Evolution of Disruption Resilience in the Wood Forest Products Trade Network, Considering the Propagation of Disruption Risks and Underload Cascading Failure

Abstract

With the intensification of global resource competition, the issue of timber supply has escalated from an economic concern to a significant strategic challenge. This study focuses on the evolution of disruption resilience in the global trade network for wood forest products, aiming to reveal the patterns of resilience dynamics under disruption risks by simulating underload cascading failure phenomena. The study provides theoretical support for enhancing the security and stability of the global wood forest product supply chain. Utilizing global trade data from the UN Comtrade Database 2023, a directed weighted complex network model was constructed, spanning upstream, midstream, and downstream sectors, with trade intensity distances serving as edge weights. By developing an underload cascading failure model, the evolution of disruption resilience was simulated under various disruption scenarios from 2002 to 2023, and the long-term impacts of critical node failures on network performance were analyzed. The results demonstrate significant spatiotemporal heterogeneity in the disruption resilience of the global wood forest product trade network. The upstream network exhibits improved resilience in total node strength but reduced global efficiency. The midstream network shows marked volatility in resilience due to external shocks, such as the global financial crisis, while the downstream network remains relatively stable. Simulations reveal that failures in core nodes (e.g., China, the United States, and Germany) disproportionately degrade global efficiency and node strength, with node centrality metrics positively correlated with network performance loss. This study elucidates the evolutionary mechanisms of disruption resilience in the wood forest product trade network under risk propagation, offering actionable insights for optimizing network robustness and supply chain stability. It is recommended that policymakers promote green supply chain initiatives, accelerate afforestation projects, and enhance domestic timber self-sufficiency to reduce reliance on imported timber, thereby strengthening node resilience and fostering sustainable forest resource utilization for economic and environmental benefits.

1. Introduction

Wood forest products are widely used in various fields due to their economic, ecological, and renewable properties [1]. Their transnational trade is crucial for sustaining global economic growth, meeting timber demands, and conserving forest resources [2]. Global timber production has reached a record annual volume of 4 billion cubic meters, with wood forest product exports hitting a historic high of USD 576 billion in 2022 [3]. The uneven global distribution of forest resources [4]—which are primarily concentrated in Russia, Brazil, Canada, the United States, and China [5]—compels many countries to engage in wood forest product trading to balance supply–demand dynamics, drive economic growth, and meet market needs. This trade forms a complex transnational network, the structural and dynamic characteristics of which have attracted significant attention. With intensifying global resource competition, timber supply issues have evolved from general economic concerns into major strategic challenges [6]. Environmental protection, resource endowments, and geopolitical factors increase the risk of supply disruptions in timber-exporting countries. Once a disruption occurs and triggers a cascading failure, it can cause significant damage to the global wood forest product trade network, potentially leading to the collapse of the entire network. To address this challenge, it is necessary to use scientific models to reveal the patterns of disruption propagation and to assess and analyze network resilience. This approach helps to identify vulnerable segments and potential risks within the network when it is subjected to internal and external shocks.

Recent studies have progressively deepened the understanding of wood forest product trade networks, with particular focus on the roles of core node countries. Tian and Jiang (2016) identified the United States as the core country in the international roundwood trade, while noting the rise of emerging economies like China [7]. Long et al. (2016) revealed the multilateralization trend of international wood forest product trade networks using social network analysis [2]. Pizzol and Scotti (2017) identified marginal suppliers through a trade network analysis [8], whereas Lovrić et al. (2018) demonstrated the intense competition and complementarity between China and countries such as Austria and Germany [9]. Wang et al. (2021) found that China, together with the Netherlands, France, and the United States, forms key hubs in the global network [10]. Zhou et al. (2021) highlighted China and Thailand as core countries with high centrality and growing influence [11]. Hou et al. (2022) emphasized how trade network characteristics affect global value chain positioning, with core countries maintaining dominance [12]. Li et al. (2022) confirmed China’s core status in the Regional Comprehensive Economic Partnership (RCEP) wood forest product trade network [13]. Wang et al. (2023) analyzed global forest product trade from 2000 to 2020, revealing that processed product networks exhibit tighter connectivity and higher efficiency, dominated by high-GDP countries [14]. Liu et al. (2024) further validated the rising influence of Asian developing countries, which now jointly control the global market with North American and European nations [15]. Gao (2023) investigated the complexity and centrality shifts in these networks, arguing that free trade agreements exacerbate imbalances in global forest resources [16]. The global wood forest product network exhibits distinct small-world characteristics—high clustering coefficients with short path lengths. Over time, deepening trade relationships, expanding volumes, and increased bilateral exchanges have made the network structure more ordered. Existing research on the trade network of wood forest products has made significant progress, successfully revealing the topological structures and dynamic changes of core countries within the network and establishing an analytical framework centered on trade volume as the core weight. However, there has been little research on the weighted characteristics of trade routes, which makes it difficult to effectively incorporate weighted factors into network metrics such as the average path length, global efficiency, node-betweenness centrality, and closeness centrality. This limitation hinders the practicality and depth of network models.

As trade network structure research matures, trade security has emerged as a critical issue facing multiple threats, including natural disasters, political and economic fluctuations, and changes in trade policies. The academic community is increasingly focusing on the intrinsic relationship between network structure and security, recognizing that network resilience is a core element for ensuring system stability. This growing recognition is driving related research from traditional topological analysis to more sophisticated resilience-assessment paradigms, thereby forming a new and dynamic research hotspot. Originating from mechanics [17], the concept of resilience refers to a system’s ability to recover its original state or function after disturbances. Network resilience specifically denotes the capacity of networked entities to collaboratively respond to external shocks through adaptation and transformation [18]. With advances in complex network theory, resilience analysis now spans diverse fields: biological systems [19], urban networks [20], transportation [21], economics [22], supply chains [23], and ecological networks [24]. These applications focus on analyzing system responses and recovery capabilities under disruptions.

Network resilience research has evolved from simplicity to complexity since 2007, focusing on four key aspects. The first of these concerns structural determinants: studies show that network density [25,26,27], average path length [28], clustering coefficients [29,30], global efficiency [31,32], hierarchy [33], and assortativity [34] critically influence resilience. Key nodes—particularly those with high betweenness centrality and degree—significantly affect resilience. Optimizing these features enhances disruption resistance and recovery [35]. The second focuses on responses to attack types: random failures cause limited damage, whereas targeted attacks (especially centrality-based ones) severely disrupt networks [36]. Dynamic networks exhibit self-recovery under specific conditions [37]. Effective strategies include structural adaptations, i.e., protecting critical nodes and increasing redundancy [28]. The third area concerns assessment methodologies: resilience evaluation involves complexity reduction, graph–theoretic models for vulnerability identification [38], performance curves visualizing post-attack changes [39], and multi-factor integration [40]. Simulated attacks under extreme conditions form a comprehensive assessment framework. The fourth area concerns risk transmission mechanisms: complex network models and simulations map risk propagation paths [41], revealing network response and recovery mechanisms during crises. Currently, the research on network resilience is predominantly focused on areas such as infrastructure, ecological networks, and transportation networks. Studies on trade network resilience remain in their nascent stages. The core challenge lies in the fundamental differences in dynamic behavior mechanisms following disruptions. Unlike the continuous failure propagation observed in physical networks, disruptions in trade networks trigger discrete cascading failures, characterized by asymmetric jumping patterns of risk diffusion. This distinctive feature necessitates a departure from traditional resilience evaluation frameworks and calls for the establishment of a new analytical paradigm that is specifically tailored to the resilience of trade networks.

Network disruption resilience refers to a network’s ability to maintain or restore acceptable performance under natural risks or intentional attacks [42]. Dynamic resilience assessment through cascading failure analysis under load redistribution mechanisms constitutes a critical research focus [43]. Cascading effects are defined as dynamic mechanisms where initial failures propagate through physical, social, or economic subsystems, ultimately causing severe consequences [44]. The existing studies predominantly employ load–capacity models. Crucitti et al. (2004) developed a cascading failure model with dynamic traffic redistribution, revealing the impacts of single-node failures on network efficiency [45]. Ash and Newth (2007) optimized complex networks against cascading failures using evolutionary algorithms [29]. Wang et al. (2008) established an initial node load-based model to quantify attack vulnerability in scale-free networks [46], while proposing locally weighted redistribution rules to analyze robustness in weighted networks [47]. Dueñas-Osorio and Vemuru (2009) introduced a tolerance parameter model to quantify capacity–demand relationships in infrastructure networks [48]. Recent advances focus on weighted networks and domain-specific systems. Mirzasoleiman et al. (2011) compared network performance under three weighting strategies: edge betweenness, node degree, and betweenness-degree products [49]. Mukherjee et al. (2014) investigated adaptive mechanisms for catastrophic disruptions in telecommunication networks [50]. Han (2017) proposed a tunable cascading failure model, integrating node betweenness, degree, and weight for initial load construction [51]. Li (2018) developed network connectivity entropy metrics for hierarchical network reliability assessments [52]. Cui (2021) designed network operation degree indicators to evaluate failure impacts in directed weighted supply chains [53]. Cascading failure research in trade networks has recently emerged: Li et al. (2021) simulated avalanche effects in global plastic waste trade networks [54]. Hao et al. (2023) assessed lithium trade network robustness under random/targeted attacks [55]; Fu et al. (2024) proposed two-stage recovery strategies for automotive supply chains, identifying underload nodes as primary resilience degradation drivers [56]. Yin et al. (2024) revealed crisis propagation patterns in semiconductor trade networks [57]. Wang et al. (2024) incorporated national risk absorption capacities into improved models for iron ore trade disruption analysis [58]. Finally, Ouyang et al. (2024) combined trade volume and network analysis to characterize static/dynamic resilience in lithium supply chains [59].

Existing studies demonstrate that overload cascading failure models are widely applied, yet their theoretical frameworks prove inadequate for underload cascading failure scenarios. The fundamental distinction lies in failure triggers: overload failures occur when the node load exceeds maximum capacity, whereas underload cascading failures arise from loads dropping below the minimum operational thresholds, leading to performance degradation or functional loss [60]. These differences manifest not only in failure initiation conditions but also in the dynamic characteristics of load redistribution mechanisms. Although overload failure research is relatively mature, studies on underload cascading failures in resource trade networks remain nascent. Critical aspects including modeling approaches, propagation mechanisms, and systemic impacts on global trade networks require further exploration. Particularly in global resource trade networks, underload failures may induce unique cascading effects and network reconfiguration patterns that remain uncharacterized. This research gap underscores the urgent need for theoretical and empirical investigations to advance disruption resilience studies in global resource trade networks.

This study makes theoretical contributions by proposing an innovative underload cascading failure model based on disruption risk propagation, constructing a directed weighted complex network model using global wood forest product trade data (2002–2023) and systematically revealing the long-term impact of network structure evolution on resilience. It extends the existing resilience evaluation framework and provides methodological references for other complex network studies. Practically, our research delivers three key values: the dynamic evolution model accurately characterizes network structure evolution patterns and their resilience impacts, offering a scientific basis for trade network stability optimizations. Multi-scenario simulations are used to analyze network resilience features and quantitatively assess the long-term effects of critical node failures on global efficiency and node strength. Moreover, the establishment of a network resilience evaluation system based on quantitative correlations between node characteristics and performance loss provides direct support for the formulation of risk management strategies. This research not only deepens the understanding of trade network resilience but also offers critical decision-making references for optimizing the stability and risk management of the global wood forest product trade network.

The rest of this article is structured as follows: Section 2 describes the data sources, model construction, and metric design. Section 3 analyzes the simulation results. The conclusion summarizes the key findings.

2. Data Sources and Research Methodology

2.1. Data Sources and Research Framework

Wood forest products, as direct derivatives of forest resources, comprise three structural tiers: upstream primary products (e.g., logs, sawn timber, wood pulp), midstream processed goods (e.g., artificial boards, composite materials), and downstream end-consumer products (e.g., paper, wooden furniture). Based on the HS code classification system from the literature [61] (see

Table 1. HS codes of wood forest products.

Supply Chain Links	Product Category	Commodity Code	Detailed Information Regarding HS Codes
Upstream	Logs	HS4403	Wood in the rough.
	Other Raw Materials	HS4401, HS4402, HS4404, HS4405	Various fuel wood, wood chips/sawdust/waste, wood charcoal, hoop wood/poles/stakes, wood wool/flour.
	Sawn Timber	HS4406, HS4407	Wooden sleepers/cross-ties; sawn/chipped, sliced/peeled wood.
	Wood Pulp	HS4701-HS4706	Wood pulp (mechanical, chemical types); combined pulp; recovered paper/cellulosic pulp.
Midstream	Wood-based Panels	HS4408-HS4413	Veneer, plywood, laminated wood sheets; vood (strips, friezes); particle/OSB/similar boards; fiberboard; densified wood.
Downstream	Wood Products	HS4414-HS4421	Wooden frames; packings, cable-drums, pallets; coopers’ products; tools, handles; builders’ woodwork; wood tableware, kitchenware; marquetry, inlaid wood, ornaments; furniture (excl. ch. 94); other wood items.
	Paper Products	HS48, HS49	Paper, paperboard, articles thereof; printed products, manuscripts, typescripts, plans.
	Wood Furniture	HS940161, HS940169, HS940330, HS940340, HS940350, HS940360	Wooden-framed seats (upholstered/not); wooden furniture (office, kitchen, bedroom, other).
Recycled	Waste Paper	HS4707	Waste and scrap of paper and paperboard.

), this study integrates 2002–2023 trade data from the UN Comtrade Database. The dataset systematically categorizes 1,023,568 trade records across 231 countries/regions into upstream, midstream, and downstream sectors.

For the sake of data consistency, the study utilizes import-based data. To handle missing values in trade data, a stratified mean imputation method is employed: first, the data are grouped according to HS codes and years. Within the same combination of code and year, the arithmetic mean of non-missing trade volumes is used to fill in the missing values, ensuring the homogeneity and temporal consistency of the imputed values. Additionally, regional consolidation (merging data from Hong Kong and Macau into China but not including Taiwan) and trade relationship thresholds (setting a threshold of 50 USD, below which trade relationships are disregarded) have been addressed.

Based on complex network and resilience theory, this study explores the disruption resilience of the global wood forest products trade network. To conduct a comprehensive study, we construct a directed weighted trade network model for wood forest products that encompasses upstream, midstream, and downstream sectors. The upstream network focuses on the supply of primary forest products such as logs and sawn timber; the midstream network centers on the trade of semi-finished goods such as plywood and wood pulp; and the downstream network maps the consumption market of final products such as furniture and paper products. By quantifying trade scales through weighting, we can accurately identify critical supply routes and avoid misjudging minor connections, clarifying each country’s pivotal role and competitive–complementary relationships within the global network. This provides solid data support for optimizing timber supply security and developing risk control strategies.

On this basis, the study analyzes scenarios of disruption risk propagation by constructing an overload cascade failure model to assess performance loss and average retained network performance under disruption disturbances. This approach evaluates node importance and network resilience, along with their evolutionary characteristics from 2002 to 2023, providing theoretical support and practical guidance for maintaining the stability and security of the wood forest product trade network. It contributes to building a more robust, flexible, and sustainable global trade system for wood forest products. The overall research framework is shown in Figure 1. This study not only covers the entire chain of wood forest products but also constructs a global network spanning trade relations between 231 countries and regions. Additionally, it analyzes data from 2002 to 2023, forming a 22-year multidimensional, comprehensive systematic model.

2.2. Graph Theory Model Construction

Using the countries (regions) involved in global wood forest products trade as network nodes, trade relationships between countries (regions) as edges, and trade volume and trade closeness as weights, a complex network model is constructed. The wood forest products supply network is defined as follows:

$$G_m=(V,E,W^1,W^2,T)$$

(1)

where m represents the three different types of global wood networks, namely, upstream, midstream, and downstream. The node set V represents the collection of all countries (regions); the edge set E represents the collection of trade relationships between all countries (regions); $W^1$ represents the collection of edge weights for trade volumes between all nodes; $W^2$ represents the collection of edge weights for trade closeness between all nodes; and $T$ represents the collection of years.

Here, trade volume (in kilograms) is selected as the edge weight for modeling to avoid the influence of inflation and price fluctuations, thereby accurately revealing the trade relationships and dependency levels within the supply chain, which is crucial for analyzing network characteristics. Additionally, drawing on existing research [27], trade closeness is introduced as an edge weight to explore its impact on the shortest path length. The specific calculation formula for this edge weight is as follows:

$$w_{ij}^2=1+\mathit{ln}Max\left(w_{ij}^1\right)-\mathit{ln}\left(w_{ij}^1\right)$$

(2)

where $w_{ij}^2$ represents the trade closeness between node $i$ and node $j$; $Max\left(w_{ij}^1\right)$ denotes the maximum edge trade volume in the network; and $w_{ij}^1$ represents the trade volume of wood forest products exported from node $i$ to node $j$. In practice, trade closeness is undoubtedly influenced by a multitude of complex factors, such as political relations, geographical proximity, cultural differences, and numerous other factors that are difficult to quantify. However, within the specific analytical framework of this study, we focus solely on the core element of trade volume.

2.3. Key Indicators for Analyzing Complex Network Models

On the basis of constructing the graph theory model, we further explain various metrics that are closely related to the subsequent underload cascading failure model and node characteristic analysis, as shown in

Table 2. Indicators related to complex networks.

Indicator Type	Indicator Name	Formula	Specific Description
Structural Characteristics	Number of Nodes	N	N represents the total number of nodes in the network.
	Weighted Global Efficiency	$E_{w^2}={\displaystyle \frac{1}{N\left(N-1\right)}}{\displaystyle \sum _{i\ne j}} {\displaystyle \frac{1}{d_{w^{2}ij}}}$	Weighted global efficiency $E_{w^2}$ refers to the average of the reciprocals of the weighted shortest path lengths $d_{w^{2}ij}$ between all pairs of nodes in the network, taking into account the trade closeness weights. It measures the speed and capability of information transmission within the network.
Node Characteristics	Out-Strength	$W_i^{1, out}={\displaystyle \sum _{j=1}^N} w_{ij}^1$	Out-strength $W_i^{1,out}$ refers to the sum of the export trade volume weights ($w_{ij}^1$) from node i to other nodes.
	In-Strength	$W_i^{1, in}={\displaystyle \sum _{j=1}^N} w_{ji}^1$	In-strength $W_i^{1,in}$ refers to the sum of the import trade volume weights ($w_{ji}^1$) from other nodes to node i.
	Weighted Betweenness Centrality	$B{C}_{w^{2}i}={\displaystyle \sum _{s\ne i\ne t}} {\displaystyle \frac{n_{w^{2}st}^i}{g_{w^{2}st}}}$	Weighted betweenness centrality $B{C}_{w_i^2}$ refers to the ratio of the number of weighted shortest paths $n_{w^{2}st}^i$ passing through node i to the total number of weighted shortest paths $g_{w^{2}st}$ between other trade pairs, considering trade closeness weights. It measures the importance and influence of a country (region) in the network from the perspective of its “bridge” role.
	Weighted Closeness Centrality	$C{C}_{w^{2}i}={\displaystyle \frac{1}{d_{w^{2}i}}}={\displaystyle \frac{N}{{\sum }_{j=1}^N d_{w^{2}ij}}}$	Weighted closeness centrality $C{C}_{w^{2}i}$ refers to the reciprocal of the average weighted shortest path $d_{w^{2}ij}$ from node i to all other nodes, considering trade closeness weights.
	Weighted PageRank Centrality	${PR}_{w^{1}i}=$ $\alpha {\displaystyle {\sum }_{j\in In\left(i\right)}}{\displaystyle \frac{w_{ji}\ast {PR}_{w^{1}j}}{k_i^{out}}}+\left(1-\alpha \right){\displaystyle \frac{1}{N}}$	Weighted PageRank centrality ${PR}_{w^{1}i}$ is a measure of node importance calculated by simulating a random walker that, with probability α, jumps to adjacent nodes along the outgoing edges of the current node, and, with probability (1 − α), jumps to any node in the network, considering trade volume weights. This value depends on the average importance of nodes pointing to it (${\sum }_{j\in In\left(i\right)}{\displaystyle \frac{w_{ji}\ast {PR}_j}{k_i^{out}}}$) and the global visibility of node i in the network (${\displaystyle \frac{1}{N}}$).
	Weighted Eigenvector Centrality	${EC}_{w^{1}i}={\displaystyle \frac{1}{\lambda }}{\displaystyle {\sum }_{j=1}^N}{w}_{ij}{EC}_{w^{1}j}$	Weighted eigenvector centrality ${EC}_{w^{1}i}$ refers to a centrality measure of node i in the network based on the importance of its neighboring nodes ${EC}_{w^{1}j}$, calculated through eigenvector analysis and considering trade volume weights. Here, λ is the largest eigenvalue of the network’s adjacency matrix.
Others	Modularity	$Q={\displaystyle \sum _{\begin{array}{c}i,j\\ i\ne j\end{array}}}\left({\displaystyle \frac{w_{ij}}{H}}-{\displaystyle \frac{W_i{W}_j}{H^2}}\right)\delta (V_i,V_j)$	Modularity Q, proposed by Newman [62] in 2004, is the most popular general metric for evaluating the quality of community division. It measures the quality of community division by comparing the number of edges within communities in the actual network to the expected number of such edges in a random network. The value of modularity ranges from [−0.5,1], and a value closer to 1 indicates a better community division. In the formula, H represents the total strength of all nodes in the network, $W_i$ is the sum of the out-strength and in-strength of node ${\displaystyle \frac{w_{ij}}{H}}$, denoting the average weight of edges within the same trade community, and ${\displaystyle \frac{W_i{W}_j}{H^2}}$ represents the average weight of edges that would be assigned to the same community under complete randomness. The function $\delta (V_i,V_j)$ is used to determine whether nodes i and j belong to the same community: if $V_i$ and $V_j$ are in the same community, $(V_i,V_j)$ = 1; otherwise, $\delta (V_i,V_j)$ = 0.
	Pearson Correlation Coefficient	$r={\displaystyle \frac{{\sum }_{i=1}^n(X_i-\overline{X})(Y_i-\overline{Y})}{\sqrt{{\sum }_{i=1}^n{(X_i-\overline{X})}^2}\sqrt{{\sum }_{i=1}^n{(Y_i-\overline{Y})}^2}}}$	The Pearson correlation coefficient r is used to measure the strength and direction of the linear relationship between variables, with a range of −1 to 1. A value of 1 indicates a perfect positive correlation, −1 indicates a perfect negative correlation, and 0 indicates no linear relationship, although a nonlinear relationship may still exist. In the formula, $X_i \mathrm{a}\mathrm{n}\mathrm{d} Y_i$ represent the i-th observations of variables X and Y, respectively. $\overline{X}$ and $\overline{Y}$ are the mean values of variables X and Y, respectively, and n is the number of observations.

.

The modularity Q in the table above is primarily used in the Louvain algorithm for community detection. The Louvain algorithm, proposed by Blondel et al. in 2008 [63], is an efficient community detection algorithm based on modularity optimization. By iteratively optimizing modularity Q, the algorithm identifies community structures within the network, offering advantages such as high computational efficiency and suitability for large-scale networks. Its core idea is to progressively improve modularity through local optimization, ultimately achieving a globally optimal community division result.

2.4. Disruption Resilience Evaluation Metrics

In the resilience assessment process, we conducted network disruption resilience analysis under the conditions of single-node disruptions induced by underload cascading failures. Specifically, the analysis involved examining the network performance loss rate following single-node disruptions to investigate the intrinsic relationships between node characteristics and network performance degradation. This step facilitated the identification of critical nodes and their impact levels on the overall network performance. Subsequently, the disruption resilience characteristics of the network were revealed by calculating the average network performance retention rate after disruptions to multiple core nodes. This metric reflects the network’s overall robustness and anti-disruption capabilities when facing critical node failures.

The formulas for the single-node-disruption-induced network performance loss rate and single-node disruption resilience are presented below:

$${Loss}_i^h=1-{\displaystyle \frac{P_i^h}{P_0^h}}$$

(3)

$${Resistance}^h={\displaystyle \frac{\sum _{i=1}^{N^{\prime }}{P}_i^h}{N^{\prime }{P}_0^h}}$$

(4)

Here, ${LOSS}_i^h$ represents the network performance loss rate after the disruption of node i; ${Resistance}^h$ denotes the network’s anti-disruption resilience; $P_i^h$ is the network performance retention value following the disruption of node i; $P_0^h$ indicates the initial network performance value; and ‘N’ refers to the number of core nodes in the network.

We selected global efficiency and total node strength of the network as key metrics. The propagation of node disruption risks triggers cascading decay and failure reactions, leading to increased average shortest path lengths and reduced trade volumes among nodes, thereby diminishing both global efficiency and total node strength. The formulas for global efficiency loss rate and global efficiency disruption resilience under single-node disruptions are defined as follows:

$${LOSS}_i^{E_{w^2}}=1-{\displaystyle \frac{E_{w^2,v_i}}{E_{w^2}}}$$

(5)

$${Resistance}^{E_{w^2}}={\displaystyle \frac{\sum _{i=1}^{N^{\prime }}{E}_{w^2,v_i}}{N^{\prime }{E}_{w^2}}}$$

(6)

where ${LOSS}_i^{E_{w^2}}$ denotes the global efficiency loss rate after the disruption of node i, ${Resistance}^{E_{w^2}}$ represents the global efficiency disruption resilience, $E_{w^2}$ is the initial weighted global efficiency (with trade proximity weights), ${Resistance}^{E_{w^2}}$ is the retained global efficiency value after the disruption of node i, and $N^{\prime }$ indicates the number of core nodes in the network.

The changes in total node strength under single-node disruptions directly reflect the network’s connection density, redundancy, and attack resistance capabilities. The formulas for total node strength loss rate and total node strength disruption resilience under single-node disruptions are expressed as:

$${LOSS}_i^w=1-{\displaystyle \frac{\sum _{j=1}^N{w}_j^{v_i}}{\sum _{j=1}^N{w}_j}}$$

(7)

$${Resistance}^w={\displaystyle \frac{\sum _{i=1}^{N^{\prime }}\sum _{j=1}^N{w}_j^{v_i}}{N^{\prime }\sum _{j=1}^N{w}_j}}$$

(8)

Here, ${LOSS}_i^w$ represents the total node strength loss rate, $\sum _{j=1}^n{w}_j^{v_i}$ denotes the sum of the remaining node strengths across the network after the stabilization of the underload cascading failure reaction caused by the disruption of node i, $\sum _{j=1}^n{w}_j$ is the initial total node strength of the network, and $N^{\prime }$ refers to the number of core nodes.

3. Construction of the Disruption Risk Propagation Model

3.1. Model Selection

This study focuses on the underload cascading failure in the trade network of wood forest products. Underload cascading failure occurs when a node’s trade volume is insufficient, leading to its failure, which subsequently affects downstream nodes, causing the disruption to propagate and amplify across the network. Previous studies on cascading failures have mainly focused on infrastructure networks such as power grids, transportation, and communication networks. However, the underload cascading failure in the wood forest product trade network differs fundamentally from these models. Specific differences are compared in

Table 3. Comparison of cascading failure mechanisms between infrastructure networks and the global wood forest product trade network.

Comparison Dimension	Infrastructure Networks	Global Wood Forest Product Trade Network
Type of Cascading Failure	Overload failure: after a node’s interruption, the load is transferred to adjacent nodes, exceeding their capacity and causing failure.	Underload failure: the interruption of a supply node leads to resource shortages in downstream nodes, triggering a reduction in export volumes.
Failure Trigger Conditions	Node or edge interruption causes physical load to exceed capacity limits.	Node or edge interruption causes resource supply to fall below demand thresholds.
Load Allocation Logic	Uniform distribution or non-uniform selective distribution: stronger relationships receive more load.	Non-uniform selective distribution: lower relationship strength receives higher allocation proportion.
Propagation Path of Failure	Spreads along physical topology proximity.	Spreads along supply dependency relationships.

.

On this basis, this study innovatively develops a cascading failure model that is closely tailored to the disruption risk propagation mechanisms specific to the wood forest products trade network. To model this, trade volume is treated as network load, and the network is simplified into an upstream-to-downstream directed structure. A load–capacity framework is adopted, where nodes are assigned initial loads, load decay thresholds, and failure lower bounds. After a disruption, loads are redistributed according to predefined strategies until network stabilization is achieved. The model is constructed based on four aspects—the initial load configuration, decay and failure capacities, load decay functions, and load redistribution mechanisms—in order to provide a foundation for simulating cascading failure dynamics and analyzing network performance evolution.

3.2. Initial Load Configuration

The initial load defines the starting point of the global wood forest product supply network in the underload cascading failure model, encompassing the import and export loads of nodes, as well as edge loads. These load distributions characterize the initial resource allocation and provide a baseline for dynamic simulations. The system vulnerability analysis, underload reallocation, and cascading failure propagation depend on the initial load settings. By establishing a clear baseline, the initial load enables the model to accurately reveal the response patterns of the network under disruption events and assess its resilience. The initial load configuration encompasses a node’s initial import load, initial export load, and the initial load on node i’s outgoing edges. The specific formulas are defined as follows:

$$L_i^{in}=W_i^{1, in}$$

(9)

$$L_i^{out}=W_i^{1, out}$$

(10)

$$L_{ij}=w_{ij}^1$$

(11)

where $L_i^{in}$, $L_i^{out} \mathrm{a}\mathrm{n}\mathrm{d} L_{ij}$ represent node i’s initial import load, initial export load, and the initial load on the outgoing edge from node i to node j, respectively. These correspond to node i’s in-strength $W_i^{1,in}$, out-strength $W_i^{1,out}$, and the trade volume weight $w_{ij}^1$ of the outgoing edge from node i to node j.

3.3. Decay Capacity and Failure Capacity

In the underload cascading failure model, the dynamic response behavior of nodes is divided into two stages. When a node’s load reaches its decay capacity, it enters an initial adaptive adjustment phase, known as the decay state, during which the node reduces its export volume to mitigate the underload caused by import reduction or interruption. Subsequently, when the node’s load reaches its failure capacity, it enters an irreversible functional collapse phase, termed the failure state. During this phase, the node interrupts its export volume to address underload caused by import reduction or interruption. This can potentially trigger a chain reaction of multi-layer failures. The formulas for decay capacity and failure capacity are defined as:

$$C_{i\left(dec\right)}={\alpha }_1{L}_i^{ in} 0\le {\alpha }_1\le 1$$

(12)

$$C_{i\left(min\right)}={\alpha }_2 L_i^{\mathrm{i}\mathrm{n}} 0\le {\alpha }_2\le {\alpha }_1\le 1$$

(13)

where $C_{i\left(dec\right)}$ and $C_{i\left(min\right)}$ denote the decay capacity and failure capacity of node i, respectively; ${\alpha }_1$ is the decay threshold, a key parameter regulating decay capacity during simulations; and ${\alpha }_2$ is the failure threshold, governing failure capacity.

Different nodes exhibit distinct decay and failure coefficients. A node decay state function is further formulated as:

$$f_i\left(t\right)=\left\{ \begin{array}{c}0 L_i^{in}\left(t\right)\ge C_{i\left(dec\right)} \\ {\displaystyle \frac{L_i^{in}\left(t\right)}{L_i^{in}}} C_{i\left(min\right)}\le L_i^{in}\left(t\right)\le C_{i\left(dec\right)} \\ 1 L_i^{in}\left(t\right)\le C_{i\left(min\right)}\end{array}\right.$$

(14)

where $f_i\left(t\right)$ is the decay state parameter, by which fi(t) = 1 indicates failure, fi(t) = 0 represents normal operation, and ${\alpha }_2$ ≤ fi(t) ≤ ${\alpha }_1$ corresponds to the decay state.

3.4. Export Load Decay Function

Before determining the allocation process for export decay amounts, first, the magnitude of the export decay is calculated using a decay function, which is set based on the coupling relationship between the import underload of a node and its load characteristics. Second, nodes are classified into three types according to their import load characteristics (as shown in

Table 4. Export load decay node types.

Node Types	Import–Export Load Characteristics	Decay Characteristics
Type 1 (Import-Dominant)	The import load is greater than or equal to the export load.	The export load exhibits three operational states—normal, decay, and failure—where the decay magnitude is jointly influenced by the import–export load ratio and the node’s decay state.
Type 2 (Balanced Import–Export)	The import load is slightly less than the export load.	The export load similarly demonstrates three states (normal, decay, and failure), with the decay state proportionally diminishing according to the import quantity.
Type 3 (Export-Dominant)	The import load is significantly lower than the export load.	The export load only transitions between normal and decay states, omitting the failure state entirely.

), and different decay functions are determined based on the node type, thereby achieving differentiated dynamic responses in the decay amounts.

Based on the node types defined in Table 3 and the node decay state function (Equation 14), the export load decay functions are further constructed as follows:

(1)

Export Load Decay Function for Type 1 (Import-Dominant) Nodes

The export load decay of import-dominant nodes is jointly influenced by the import–export load ratio and the node decay state. The function is formulated as:

$$∆L_i^{out}\left(t\right)=\left\{\begin{array}{c}0 f_i\left(t\right)=0\\ {L_i^{out} \ast (1-\alpha }_3 \ast f_i\left(t\right)) 0<f_i\left(t\right)<1\\ L_i^{out} { f}_i\left(t\right)=1\end{array}\right.$$

(15)

where $∆L_i^{out}\left(t\right)$ represents the export load decay at node i at time t. When $f_i\left(t\right)=0$, the node operates normally with zero decay. At $f_i\left(t\right)=1$, the node fails, and the export load drops to zero. For intermediate states ($0<f_i\left(t\right)<1$), the decay depends on $f_i\left(t\right)$ and ${\alpha }_3$. The parameter ${\alpha }_3$ quantifies the proportional relationship between export and import loads, calculated as:

$${\alpha }_3={\displaystyle \frac{1}{1+\mathit{ln}\left(W_i^{1, in}\right)-\mathit{ln}\left(W_i^{1,out}\right)}} {W_i^{1,out}\le W}_i^{1,in}$$

(16)

When $W_i^{1,in}=W_i^{1,out}$, the logarithmic difference vanishes (${\alpha }_3$ = 1), aligning the decay rates of the export and import loads. For $W_i^{1,in}>W_i^{1,out}$, the positive logarithmic difference reduces ${\alpha }_3$, amplifying the export load decay proportion (${1-\alpha }_3 \ast f_i\left(t\right)$) compared to the import load decay ($1-f_i\left(t\right)$). This reflects the heightened sensitivity of the export load to supply disruptions when import dependence is significant.

In summary, the α₃ parameter plays a critical role in the export load decay model of import-dominant nodes. By dynamically adjusting the degree of export load decay based on the node’s import–export load ratio, it enables the model to precisely characterize the decay behavior of nodes across varying operational states. This mechanism holds substantial implications for understanding and analyzing how node failures in complex networks influence overall network performance.

(2)

Export Load Decay Function for Type 2 (Balanced Import–Export) Nodes

For nodes with slightly smaller import loads than export loads ($L_i^{in}$ ≥ ${{\alpha }_{4}L}_i^{out}$; ${\alpha }_4$ = 1/5), the decay function is:

$$∆L_i^{out}\left(t\right)=\left\{\begin{array}{c} 0 f_i\left(t\right)=0\\ L_i^{in}-L_i^{in}\left(t\right) 0<f_i\left(t\right)<1\\ L_i^{out} f_i\left(t\right)=1 \end{array}\right.$$

(17)

In intermediate states ($0<f_i\left(t\right)<1$), the export load decay equals the reduction in the import load ($L_i^{in}-L_i^{in}\left(t\right)$), maintaining proportional decay.

(3)

Export Load Decay Function for Type 3 (Export-Dominant) Nodes

For nodes with import loads significantly smaller than export loads ($L_i^{in}<{{\alpha }_{4}L}_i^{out}$), the decay function simplifies to:

$$∆L_i^{out}\left(t\right)=\left\{\begin{array}{c}0 f_i\left(t\right)=0\\ L_i^{in}-L_i^{in}\left(t\right) 0<f_i\left(t\right)\le 1\end{array}\right.$$

(18)

In this formulation, only two states are defined: normal and decay, with no failure state. When $0<f_i\left(t\right)\le 1$, the export load decay equals the initial import load $L_i^{in}$ minus the import load at time $L_i^{in}\left(t\right)$. However, since the export load is significantly larger than the import load, the decay magnitude has a negligible impact on the export capacity.

3.5. Export Load Redistribution

When export load decay occurs, the decay amount $∆L_i^{out}\left(t\right)$ must be redistributed to downstream nodes according to specific rules. Two scenarios are considered: first, if a node fails completely, its export load to all adjacent nodes drops to zero $∆L_i^{out}\left(t\right)=W_i^{\mathrm{o}\mathrm{u}\mathrm{t}}$, and the edge load between node i and its neighbors decays to zero ($∆L_{ij}=w_{ij}^1$). Second, if the node decays but remains functional, the export load is redistributed inversely proportionally to the strength of business relationships. This study posits that, during underload cascading failure, nodes with weaker relationships should receive a larger share of the decayed load, starting from the least critical trade partner, until the decay amount is fully allocated.

In the underload cascading failure model of the global wood supply network, the dynamic allocation mechanism of export reduction differs fundamentally from that in infrastructure network models. First, it follows the principle of global–local coupling assessment, where the importance of downstream nodes is evaluated based on both local supply strength and global topological influence to avoid underestimating the strategic value of nodes with high centrality but low export volumes, thereby improving risk identification accuracy. Second, it adopts the inverse proportion allocation logic principle, wherein lower relationship strength results in a higher allocation proportion, prioritizing the reduction of exports to weaker connections to safeguard critical links, reflecting a self-protection mechanism where nodes prioritize vital supply relationships under resource constraints.

To operationalize this, the importance of trade partner relationships between nodes is defined as:

$$O_{ij}=w_{ij}^1 \ast {EC}_j$$

(19)

where $O_{ij}$ represents the trade partner importance, $w_{ij}^1$ is the trade volume between nodes i and j, and ${EC}_j$ is the eigenvector centrality of node j. The export neighbors of node i are ranked by ascending ${\mathrm{O}}_{\mathrm{i}\mathrm{j}}$ to form a sequence $\mathsf{\sigma }={\mathsf{\epsilon }}_1, {\mathsf{\epsilon }}_2,\cdots {\mathsf{\epsilon }}_{{\mathrm{k}}_{\mathrm{i}}}$, where ki is the out-degree of node i. The residual allocatable decay amount $R_{\mathrm{i}{\mathsf{\epsilon }}_{\mathrm{j}}}$ is calculated as:

$$\left(R_{i{\epsilon }_1},R_{i{\epsilon }_2},\cdots ,R_{i{\epsilon }_{k_i}}\right)$$

(20)

$$R_{i{\epsilon }_j}=∆L_i^{out}-∆L_{i{\epsilon }_1}-∆L_{i{\epsilon }_2}-\cdots -∆L_{i{\epsilon }_{j-1}}$$

(21)

where $R_{i{\epsilon }_j}$ denotes the remaining allocatable decay amount for node i’s edge to neighbor ${\epsilon }_j$, and $∆L_{i{\epsilon }_j}$ is the decay amount allocated to that edge.

For decay allocation in cycle t (starting with $j=1$):

Step 1: Calculate the decay allocation for the neighbor:

If ${\displaystyle \frac{k_i-{\epsilon }_j}{k_i}}$ > $f_i\left(t\right)$, compare $w_{i{\epsilon }_j}\ast {\displaystyle \frac{k_i-{\epsilon }_j}{k_i}}$ with $R_{i{\epsilon }_j}\left(t\right)$. If the former is larger, set $∆L_{i{\epsilon }_j}\left(t\right)=W_{i{\epsilon }_j}\ast {\displaystyle \frac{k_i-{\epsilon }_j}{k_i}}$; otherwise, $∆L_{i{\epsilon }_j}\left(t\right)=R_{i{\epsilon }_j}\left(t\right)$. If ${\displaystyle \frac{k_i-{\epsilon }_j}{k_i}}\le f_i\left(t\right)$, compare $W_{i{\epsilon }_j}\ast f_i\left(t\right)$ with $R_{i{\epsilon }_j}\left(t\right)$. Assign $∆L_{i{\epsilon }_j}\left(t\right)$ accordingly.

Step 2: Update the residual decay amount for the next neighbor:

$$R_{i{\epsilon }_{j+1}}\left(t\right)=∆L_i^{out}\left(t\right)-∆L_{i{\epsilon }_1}\left(t\right)-∆L_{i{\epsilon }_2}\left(t\right)-\cdots -∆L_{i{\epsilon }_{j-1}}\left(t\right)-∆L_{i{\epsilon }_j}\left(t\right)$$

(22)

Step 3: Repeat Steps 1–2 until all export edges of node i are processed.

The redistributed load alters adjacent nodes’ loads, triggering iterative updates until the underload cascading failure process halts:

(a) Compute the updated export load from node i to j in cycle t + 1:

$$L_{ij}\left(t+1\right)=L_{ij}\left(t\right)-∆L_{ij}\left(t\right)$$

(23)

(b) Update the import load for all nodes in the new cycle:

$$L_j^{in}\left(t+1\right)=\sum _{i\in \mathrm{\varnothing }\left(j\right)}{L}_{ij}\left(t+1\right)$$

(24)

4. Results Analysis

4.1. Analysis of Overall Network Characteristics

This study examines the overall changes in the trade volume and trade value of global upstream, midstream, and downstream wood forest products from 2002 to 2023, as illustrated in Figure 2.

Figure 2 shows that the trade volume and trade value of global wood forest products have shown a steady upward trend amidst fluctuations. Notably, upstream wood forest products have a large trade volume but low unit prices, accounting for the largest share of the total trade volume—over half—while their share of the total trade value is only about one-quarter. In contrast, downstream wood forest products have high trade value and unit prices, contributing nearly three-fifths of the total trade value, but only one-quarter of the total trade volume. The following analysis primarily focuses on trade volume to examine the wood forest products trade network.

To clearly illustrate the trade volume relationships and proportional distributions among countries (regions) in the wood forest products trade network, this study employs chord diagram visualization to characterize trade patterns in three types of networks (Figure 3). In the diagram, the thickness of arcs represents trade volumes between countries (regions), with arrows indicating trade directions. Distinct trade dynamics emerge across different types of trade networks among countries (regions), reflecting variations in market vitality, trade relationships, and network balance. Regarding trade scale, the polarization degree of upstream networks significantly surpasses that of midstream and downstream networks.

In the upstream network, China, the United States, Germany, Canada, and Russia serve as core nations, with their combined trade volume accounting for nearly one-third of the total upstream trade. This highlights the uneven distribution of wood forest product resources. As a major timber importer, China has established long-term cooperative relationships with countries rich in forest resources by integrating global supply chain resources, forming stable trade chains. This strategy has effectively enhanced its dominance in international markets and strengthened node resilience. In the midstream network, which is dominated by wood-based panels, the United States, Germany, China, and Canada collectively contribute nearly one-quarter of global trade volume. These nations are not only pivotal producers and consumers of wood-based panels but also possess advanced manufacturing industries and stable market demand. These advantages grant the midstream network robust recovery capabilities and resilience when facing external disruptions. In the downstream network, the United States, China, and Germany similarly occupy central positions, accounting for nearly one-quarter of global trade volume. China’s exports in this segment far exceed its imports, demonstrating the sophistication of its furniture manufacturing sector and its critical role in global markets. This dynamic also enhances the resilience and diversity of the downstream network.

After determining the topological structure of the wood forest products trade network, we applied the Louvain community detection algorithm to divide trade communities in the upstream, midstream, and downstream networks. This approach further reveals clustering relationships among countries (regions) and the characteristics of community structures within the network, with the results illustrated in Figure 4.

For ease of discussion, we define the largest node within each trade group as the core of the trade group; this node occupies a dominant position in the network. In 2023, the upstream wood forest products trade network could be divided into four major trade groups centered around China, Germany, the United States, and Switzerland. The midstream wood forest products trade network could be divided into four major trade groups centered around China, Germany, the United States, and Russia. The downstream wood forest products trade network could be divided into three major trade groups centered around China, Germany, and the United States. The division of trade groups and their core members in the upstream, midstream, and downstream networks are detailed in

Table 5. Classification of trade blocs for major countries (regions) in the upstream, midstream, and downstream networks.

Network Type	Classification of Trading Blocs
Upstream Network	CHN BRA VIE NZL RUS IND THA CHL MYS PNG UAE SLB BLR CMR PHL	DEU AUT ITA FRA NLD BEL POL CZE SVN SVK UKR HRV ROM HUN CHE LUX BIH SRB GRC	USA CAN JPN GBR AUS TUR MEX IRL DOM	SWE FIN LVA NOR DNK EST LTU EGY KSA MAR ISR PAK TUN JOR ISL
Midstream Network	CHN IND THA VIE MYS IDN JPN NPL AUS KSA UAE NZL PHL NGA UGA SGP GAB ISR MMR KEN TZA KWT JOR OMN QAT CMR PAK LKA	DEU NLD BEL POL FRA ITA ESP GBR AUT ROU CZE PRT LVA HUN SWE FIN DNK LTU SVK IRL CHE UKR LUX EST HRV SVN NOR SRB BIH MDA	USA CAN BRA MEX CHL PER ECU COL ARG KHM URY DOM GTM BHS BOL PRY CRI JAM	RUS TUR KAZ UZB BLR BGR AZE GRC EGY MAR GEO KGZ TUN ARM MKD LBN CYP
Downstream Network	CHN JPN IDN IND MYS AUS RUS UAE THA SGP KSA KOR PHL EGY NZL KAZ NGA UZB KWT JOR LKA PAK KEN LAO OMN CIV AZE BLR LBN QAT MMR ETH GHA TZA BHR ARM	DEU FRA POL ITA GBR NLD SWE AUT ESP BEL FIN CZE CHE TUR PRT DNK HUN ROU IRL LTU SVK NOR GRC UKR SVN SRB BGR HRV LVA ISR MAR LUX EST BIH TUN MLT GEO MKD MDA CYP SEN	USA CAN MEX VIE BRA ZAF CHL COL GTM ARG CRI PER DOM SLV ECU PAN PRY URY NIC KHM BOL

.

4.2. Simulation Analysis of Underload Cascading Failure Propagation Process

After analyzing the structural characteristics of the wood forest products network, we further investigated the performance and evolution of its disruption resilience, with a focus on underload cascading failures triggered by node disruptions. Using Python 3.12-based tools, we simulated the trade network based on an underload cascading failure model to capture the failure diffusion paths following node disruptions. Notably, Canadian nodes in the upstream network and Chinese nodes in the midstream and downstream networks exhibited prominent failure propagation effects. We specifically selected these critical nodes to illustrate the underload cascading failure propagation patterns among core exporting countries in the wood forest products trade network (Figure 5, Figure 6 and Figure 7).

As a leading upstream exporter of wood forest products, Canada plays a pivotal role in global trade networks. As shown in Figure 5, the disruption of this node triggered a chain reaction that stabilized after four rounds of underload cascading failure propagation. During the first-round risk transmission, failures were observed in two nodes: the United States and Iceland. Moving into the second round, 11 additional nodes failed, including four countries (the United Kingdom, Japan, Mexico, and Colombia) and seven island nations within the Caribbean Sea region. The third round witnessed the failure of two more nodes: Turkey and the Philippines. The fourth and final round of propagation culminated in the failure of Aruba, a Caribbean node. Beyond directly causing the collapse of 16 nodes, this risk transmission process weakened 34 nodes while leaving 148 nodes unaffected.

As a critical downstream supplier of wooden consumer goods, China’s node disruption—illustrated in Figure 7—triggered cascading failures that persisted across twelve rounds before stabilizing. The first round saw only Nigeria’s failure, followed by the weakening of nodes that progressively expanded in subsequent rounds. Subsequent rounds witnessed the sequential failures of Australia, Japan, Fiji, Mexico, and others. The seventh and eighth rounds marked the collapse of Canada and the United States, while the ninth round resulted in the failure of South Africa and other nations. The tenth and eleventh rounds experienced an expansion in the scope of failures. Overall, the process led to the failure of 34 nodes, the weakening of 82 nodes, and 114 countries remaining unaffected. Compared to midstream disruptions, downstream risk propagation demonstrated broader reach and greater persistence.

4.3. Node Importance Analysis Under Disruption Risk Propagation

By simulating the cascading failure process triggered by single-node disruption risk propagation, we further calculate the network performance loss after cascading failure stabilization to precisely quantify the extent of the damage caused by node failures on the network. This approach intuitively reveals the influence and importance of nodes from the perspective of disruption impact. Figure 8, Figure 9 and Figure 10 present the distribution of global efficiency loss rates and total node strength loss rates following single-node disruptions.

As illustrated in Figure 8a–d, the horizontal axes of each subplot, respectively, represent node out-strength, betweenness centrality, closeness centrality, and PageRank centrality (the same convention applies hereafter). The analytical results demonstrate significant positive correlations between node centrality metrics and network performance loss rates. However, the strength of the association between individual centrality indicators and network performance loss rates exhibits differential characteristics, which are thoroughly discussed in subsequent sections.

In the upstream trade network of wood forest products, only a few nodes exhibit significant disruptive potential for the network; these are highlighted with dashed boxes as critical nodes, further validating the scale-free property of the network. Specifically, the disruption of nodes such as the United States, Canada, South Africa, Brazil, and Germany would cause the most severe damage to global efficiency, while nodes including China, the United States, Canada, and Germany demonstrate the greatest destructive impact on the total node strength of the network. These nodes not only play pivotal roles in maintaining network functionality but also represent vulnerable components, the failure of which could trigger catastrophic consequences for the entire system.

In the midstream trade network of wood forest products, nodes such as China, Canada, Brazil, the United States, Germany, Russia, Turkey, Thailand, and South Africa exhibit particularly significant disruptive impacts on global efficiency. Among them, the Chinese node demonstrates a disruptive impact value as high as 0.43, highlighting its dominant influence within the network. Simultaneously, nodes including Germany, Canada, China, and the United States also hold critical positions in terms of their disruptive effects on the total node strength of the network. This pattern underscores the structural vulnerabilities and differentiated disruption resilience characteristics within the global midstream trade system of wood forest products.

In the downstream trade network of wood forest products, although the number of nodes with significant disruptive impacts is notably low compared to the upstream and midstream networks, key nodes such as China, the United States, and Germany still demonstrate the highest disruptive effects on global efficiency and total node strength. Among these, the Chinese node exhibits particularly pronounced destructive impacts, reaching 0.4 and 0.5 for global efficiency and total node strength, respectively. This observation emphasizes the persistent structural vulnerabilities in downstream trade dynamics, where a limited number of dominant nodes disproportionately influences network stability, despite reduced systemic exposure to cascading disruptions.

As illustrated in Figure 8, Figure 9 and Figure 10, the global efficiency loss rate caused by single-node interruptions is significantly lower than the total node strength loss rate, indicating that single-node disruptions have relatively limited impacts on overall network efficiency. This suggests that the trade network of wood forest products possesses inherent redundancy and robustness, enabling it to partially mitigate shocks from individual node failures. In contrast, greater attention should be directed toward maintaining the stability of total node strength to ensure efficient and stable network operations.

Table 6. Ranking of top 10 nodes by network performance loss rate under single-node interruptions.

Ranking	Upstream Network				Midstream Network				Downstream Network
	Global Efficiency Loss Rate		Node Strength Loss Rate		Global Efficiency Loss Rate		Node Strength Loss Rate		Global Efficiency Loss Rate		Node Strength Loss Rate
	Node	Value	Node	Value	Node	Value	Node	Value	Node	Value	Node	Value
1	USA	0.25	CHN	0.34	CHN	0.43	DEU	0.24	CHN	0.40	CHN	0.50
2	CAN	0.25	USA	0.31	CAN	0.14	CAN	0.21	DEU	0.03	USA	0.26
3	ZAF	0.12	CAN	0.31	BRA	0.12	CHN	0.20	USA	0.19	DEU	0.26
4	BRA	0.12	DEU	0.17	USA	0.11	USA	0.20	CAN	0.02	CAN	0.10
5	DEU	0.10	BRA	0.09	DEU	0.11	NLD	0.10	FRA	0.02	FRA	0.09
6	RUS	0.07	SWE	0.09	RUS	0.10	BEL	0.08	POL	0.02	POL	0.09
7	FIN	0.06	JPN	0.08	TUR	0.09	RUS	0.07	ITA	0.02	ITA	0.09
8	ARE	0.05	NLD	0.06	THA	0.08	POL	0.07	GBR	0.04	GBR	0.08
9	ESP	0.05	VNM	0.06	ZAF	0.08	THA	0.07	NLD	0.02	NLD	0.07
10	CHN	0.05	NZL	0.06	CHL	0.05	FRA	0.06	SWE	0.02	SWE	0.05

identifies the top 10 nodes exhibiting the maximum network performance loss rates under single-node interruption scenarios.

The disruption levels of single-node interruption on network performance exhibit significant heterogeneity, with particularly notable variations observed in certain nodes. To address this, we constructed a composite radar analysis map (Figure 11) under core node failure scenarios, incorporating both the global efficiency loss rate and node strength loss rate metrics. This visualization model effectively reveals sensitivity disparities across multiple network performance dimensions towards nodal failures, providing a quantitative analytical tool for assessing vulnerability characteristics in trade networks.

As shown in Figure 11, in the upstream network, the interruption of the Chinese node resulted in a node strength loss rate of 0.34, while the global efficiency loss rate remained at only 0.05. This marked discrepancy indicates that the Chinese node and its neighboring nodes account for a substantial proportion of total trade volume, meaning their interruption would significantly compromise network-wide strength. However, the limited impact on average path length suggests relatively preserved global connectivity. Nodes exhibiting similar characteristics include Sweden and Vietnam in the upstream network, Germany, the Netherlands, and Belgium in the midstream network, as well as Germany, Poland, Italy, Canada, and France in the downstream network. Notably, if such nodes establish strong interdependencies with high-betweenness nodes, their interruption may trigger extensive chain reactions, potentially leading to severe cascading failure consequences across the network.

The Brazilian node in the midstream network exhibits distinct destructive characteristic patterns. Its interruption caused a global efficiency loss rate of 0.12, whereas the node strength loss rate remained at merely 0.05—less than half of the global efficiency loss. This phenomenon indicates that the Brazilian node occupies a structurally central position, whereby its disruption significantly degrades network transmission efficiency. However, its limited trade volume with neighboring nodes minimizes the impact on the overall network strength. Nodes sharing similar traits include South Africa in the upstream and downstream networks, as well as China in the midstream network. Although these nodes contribute modestly to network-wide strength, they play pivotal roles in maintaining global information flow and operational efficiency.

An integrated analysis reveals that nodes’ destructive impacts are intrinsically linked to their structural positions and functional attributes within networks. Trade volume predominantly governs network strength degradation, while topological positioning determines the nodes’ influence on global efficiency. These findings provide novel insights into node criticality in complex networks, offering strategic guidance for risk mitigation.

The scatterplot analysis demonstrates a general positive correlation between node centrality metrics and their disruption-induced network performance degradation, though correlation strengths vary across performance indicators. To quantify these relationships, we calculated Pearson correlation coefficients and visualized the interdependencies between node centrality and single-node disruption impacts, as illustrated in Figure 12.

The interpretation criteria for Pearson’s correlation coefficient (r) are as follows: |r| > 0.8 indicates an extremely strong correlation, 0.6 ≤ |r| < 0.8 represents a strong correlation, 0.4 ≤ |r| < 0.6 suggests a moderate correlation, 0.2 ≤ |r| < 0.4 denotes a weak correlation, and |r| < 0.2 signifies a very weak or negligible correlation. According to Figure 12, we can derive the following information: (1) node out-strength demonstrates strong correlations with all types of network performance loss rates, indicating that the out-strength of nodes significantly impacts the overall performance and stability of networks. Nodes with high out-strength may play crucial roles in information dissemination or resource allocation within networks. (2) Node betweenness centrality shows a strong correlation with the node total strength loss rate, suggesting that bridge nodes exert an important influence on node-level performance loss. In midstream and downstream networks, betweenness centrality also maintains strong correlations with the global efficiency loss rate, while its correlation weakens in upstream networks. This implies that upstream network structures and functions might be more complex, with node influence distributed more diffusely. (3) PageRank centrality exhibits strong correlations with the node total strength loss rate but only a moderate correlation with the global efficiency loss rate, indicating that nodes with high PageRank centrality primarily exert influence at local rather than global scales. (4) Although nodes with high closeness centrality possess shorter path lengths in networks, the correlations between node closeness centrality and both the node total strength loss rate and global efficiency loss rate remain moderate. This suggests that a node’s positional advantage in networks has relatively weak impacts on network performance and may not be a critical determinant of network performance degradation.

4.4. Analysis of Disruption Resilience Evolution Under Risk Propagation

By conducting simulations of underload cascading failure triggered by single-node disruptions in the wood forest products trade network from 2002 to 2023, we calculated the average values of network performance retention rates during core node failures to evaluate disruption resilience. Figure 13, Figure 14 and Figure 15 visually demonstrate the dynamic evolution of disruption resilience.

As shown in Figure 13, the disruption resilience based on total node strength exhibited a significant upward trend in the upstream wood forest products trade network from 2002 to 2023, indicating that continuous network evolution and optimization have strengthened inter-node connectivity and diversity, thereby reducing dependency on high-strength nodes—a positive signal of enhanced robustness and resistance to deliberate disruptions. However, the disruption resilience based on global efficiency showed a slight decline, suggesting that failures of nodes with high betweenness prolonged the shortest paths and perpetuated bottlenecks and congestion, highlighting growing vulnerabilities in network connectivity and transmission efficiency. This reflects the complexities and challenges encountered during network expansion and upgrading.

Figure 14 reveals a continuous decline in midstream network disruption resilience from 2002 to 2023, implying heightened reliance on core nodes and weakened recovery capacity and robustness against failures or attacks. Notably, data from 2008 showed significant fluctuations, with a sharp drop in resilience metrics followed by a rapid rebound in 2009. This pattern aligns with the global financial crisis, which disrupted furniture manufacturing and triggered volatility in the disruption resilience of the midstream trade network dominated by wood-based panels.

Figure 15 demonstrates that, from 2002 to 2023, the disruption resilience based on global efficiency declined in the downstream network, while resilience based on node total strength displayed a marginal increase—a trend similar to the upstream network but with gentler slopes. This suggests that the downstream trade network, which is characterized by higher globalization, market maturity, and competitive intensity, exhibited more stable resilience evolution compared to the upstream network.

5. Conclusions and Discussion

This study comprises an in-depth analysis of the global wood forest products trade network from 2002 to 2023, exploring the evolution patterns of its disruption resilience under risk propagation scenarios. The main conclusions are as follows:

(1)

The global wood forest products trade network has shown fluctuating growth in terms of both trade volume and value during this period. Upstream products exhibit large trade volumes with low unit prices, while downstream products demonstrate higher trade values and unit prices, making significant contributions to the global economy. Network topology reveals that core countries including China, the United States, and Germany dominate global trade through stable trade chains. The network has grown increasingly complex and interconnected, with diversified trade relationships among countries/regions.

(2)

The simulation results indicate substantial variations in node disruption impacts across the network. Failures of core nodes significantly damage global efficiency and total node strength. Node centrality metrics (out-strength, betweenness centrality, etc.) generally correlate positively with network performance degradation, though correlation strengths differ by metric. This highlights the combined influence of the node position and attributes on network importance. Diverse evolution trends of disruption resilience across the network performance metrics provide multi-dimensional insights into network robustness.

(3)

From 2002 to 2023, global efficiency disruption resilience declined across all wood forest product trade networks, reflecting the growing influence of core nodes and weakening connectivity robustness after their disruptions. Total node strength resilience showed varied patterns: upstream networks demonstrated improved resilience through diversified connections, midstream networks displayed reduced resilience due to intensified core node dependence, and downstream networks maintained relatively stable resilience owing to mature supply chains and diversified trade channels [1].

This study provides critical policy insights for enhancing the resilience of the global wood forest products trade network. First, policymakers should focus on the stability of core nodes by diversifying supply channels, establishing regional backup nodes, and strengthening international cooperation to reduce dependence on single nodes and improve overall network resilience. Second, the continuous decline in midstream resilience highlights the risks in this segment, necessitating enhanced node robustness through optimized inventory strategies, increased redundancy, and intelligent management. Finally, the study reveals the close link between sustainable development and supply chain resilience. Policymakers should promote green supply chain initiatives, accelerate afforestation projects, and enhance domestic timber self-sufficiency to reduce reliance on imported timber, thereby strengthening node resilience and fostering sustainable forest resource utilization for economic and environmental benefits [64,65].

Future research should focus on resilience optimization strategies and investigate external factors including geopolitical factors, trade policies, climate change, and technological advancements to support the sustainable development of the global wood forest product trade.