on international flow patterns. The United States exported 0.83 × 10³ km² of rice virtual land to Mexico and 0.10 × 10³ km² of rice virtual land to Turkey. The primary exporter of virtual land incorporated in rice trade with Mexico in 2023 is still the United States (0.52 × 10³ km²), followed by Brazil (0.44 × 10³ km²).

The net virtual land flow patterns of corn in 2013 and 2023 are presented in Figure 3. An analysis of virtual land flows in international corn trade revealed that the largest net import of virtual land in 2013 was Japan’s import of 23.63 × 10³ km² to the United States, followed by Mexico’s import of 20.58 × 10³ km² to the United States. In 2023, Mexico imported 40.91 × 10³ km² of corn virtual land from the United States, followed by Japan’s import of 25.15 × 10³ km² from the United States. Brazil accounted for the largest net export of virtual land embodied in corn trade in 2013 (7.11 × 10³ km²), primarily destined for Japan, while in 2023, the largest net export area (27.27 × 10³ km²) was from Brazil to China, followed by the virtual land from the United States to Mexico, which was 16.78 × 10³ km². Japan demonstrates heavy reliance on corn imports, particularly highlighting its long-term dependence on the United States. The rise in Brazil’s corn trade with China reflects the potential for cooperation between the two sides in the field of grain and the growing demand for market docking.

The net virtual land transfer trends for soybean in 2013 and 2023 are presented in Figure 4. From the perspective of China’s soybean virtual land trade patterns, in 2013 and 2023, China imported the largest amount of soybean virtual land from Brazil, the United States, and Argentina. In 2013, China imported 180.73 × 10³ km² of soybean virtual land from Brazil, 126.35 × 10³ km² from the United States, and 34.80 × 10³ km² from Argentina. In 2023, China imported 3666.63 × 10³ km² of soybean virtual land from Brazil, 135.74 × 10³ km² from the United States and 10.20 × 10³ km² from Argentina. The importer of the largest area of soybean virtual land exported by the United States and Brazil in 2013 and 2023 is China. It is likely that the Sino–US trade friction since 2018 has led China to reduce soybean imports from the United States and instead increase imports from Brazil, Argentina, and other countries. Although Sino–US relations had eased by 2022, Brazil has progressively strengthened its presence in the Chinese market.

3.2. Analysis of Virtual Land Trade Network of Grain Products

3.2.1. Comprehensive Assessment of Virtual Land Trade Networks

After establishing the basic flow pattern, we now turn to the network structure that controls these flows. Trade networks can be analyzed by building a trade network diagram. Figure 5 shows the weighted trade network diagram of wheat virtual land in 2013 and 2023. It depicts participating countries engaged in wheat virtual land trade, with node size reflecting each country’s centrality, and connecting lines denoting trade relationships between countries. The connecting lines indicate the trade direction from wheat virtual land export countries to import countries. The area of wheat virtual land trade between the two countries is represented by the thickness of the edge. The overall structure shows a relatively dense trade network of virtual land area for wheat. In 2013 and 2023, the United States, Canada, Argentina, and Brazil had the largest trade exchanges of wheat virtual land, holding significant positions in the weighted trade network. In 2013, the area of wheat virtual land exported by Germany to France, Canada to the United States, and Argentina to Brazil was large. By 2023, this area had significantly increased.

Table 4. Comprehensive features of virtual land trade networks in grain commodities.

Grain Type	Year	Network Density	Degree Center Potential	Average Degree	Average Clustering Coefficient	Average Path Length
Wheat	2013	0.497	0.3529	8.947	0.642	1.484
	2023	0.468	0.2476	8.421	0.666	1.469
Rice	2013	0.146	0.2348	2.632	0.226	1.921
	2023	0.143	0.3455	2.579	0.253	2.35
Corn	2013	0.439	0.3417	7.895	0.552	1.595
	2023	0.465	0.2476	8.368	0.579	1.458
Soybean	2013	0.374	0.4779	6.737	0.539	1.682
	2023	0.322	0.4505	5.789	0.514	1.672

offers a comparative assessment of the structural properties of virtual land trade networks in grain product markets between 2013 and 2023. The density of wheat virtual land trade network increased, the average degree decreased, the average clustering coefficient decreased, and the average path length decreased. It shows that the centralization of the wheat virtual land trade network is weakened, the distribution of trade power tends to be decentralized, and the efficiency of transnational virtual land flow is improved.

3.2.2. Individual Characteristics of Virtual Land Trading Network

We examined the node-specific attributes of grain product virtual land trade networks through relative centrality, intermediary centrality, and eigenvector centrality analyses.

Table 5. The top ten nations ranked by centrality in the virtual land trade network for grain products (weighted).

Grain Type	Year	Relative Centrality
Wheat	in-degree
	2013	USA	IDN	BRA	CAN	FRA	MEX	DEU	UKR	SAU	CHN
	2023	BRA	USA	FRA	MEX	CAN	DEU	IDN	UKR	SAU	CHN
	out-degree
	2013	USA	CAN	IND	TUR	ITA	DEU	FRA	AUS	RUS	IDN
	2023	ARG	CAN	ITA	DEU	TUR	IND	JPN	FRA	MEX	UKR
Rice	in-degree
	2013	MEX	TUR	BRA	ZAF	ITA	FRA	CHN	IDN	SAU	USA
	2023	MEX	FRA	ITA	UKR	RUS	DEU	CAN	USA	BRA	IDN
	out-degree
	2013	USA	RUS	IND	ARG	FRA	ITA	CHN	DEU	UKR	BRA
	2023	USA	BRA	ITA	FRA	SAU	DEU	CAN	TUR	UKR	CHN
Corn	in-degree
	2013	JPN	KOR	IDN	MEX	CHN	USA	SAU	TUR	ITA	UKR
	2023	CHN	MEX	JPN	KOR	SAU	CAN	IDN	USA	ITA	UKR
	out-degree
	2013	BRA	USA	ARG	IND	RUS	ZAF	FRA	CAN	DEU	AUS
	2023	BRA	USA	ARG	ZAF	CAN	FRA	TUR	DEU	AUS	MEX
Soybean	in-degree
	2013	CHN	MEX	JPN	DEU	IDN	USA	KOR	ITA	UKR	SAU
	2023	CHN	MEX	ARG	JPN	DEU	ITA	IDN	TUR	KOR	RUS
	out-degree
	2013	BRA	USA	ARG	CAN	IND	RUS	ITA	AUS	DEU	FRA
	2023	BRA	USA	ARG	CAN	CHN	TUR	IND	FRA	ITA	DEU

presents the top ten countries ranked by relative centrality in the weighted virtual land trade network of four food products for 2013 and 2023, demonstrating their network centrality and revealing dynamic patterns in grain virtual land trade among G20 countries.

In the 2013 wheat virtual land trade network, the United States, Indonesia, and Brazil were highly weighted. By 2023, Brazil became the highest weighted country, but the drop in Indonesia’s ranking indicates that Brazil has always played a role in the wheat import trade. France and Mexico are also emerging as significant wheat importers, enhancing their influence in international markets. In terms of weighted output, the United States, Canada, and India took the lead in 2013. However, in 2023, the United States fell out of the top 10, and Argentina rose rapidly to become the country with the highest weighted export, showing its strong competitiveness in wheat exports.

In the 2013 rice virtual land trade network, Mexico had the highest weighted penetration, followed by Turkey and Brazil. By 2023, Mexico was still the most important rice importer, while France and Italy were more prominent as important rice importers. Russia, Germany, and Canada also demonstrated substantial demand in the rice market, while Turkey and Brazil’s import status declined rapidly. In 2013, the United States, Russia and India ranked higher in the weighted output. By 2023, the United States was still the country with the highest weighted output, followed by Brazil and Italy; this shows that the United States plays an important role in the import and export of rice virtual land trade. Russia, India, and Argentina fell out of the top ten countries with weighted exports and were replaced by Saudi Arabia, Canada, and Turkey.

For the weighted penetration of the corn virtual land trade network in 2013 and 2023, the top ten countries remained basically unchanged, except that Canada replaced Turkey in 2023. In 2023, China became the country with the highest weighted participation, and the ranking of Japan, South Korea, and the United States declined significantly. Brazil, the United States, and Argentina maintained their dominant positions in corn exports in both 2013 and 2023, as measured by weighted export shares, while India and Russia experienced a relative decline during the same period, while France and Turkey rose to become important exporters of corn virtual land trade, reflecting the increase in corn market trade between France and Turkey. In the trade of soybean virtual land in 2013 and 2023, China and Mexico are still stable in the front in terms of weighted entry, indicating that China and Mexico hold significant positions in soybean virtual land trade through their import and export activities. Germany and the United Kingdom fell out of the top 10, while Argentina and Russia ranked in the top 10, indicating that Argentina and Russia have a large demand for soybeans. In terms of weighted exports, Brazil, the United States, Argentina, and Canada have stable positions and continue to dominate soybean exports, while China and Turkey have increased their positions, indicating that China and Turkey have increased their exports of soybeans.

With the globalization of world trade, the national grid of food trade participation is evolving. The shifts in these countries’ rankings reflect not only evolving patterns of food production and consumption globally but also emerging realignments in trade relations among major food-exporting countries. Countries should prioritize monitoring the evolving dynamics of virtual land trade in global agricultural markets, enhance collaboration with economically advanced countries, bolster their competitive edge, adapt nimbly to market fluctuations, and optimize the utilization of food trade and resource allocation.

Table 6. Betweenness and eigenvector centrality rankings in the weighted grain virtual land trade network.

Grain Type	Year	Intermediary Centrality
Wheat	2013	USA	FRA	ITA	BRA	KOR
		12.792	9.442	6.458	3.868	3.274
	2023	FRA	ITA	BRA	USA	DEU
		4.285	4.285	4.285	4.285	2.2
Rice	2013	TUR	UKR	USA	IND	DEU
		9.7	8.917	8.838	8.576	7.031
	2023	BRA	IND	UKR	DEU	USA
		21.442	13.537	12.536	9.38	7.852
Corn	2013	ARG	USA	ZAF	BRA	IND
		7.008	7.008	4.802	4.078	3.615
	2023	BRA	ZAF	USA	FRA	DEU
		3.558	3.558	3.558	2.913	2.027
Soybean	2013	USA	CHN	CAN	BRA	IND
		16.483	12.912	7.366	7.299	6.886
	2023	USA	BRA	CHN	CAN	UKR
		13.502	7.502	5.752	4.986	2.633
Grain type	Year	Centrality of eigenvector
Wheat	2013	USA	AUS	JPN	CHN	KOR
		1	0.928205	0.79255	0.792149	0.763876
	2023	BRA	FRA	USA	ITA	TUR
		0.292	0.292	0.292	0.292	0.284
Rice	2013	DEU	USA	UKR	ITA	TUR
		0.391	0.389	0.373	0.356	0.314
	2023	BRA	UKR	USA	DEU	ITA
		0.388	0.348	0.335	0.31	0.308
Corn	2013	ARG	USA	FRA	BRA	ZAF
		0.315	0.315	0.292	0.289	0.282
	2023	BRA	USA	ZAF	FRA	DEU
		0.3	0.3	0.3	0.283	0.27
Soybean	2013	USA	CHN	CAN	BRA	UKR
		0.341	0.303	0.3	0.28	0.279
	2023	USA	BRA	CAN	CHN	ITA
		0.351	0.343	0.329	0.304	0.293

lists the five highest-ranking countries in terms of intermediary centrality and eigenvector centrality of the virtual land trade weighted network of four food products in 2013 and 2023. Intermediary centrality directly reflects the ability of nodes to control resources. The higher the value, the greater its impact on the virtual land trade of grain products in other economies. The United States had the highest intermediary centrality in the wheat virtual land trade network in 2013, followed by France and Italy. In 2023, France became the country with the highest degree of intermediary center of wheat virtual land trade, and Italy ranked second, while the influence of the United States and South Korea declined. In the weighted network of rice virtual land trade in 2013, Turkey had the highest degree of intermediary centrality but fell out of the top 5 in 2023. Brazil jumped to become the country with the highest degree of intermediary centrality in rice virtual land trade, and India, Britain, the United States, and Germany ranked among the top five countries in the world. In the corn virtual land trade network, Argentina ranked first in the intermediary centrality in 2013, while Brazil ranked first in 2023, becoming the center of the corn market. South Africa and the United States were key countries in the corn virtual land trade in both years, while the influence of Argentina and India declined. In the soybean virtual land trade network, the United States ranked first in 2013 and 2023, leading the soybean market. The influence of China and Canada declined slightly, while Brazil’s influence in the soybean market increased significantly in 2023.

The eigenvector centrality of nodes in the grain products virtual land trade network quantifies their structural influence through weighted connections with highly central trading partners. In the wheat virtual land trade network, the influence of the United States fell from the first in 2013 to the third in 2023. The centrality of Brazil’s eigenvector was ranked first in 2023, becoming the country with the largest overall influence on the wheat virtual land trade. The overall influence of France, Italy, and Turkey increased in 2023. In 2013, Germany held the highest ranking in the rice virtual land trade network, with the United States and the United Kingdom following in second and third place, respectively. In 2023, Brazil’s eigenvector centrality ranked first, becoming the country with the highest overall influence in the rice virtual land trade network. Germany’s overall influence declined, and the positions of the United States and the United Kingdom were stable. In the corn virtual land trade network, the United States, Brazil, France, and South Africa are the central countries, and Argentina’s status declined significantly in 2023. The United States ranked first in the overall influence of soybean virtual land trade in 2013 and 2023, reflecting the absolute dominant position of the United States in the soybean market. China’s ranking fell from second in 2013 to fourth in 2023. The positions of Brazil and Canada were relatively stable.

In general, although the United States, Brazil, Argentina and other more developed countries have a higher centrality in food products than other countries, they also have their own backward areas. For example, the centrality of the intermediary and eigenvector of the United States in the rice market is not high; China exhibited relatively weak performance in the wheat and corn markets; and Argentina demonstrated limited comparative advantage in both wheat and rice markets. Consequently, these countries should enhance agricultural science and technology innovation in relation to their underperforming food commodities while improving crop climate adaptability. Simultaneously, trade hub countries should exert robust guidance to facilitate exchange and cooperation in food production technologies. China’s intermediary centrality ranking is generally on the rise, indicating that China is gradually taking the central control position in the grain virtual land trade network, and its role as a “bridge” in the grain virtual land trade network is more prominent.

3.3. Research on Influencing Factors: Exponential Random Graph Model

In order to understand what drives the formation of this network, we turn from structural description to causal reasoning. ERGM framework captures endogenous structures, such as reciprocity, that cannot be identified by traditional gravity models. Gravity model assumes that trade relations are independent; ERGM reveals that virtual land trade is self-organized—the link from a to B will increase the possibility of reverse link. This confirms that virtual land analysis is a unique framework, revealing the redistribution of land use pressure and its driving mechanism.

3.3.1. Role of Endogenous Network Structure

The endogenous mechanism of the network refers to the self-evolution of network relations through the internal structure to form different patterns, which will affect the later evolution process. This endogenous mechanism can reveal the structure-dependent characteristics of network formation and evolution [27]. The reciprocity effect can measure the trend of the reciprocal relationship at each node, indicating that there is a mutual relationship between virtual land trade import and export economies. This describes the tendency of economies to interact in the trade network relationship. If country A has an export relationship with country B, country B is more likely to export to country A than other countries due to low transaction and information costs and moral hazards [28].

3.3.2. Role of Exogenous Node Attributes

The network exogenous mechanism refers to the influence of the exogenous attributes of network nodes on the formation and evolution of network relations. The exogenous mechanism is composed of actor attributes and network covariate effects. Actor characteristics explain the network relationship generated in the social process, including sender effect and receiver effect. Sender effect means that economies with certain characteristics are more likely to be exporters in virtual land trade, while receiver effect means that economies with certain characteristics are more likely to be importers in virtual land trade. The degree of development, population scale, and land scale of each country affects the import and export behavior of virtual land trade and the choice of trading partners. Therefore, we selected economic strength (GDP), population scale (POP), cultivated land scale (CAL), per capita arable land area (PCAL), and labor resources (WORKs) as actor attribute variables. Network covariate means that the interaction between countries will also affect trade behavior. First of all, language relations will affect trade behavior. The greater the language difference, the greater the communication cost, thus inhibiting trade behavior. Secondly, geographical factors are important constraints on the behavior and scale of trade. Due to more convenient and economical transportation between adjacent economies, it is easier for adjacent economies to establish virtual land trade relations. Therefore, the language proximity among economies (NN1) and the distance between national capitals (NN2) are taken as network covariates to explore their impact on virtual land trade relations.

3.3.3. Analysis of Empirical Results

The average virtual land outflow of the four major grain products—wheat, rice, corn and soybeans—among G20 countries in 2013, 2018, 2020, and 2023 were taken as the data of the virtual land trade network of grain products. The virtual land trade network was estimated and fitted based on the exponential random graph model, as shown in

Table 7. Empirical regression results of index random graph model of the virtual land trade network among G20 countries.

Network Statistics	Model 1	Model 2	Model 3	Model 4	Model 5
edges	1.69422 ***			0.73263 **	−2.21857 ***
mutual		2.31072 ***			1.66632 **
nodeicov.gdp			17.98956 ***		23.74397 ***
nodeicov.pop			40.02059 *		76.96755 **
nodeicov.cal			−1.77723		−3.86616 *
nodeicov.pcal			1.30386		2.70538 *
nodeicov.work			−38.89923		−73.43941 **
nodeocov.gdp			16.85255 ***		21.91453 ***
nodeocov.pop			42.85092 *		82.31502 **
nodeocov.cal			−1.02113		−2.66600
nodeocov.pcal			0.93802		2.10366
nodeocov.work			−43.34987 *		−81.53349 **
absdiff.gdp			−15.45694 ***		−20.41380 ***
absdiff.pop			−33.99972 *		−71.53208 **
absdiff.cal			−0.66924		0.33090
absdiff.pcal			−0.24733		0.07474
absdiff.work			33.60258		70.16371 *
edgecov.NN1				2.54893 *	1.51478
edgecov.NN2				1.08095 ***	−0.83722 *
AIC	−176.59658	−204.57366	−202.85059	−53.60870	−220.19409
BIC	−172.76177	−200.73885	−145.32843	−45.93908	−147.33269
Log Likelihood	89.29829	103.28683	116.42530	28.80435	129.09705

Note: ***, **, * = p at 0.1%, 1%, 5%, respectively. Blanks indicate that the variable is not considered in the model. See Table 1 for the explanation of variables.

. Model 1 is the basic model and only contains edge statistics; Model 2 is an endogenous structural effect model, including reciprocity statistics; Model 3 is an actor attribute variable, including sender effect and receiver effect; Model 4 is the network covariate effect, including the statistical items of language proximity and geographical proximity; and Model 5 is a comprehensive model, which integrates all variables into the same statistical model to comprehensively assess the influence of different statistical items on the formation of virtual land trade network. This paper analyzes the comprehensive Model 5, including endogenous and exogenous variables.

The coefficient of reciprocity is significantly positive at the level of 1%, indicating that there are exports and imports of grain virtual land among G20 countries, and that there is a high degree of dependence on this trade among economies. In terms of sender effect, GDP passed the significance level of 0.1% and the coefficient was positive, and POP passed the significance level test of 1% and the coefficient was positive, indicating that economically developed countries or countries with large populations are more likely to export grain virtual land to the outside world, and that the economic scale improves the supply capacity through capital investment and production technology. As the world’s largest economy in terms of GDP, the United States has highly developed modern agriculture, with a large amount of grain surplus exported to all parts of the world, and has become one of the world’s largest net exporters of virtual land, especially in soybeans and corn. China is the world’s most populous country and also a large agricultural country. Although China is a net importer of virtual land on the whole (especially in soybeans), it is also an important exporter of some crops. CAL is significant at the 5% level and the coefficient is negative, which may lead to low efficiency due to excessive dependence on extensive planting. PCAL is at the level of 5% and the coefficient is positive, and WORK is significantly negative at the level of 1%. The total area of cultivated land in India is even slightly higher than that in China, ranking first in the world. But at the same time, it is also the world’s most populous country. In order to feed its huge population, India’s land is under great pressure, and its agricultural production is more to meet domestic demand than large-scale export. Argentina has the famous pampas grassland, rich in cultivated land resources and relatively moderate population, so the per capita cultivated land area is also very considerable. This makes it one of the world’s major exporters of soybeans, corn and wheat, and a key sender in the virtual land trade network. Labor resources are scarce in the United States, but relying on large-scale mechanized farms, a farmer can cultivate thousands of acres of land. This model makes the planting area of corn, soybean and other crops huge, making it the core sender of virtual land.

The promotion of export by per capita cultivated land area can reflect the efficiency advantage of land intensive management, which indicates that countries with large per capita cultivated land area or small labor force are more likely to export grain virtual land. In terms of the recipient effect, GDP passed the significance level of 0.1% and the coefficient was positive, and the coefficient of POP was positive and passed the significance level test of 1%. The grain import demand of economically developed countries was stronger, which is due to the increase in purchasing power and the upgrading of high value-added food consumption. The change in population size would drive the import demand, which showed that the more developed the economy and the higher the population size of the economy, the greater the opportunity to receive the import of grain virtual land trade. Japan is a highly developed economy, but its cultivated land resources are extremely limited. Its high GDP enables it to import a large amount of corn, wheat and soybeans from the world to meet the needs of domestic animal husbandry and food processing industry. As the fourth most populous country in the world, Indonesia has more than 270 million people. Although rice is produced in China, with the growth of population and the change in diet structure, its demand for wheat is increasing day by day. However, domestic production is insufficient, and it needs to import a large amount of wheat from Australia, Canada and other countries, becoming an important food importer. CAL and PCAL coefficients are positive but not significant at the 5% level, indicating that the cultivated land index does not significantly influence the import propensity, indicating that the import decision is more dependent on the demand side than the land resource endowment. Some countries with large CAL (such as China and India) also have a large population, resulting in insufficient arable land per capita and still need to import a large amount. Other countries with large CAL (such as the United States and Brazil) export a lot because of their relatively small population and high production efficiency. Even countries with high PCAL (such as Australia) may mainly export rather than import if their population is small and their demand is small. Work is significant at the 1% level and the coefficient is negative, indicating that countries with a small labor force have greater opportunities to accept virtual land trade imports. Japan’s agricultural labor force is in serious shortage and aging. The high labor cost makes it impossible to grow feed grain on a large scale. Therefore, Japan chose to import a large number of corns, soybeans and wheat from the United States, Brazil and other countries. The coefficient of the GDP difference index is significantly negative at the 0.1% level, indicating that the smaller the difference in GDP, the higher the probability of forming a connection between nodes, which means that countries with similar economic scales are more likely to form trade partnerships. POP difference index passed the significance level of 1% and the coefficient was negative, indicating that the food virtual land trade between countries and partners with similar population size was more closely linked. The coefficient of WORK difference index is significantly positive at the 5% level, suggesting that the bigger the difference in labor structure among countries, the higher the probability of forming food trade relations.

In terms of network covariates, language proximity is not significant but the coefficient is positive, indicating that whether the two countries use the same language exerts a modest positive influence on the formation of virtual land trade network. In the virtual land trade, the driving force of economic fundamentals such as economic scale, population demand and resource endowment is much stronger than that of language and culture. Once there is strong economic complementarity (for example, China needs soybeans and Brazil can supply them), language differences will not prevent trade from being reached. Geographical proximity is significant at the 5% level, and the estimated coefficient is negative. The negative coefficient means that the enhancement of geographical proximity inhibited the formation of the connection of the trade network, because the geographical distance is directly related to the transportation cost, time delay, and supply chain risk. An increase in distance leads to a rise in logistics costs, reduces the profit space of trade, and thus inhibits the establishment of trade relations. Although there are trade relations between the two countries (for example, Japan imports corn and soybeans from Brazil), the long distance does limit the scale and flexibility of trade. If the United States can provide corn of the same quality, Japan will usually give priority to the United States because of shorter transportation time and lower cost. This reflects the inhibitory effect of geographical distance on trade.

3.3.4. Goodness of Fit Diagnosis

The goodness-of-fit diagnostics for the ERGM, including degree distributions and geodesic distances, are presented in Appendix A (Figure A1). The results confirm that the model provides an adequate representation of the observed network structure.

3.4. Dual Heterogeneity Analysis of Country and Grain Types

Finally, we reveal the heterogeneity under the general pattern and reveal how the roles of countries are systematically different depending on the development status and food types. G20 countries exhibit significant differences in economic development levels and resource endowments, while food grains (wheat, rice) and feed grains (corn, soybean) possess distinct strategic attributes. Based on Table 4 and Table 5, this section conducts an interactive analysis from a dual heterogeneity perspective.

3.4.1. Country Differentiation in Food Grain Networks

In food grain trade, developed and developing countries display a clear “in-degree out-degree” division. From Table 5, high in-degree countries in wheat and rice networks are predominantly populous developing nations (Mexico, Brazil), confirming the driving role of GDP and POP on import demand. Out-degree centrality, however, concentrates in land-abundant countries: the United States and Canada maintain high out-degree in both food grain types; Argentina’s out-degree ranking in wheat networks surged from 9th in 2013 to 1st in 2023, reflecting its significantly enhanced export competitiveness. Notably, developed countries exhibit internal divergence: the United States and Canada are core exporters, while Japan and Germany are typical importers, revealing the “resource endowment determinism” in food grain trade.

3.4.2. Core-Periphery Structure in Feed Grain Networks

Feed grain trade presents a clearer North–South division. From out-degree centrality in Table 5, high out-degree countries for corn and soybean are highly concentrated in the Americas (United States, Brazil, Argentina, and Canada), confirming the PCAL sender effect—per capita cultivated land endowment is the decisive factor for becoming a feed grain exporter. Regarding in-degree, high in-degree countries are primarily in East Asia (China, Japan, and Korea) and Europe (Germany), nations generally constrained by limited per capita cultivated land. China balances in the ration network (wheat import and rice export) and is the “super receiver” in the feed grain network (soybeans rank first), reflecting the dual logic of safe self-sufficiency in ration and the drive of feed grain market; Brazil is a “super sender” in both types of networks, reflecting its resource endowment advantage. The major grain producing countries (the United States, Brazil, Argentina, and France) generally have higher intermediary control in the network. They are not only trade suppliers, but also hubs connecting different regions, and play an important role in regulating the flow of virtual land resources.

4. Discussion

4.1. Comparison with Existing Literature

Our finding that the U.S. and Brazil dominate virtual land exports while China, Japan, and Germany are primary importers aligns with Qiang core–periphery structure based on physical trade volume [4]. The centrality of the eigenvector in Table 6 reveals the structural dominance beyond trade volume. The United States maintains the highest eigenvector centrality in both corn and soybean networks, confirming its core position in global feed grain trade—consistent with its comparative advantage in land-intensive, mechanized agriculture. Brazil’s eigenvector centrality in soybeans increased from 0.28 (2013) to 0.343 (2023), reflecting its rising structural influence as its share of the Chinese market expands—a shift driven by Sino–US trade friction.

Intermediary centrality in Table 6 identifies the key intermediary countries that control resource flows. Argentina’s high betweenness in the corn network reflects its critical role linking South American producers to global markets—despite not being the largest physical exporter. This aligns with its comparative advantage in extensive production: lower yields mean each ton of corn embodies more virtual land, elevating its position in land-use pressure redistribution networks. Conversely, the United States’ persistently high betweenness in soybeans confirms its role as a system hub whose removal would disrupt numerous trade paths—structural power gravity models cannot capture.

Fourth, the network density and clustering coefficient in Table 4 reflect the evolution and integration of virtual land trade. The increasing density and decreasing average path length of the corn network indicate improved trade efficiency—consistent with comparative advantage logic that liberalization enables specialization according to resource endowments. In contrast, the relative stability of wheat and rice networks reflects stronger food security policy constraints, limiting pure market-driven specialization. Our ERGM results confirm Zhou and Yanan’s findings that GDP and population size positively influence trade flows [15,16]. However, we further reveal that reciprocity effects (mutual = 1.666, p < 0.05) operate independently of these exogenous factors—a dynamic unidentifiable in gravity models. This demonstrates that trade networks are self-organizing: once established, bilateral dependencies self-reinforce, creating path dependencies. This challenges gravity models’ assumption of independent trade relations, revealing how trust, logistical familiarity, and institutional ties co-evolve with resource flows.

Furthermore, Weijiao found that China’s role in ration and feed grain is differentiated, and the balance of ration and feed grain are highly dependent [29]. We found that not only China but also Brazil are senders in both types of networks. The United States and Canada are exporters in rations and still dominate in feed grains. Japan and Germany are receivers in both types of networks. This shows that the position of countries in global land governance is not a single unchanged, but a differentiated positioning based on resource endowment and food security strategy.

4.2. Normative Significance: Efficiency, Fairness and Risk

It is important to acknowledge that virtual land trade is not normatively neutral; it entails both potential benefits and risks, which have been the subject of vigorous scholarly debate. On the one hand, virtual land trade can be viewed through the lens of comparative advantage, where land-abundant countries specialize in land-intensive crops, enhancing global resource efficiency and food security [4,30]. From this perspective, the “robust development” of global land trade is desirable because it allows land-scarce countries to meet food demand without further stressing their domestic ecosystems. On the other hand, a critical body of the literature frames virtual land trade as “land grabbing” or “ecologically unequal exchange” [31]. From this viewpoint, affluent nations displace their environmental burdens onto poorer, land-abundant countries by importing land-intensive products, thereby externalizing the ecological costs of their consumption [32]. This raises concerns about environmental load displacement and the reinforcement of global inequalities. Furthermore, geopolitical risks emerge when food-importing countries become overly dependent on a few exporting nations, making their supply chains vulnerable to trade disruptions, sanctions, or climate shocks [33].

Rather than advocating for or against the expansion of virtual land trade, this study aims to provide an empirical foundation for these normative debates. By mapping the structure of the virtual land trade network and identifying key nodes and flows, we offer insights that can inform both efficiency-oriented policies (e.g., optimizing trade partners) and equity-oriented interventions (e.g., compensating exporting countries for ecological losses). Ultimately, whether the “robust development” of global land trade is desirable depends on how its benefits and costs are distributed—a question that our network analysis helps to illuminate.

5. Conclusions and Suggestions

5.1. Main Findings

This study investigates the flows of virtual land associated with wheat, rice, corn, and soybean trade, with a focus on flow patterns and regional disparities in G20 countries, and constructs a virtual land and food product trade network of four food crops in 2013 and 2023. Through network analysis of food trade flows, this study evaluates the strategic positions of different countries and anticipates future food development trajectories. Furthermore, the virtual land flows of four major grain products are aggregated to construct a comprehensive virtual land trade network for total grain trade, followed by an analysis of key variables influencing this network:

• Virtual land trade is essentially a redistribution mechanism of land use pressure, not just the flow of food. The United States and Brazil dominate the export of virtual land, while China, Japan and Germany are the main importers. This finding reflects the global division of labor in land use: land-rich countries with high PCAL export virtual land, while land-scarce, labor-scarce or high-income countries import virtual land. The virtual land perspective reveals the problems covered by the volume of physical trade. Argentina’s central position in the corn network has improved. Although it is not the largest physical exporter, it reflects its low production, so the content of land per ton is high.
• The formation of network is driven by exogenous economic factors and endogenous relations. While GDP and population size have positive effects on export and import propensity, which confirms the role of economic scale and consumer demand. Reciprocity is significantly positive at the 1% level, indicating that virtual land trade is self-organized. Trade relations have a reverse relationship, indicating that trust, familiarity with logistics, institutional linkages and resource flows develop together. This kind of endogenous dynamics that cannot be observed in the gravity model means that once established, the bilateral trade dependency will strengthen itself and form the path dependency of the long-term resource allocation model.
• The role of the state in the network is not single and unchanged, but changes systematically with food types and development stages. Developed countries are mainly the recipients of virtual land (Japan, Germany) or two-way participants (the United States, Canada), while developing countries are divided into senders (Brazil, Argentina) and recipients (China, Mexico), reflecting the differentiated positioning of countries based on resource endowment and food security strategies. The grain ration trade is strongly constrained by the food security policy, the network pattern is relatively stable, and the control power of the main producing countries continues. Feed grain trade is driven by market mechanism, with higher network density and closer trade links, and the status of emerging market countries has increased significantly. The intermediary centrality of major producing countries in the network reflects their key role in the redistribution of global land resources.

5.2. Policy Implications

Based on the above conclusions, in order to promote the development of virtual land trade in countries around the world, the following measures and suggestions are put forward:

In view of the significant differences in virtual land flow for different food products in different countries, the allocation and management of land resources should be optimized. According to the virtual land content of imported agricultural products, the trade structure of land-intensive crops and low-land-demand crops should be accurately matched to maximize the efficiency of resource utilization. Countries should also explore diversified channels for food import, reduce dependence on individual countries, and ensure the stability of the supply chain. On this basis, in order to promote the efficient use and sustainable management of land resources, targeted import security and supply chain security measures should be put forward to improve the food security and stability of land resources in various countries.

The virtual land trade between the core nodes is highly interactive. Strengthening the contact and cooperation between the network edge countries and the core node countries of the virtual land trade network is conducive to expanding their influence in the network and meeting more trading partners. The virtual land trade network is becoming more and more complex, with only a few core countries such as the United States, Brazil and Germany having leading power. Recognizing that the export of virtual land brings ecological costs, deforestation, soil degradation and water consumption, it is required to integrate sustainability into trade policies. Mechanisms such as ecological compensation or sustainability certification can combine export earnings with long-term environmental management to prevent the depletion of the resource base that weakens export competitiveness.

Rations are related to the national security strategy and may require targeted domestic productivity improvement and strategic reserve investment. Driven by the market, feed grain may benefit from liberalization and diversification strategies and reduce concentration risk while taking advantage of global comparative advantages.

5.3. Limitations and Future Research

This study still has the following limitations: first, the limitations of data and accounting methods. Limited by the FAO trade matrix, the study only covers four major crops and does not include all land intensive agricultural products, which may underestimate the total scale of virtual land flow. At the same time, the calculation uses the unit output data of various countries, without excluding the impact of entrepot trade, which may lead to the misjudgment of some flows. Second, the limitations of model assumptions. Based on static network inference, ERGM compares the changes in 2013 and 2023, but it is difficult to capture the immediate impact of external shocks such as geographical conflicts and trade frictions on network relations. Third, the limitation of conceptual boundary. Virtual land only reflects the quantitative dimension and does not distinguish the differences in land quality and ecological carrying capacity. The dynamic network model can be introduced into future research, and the weighted analysis can be carried out in combination with the degree of land degradation.