The financial systemic risk literature provides the theoretical foundation for our framework. Eisenberg and Noe [5] developed the foundational model of financial contagion through interconnected balance sheets, demonstrating how localized shocks propagate through financial networks via default cascades. Elliott et al. [9] extended this framework to incorporate more general network structures and threshold effects in contagion transmission.

The DebtRank algorithm introduced by Battiston et al. [6] provides a practical methodology for quantifying systemic importance in financial networks, measuring each institution’s potential impact on the entire system through stress propagation. This approach has been successfully applied to banking networks [10] , sovereign debt analysis [11] , and corporate credit risk assessment [12] .

Recent developments in systemic risk measurement include network-based approaches [13] . Stress testing methodologies have evolved to incorporate complex interdependencies [14] and macroeconomic feedback effects [15] .

Supply chain network analysis has focused primarily on operational resilience and vulnerability assessment. Acemoglu et al. [8] demonstrated how firm-level shocks can generate aggregate fluctuations through input-output networks, establishing the theoretical basis for systemic effects in production networks.

Network-based approaches to supply chain risk have examined structural vulnerabilities [16] , cascade effects [17] , and resilience strategies [18] . Geographic concentration and supplier diversification have been identified as key risk factors [19] .

However, existing supply chain literature lacks integration with financial contagion models, limiting understanding of how financial distress propagates through operational relationships and how operational disruptions create financial spillovers. This gap represents a significant opportunity for methodological advancement and policy application.

This work constructs a synthetic supply chain network representing realistic multi-tier dependencies and financial relationships. The network architecture reflects empirical supply chain structures with hierarchical tier organization and realistic degree distributions [20] .

The synthetic network comprises 500 nodes distributed across three supply chain tiers based on empirical tier size distributions from automotive and electronics industries [20] [21] . Upstream suppliers represent 300 nodes (60%) providing raw materials and components, consistent with supplier proliferation observed in global manufacturing networks. Mid-tier manufacturers comprise 80 nodes (16%) conducting assembly and manufacturing operations, reflecting concentration patterns in production stages. Downstream retailers consist of 120 nodes (24%) handling distribution and retail operations, calibrated to retail sector concentration ratios.

Network connectivity follows preferential attachment mechanisms with degree distributions calibrated to empirical supply chain data. The power-law exponent of 2.3 for supplier degree distribution matches observations from automotive supply networks [20] . Manufacturer nodes exhibit higher average degree (15.2), reflecting hub-like positions, while retailers show moderate connectivity (degree 8.4), consistent with distribution network structures. Directed edges represent supplier-customer relationships, with 4786 total connections yielding network density of 0.019, within the empirical range of 0.015 - 0.025 observed in manufacturing supply chains [21] .

Node attributes include comprehensive financial and operational characteristics derived from industry benchmarks [22] . Financial metrics encompass revenue measured in millions USD following log-normal distributions by tier (suppliers: $\mu =2.5$, $\sigma =1.2$; manufacturers: $\mu =3.8$, $\sigma =0.9$; retailers: $\mu =3.2$, $\sigma =1.1$), calibrated to match revenue distributions from S&P Capital IQ industry data [23] . Debt-to-equity ratios follow Beta distributions with tier-specific parameters (suppliers: $\alpha =2$, $\beta =5$; manufacturers: $\alpha =3$, $\beta =4$; retailers: $\alpha =2.5$, $\beta =3.5$) calibrated to industry leverage patterns [24] . Liquidity ratios follow Gamma distributions ( $k=2$, $\theta =0.8$) reflecting working capital management practices, and working capital days follow normal distributions with operational constraints ( $\mu =45$, $\sigma =15$ days).

Operational characteristics include supplier diversification indices reflecting dependency concentration, customer concentration ratios measuring downstream dependencies, geographic locations with regional clustering and distance-based relationships [25] , and contract terms capturing payment schedules and relationship stability metrics.

Edge attributes capture transaction relationships through transaction volumes representing revenue-weighted relationship strength, dependency strength measuring operational criticality of supplier relationships, lead times reflecting supply chain timing constraints, and payment terms characterizing financial relationship dynamics.

This work adapts the DebtRank algorithm [6] to supply chain networks by replacing financial exposures with supply dependencies. For each node $i$, the systemic importance $S{I}_i$ captures the potential impact of node $i$’s failure on the entire network through cascade propagation.

The algorithm proceeds in discrete time steps following the established DebtRank methodology. In the initialization step, for each node $j$, we define the relative economic size as:

$W_j=\frac{V_j}{{\displaystyle {\sum }_{k\in N}{V}_k}}$(1)

where $V_j$ is node $j$’s revenue and $N$ is the set of all nodes.

During impact matrix construction, the impact of node $i$ on node $j$ is defined as:

${\Pi }_{ij}=\frac{A_{ij}\cdot D_{ij}}{{\displaystyle {\sum }_k{A}_{kj}\cdot D_{kj}}}$(2)

where $A_{ij}$ is the adjacency matrix and $D_{ij}$ represents dependency strength, normalized by total incoming dependencies.

Finally, during cascade simulation, the systemic importance is computed as:

$S{I}_i={\displaystyle \underset{j\in N}{\sum }{h}_{ij}\cdot W_j}$(3)

where $h_{ij}$ represents the ultimate impact of node $i$’s failure on node $j$ through the complete cascade process, incorporating both direct and indirect effects.

The work constructs a composite financial fragility index $F{F}_i$ for each node $i$, combining multiple vulnerability indicators following established financial risk assessment methodologies [26] :

$\begin{array}{c}F{F}_i=w_1\cdot {\text{DebtRatio}}_i+w_2\cdot {\text{LiquidityStress}}_i\\ +w_3\cdot {\text{WorkingCapitalPressure}}_i+w_4\cdot {\text{ConcentrationRisk}}_i\end{array}$(4)

where weights $w_k$ are empirically calibrated based on financial distress prediction literature [27] and each component is normalized to [0, 1]. The index ranges from 0 (financially robust) to 1 (highly fragile).

The selection of the systemic importance threshold (SI > 0.2) follows a multi-criteria approach combining statistical analysis and regulatory benchmarking. We employ three complementary methods:

First, natural breaks classification (Jenks optimization) [28] identifies statistically significant discontinuities in the SI distribution, revealing a natural break at SI = 0.201 that maximizes between-class variance while minimizing within-class variance.

Second, comparison with financial sector standards shows that our 0.2 threshold captures 59.2% of network nodes, comparable to the Basel III framework’s identification of 29 global systemically important banks from approximately 100 large international banks, representing a similar concentration ratio when adjusted for network size differences.

Third, sensitivity analysis across alternative thresholds demonstrates robustness of key findings:

The 0.2 threshold maintains policy stability across ±10% variations, with the number of systemically important suppliers changing by less than 15% for threshold adjustments between 0.18 and 0.22.

It computes comprehensive network centrality metrics to capture different aspects of structural importance [29] . Degree centrality measures direct connectivity as $C_D\left(i\right)=\frac{d_i}{n-1}$, where $d_i$ is node degree. Betweenness centrality captures shortest path importance as $C_B\left(i\right)={\displaystyle {\sum }_{s\ne i\ne t}\frac{{\sigma }_{st}\left(i\right)}{{\sigma }_{st}}}$, where ${\sigma }_{st}$ is the total number of shortest paths from node $s$ to node $t$ and ${\sigma }_{st}\left(i\right)$ is the number passing through node $i$. Eigenvector centrality represents influence through connections using the principal eigenvector of the adjacency matrix [30] . PageRank measures recursive importance as $PR\left(i\right)=\frac{1-d}{N}+d{\displaystyle {\sum }_{j\in \text{in}\left(i\right)}\frac{PR\left(j\right)}{\left|\text{out}\left(j\right)\right|}}$ with damping parameter $d=0.85$ [31] .

The stress testing framework encompasses multiple scenario types to provide comprehensive resilience assessment, drawing from both financial stress testing [14] and supply chain risk assessment methodologies [3] .

Monte Carlo failure simulations implement comprehensive probabilistic analysis to assess network resilience under random failure scenarios. Each simulation consists of shock generation through random selection of failed nodes based on financial fragility probabilities, cascade propagation through systematic failure transmission via supply chain dependencies using threshold-based contagion models [9] , and impact measurement through calculation of total network impact and failure statistics. We conduct 1000 independent simulation runs to ensure statistical robustness and capture tail risk characteristics [32] .

Targeted attack simulations analyze network vulnerability to strategic attacks through systematic node removal based on different targeting strategies. High-degree attacks involve sequential removal of the highest-degree nodes, reflecting potential targeting of major suppliers. High-betweenness attacks target nodes with the highest betweenness centrality, focusing on critical intermediaries. High-systemic-importance attacks remove nodes based on DebtRank scores, targeting systemically important suppliers. Random attacks provide baseline comparison with random node removal for statistical control.

Liquidity crisis propagation simulates financial contagion through liquidity stress propagation, modeling how payment delays and working capital constraints cascade through supply chain relationships [33] . The liquidity crisis model incorporates payment term dependencies between suppliers and customers, working capital constraints, cash flow timing effects, credit relationship stress, payment delay propagation mechanisms, and cross-tier contagion through financial interdependencies.

Percolation analysis conducts systematic examination of network connectivity degradation patterns through progressive node removal [34] . This involves progressive random node removal while monitoring the largest connected component size, characterizing continuous fragmentation behavior and connectivity decline patterns across the removal spectrum.

All analysis components incorporate comprehensive verification protocols ensuring methodological rigor and reproducibility [35] .

Network structure validation employs multiple consistency checks across three critical dimensions. Topology validation procedures verify directed acyclic graph properties within tiers, confirm the absence of self-loops or duplicate edges, and validate tier-based hierarchical constraints to ensure structural integrity. Attribute consistency checks confirm that all financial metrics remain within realistic bounds, with debt ratios constrained to the interval [0, 5] and liquidity ratios to [0, 3]. Furthermore, revenue distributions must match log-normal parameters within 5% tolerance, and operational metrics undergo validation against established industry benchmarks. Connectivity verification ensures that minimum degree requirements are satisfied with all nodes maintaining at least one connection to prevent isolated suppliers. The giant component must encompass more than 95% of the network, and average path length must remain within theoretical bounds appropriate for the network size.

Risk metric validation employs rigorous statistical testing through three complementary approaches. Bootstrap validation generates 1000 bootstrap samples for systemic importance scores with 95% confidence intervals, conducts stability testing across 100 random network perturbations involving 5% edge rewiring, and verifies convergence for iterative algorithms using a tolerance threshold of 10⁻⁶. Cross-validation procedures implement K-fold validation with k = 10 for financial fragility predictions, perform out-of-sample testing on a 20% holdout network subset, and compare results with null models, including random networks and configuration models, to establish statistical significance. Sensitivity analysis encompasses parameter variation testing at ±20% for all calibrated values, robustness assessment across different network generation seeds, and stability verification for threshold-dependent results to ensure findings remain consistent under parameter uncertainty.

Each computational component undergoes specific verification tailored to its algorithmic characteristics. The DebtRank implementation undergoes validation against published test cases from Battiston et al. [6] , convergence testing with a maximum of 100 iterations, and numerical stability checks for sparse matrix operations to ensure computational accuracy. Cascade propagation algorithms require verification of threshold mechanics against analytical solutions, conservation tests that ensure no value creation or destruction occurs during propagation, and timing consistency checks across both synchronous and asynchronous update protocols. Stress testing procedures incorporate Monte Carlo convergence verification requiring standard errors below 1%, reproducibility testing using fixed random seeds to ensure consistent results, and boundary condition testing that examines behavior under extreme scenarios, including empty networks and fully connected topologies.

Quantitative acceptance criteria ensure result reliability through stringent validation requirements. Network metrics must match theoretical predictions within 10% tolerance for key measures, including clustering coefficient and degree distribution exponent. Systemic importance scores must satisfy conservation properties by summing to 1.0 with a tolerance of ±0.001, ensuring proper normalization across the network. Spillover coefficients must satisfy mathematical constraints with all values constrained to the interval ${\Theta }_{ij}\in \left[0,1\right]$ while maintaining row-stochastic properties essential for probability interpretation. Cascade simulations must exhibit monotonic failure progression, preventing logical inconsistencies where network health improves during failure propagation. All statistical tests must achieve p-values below 0.05 for hypothesis rejection, maintaining standard significance levels for empirical validation.

Statistical validation encompasses cross-validation of risk metrics and simulation results using bootstrap methods [36] . Consistency checking verifies cross-module result consistency through independent calculation verification. Reproducibility protocols ensure complete documentation and code verification with version control and dependency management.

Analysis reveals significant heterogeneity in systemic risk profiles across the 500-node supply chain network. The network exhibits small-world properties with strong clustering within supply chain tiers (clustering coefficient $C=0.324$) and efficient path connectivity across tiers (average path length $L=3.47$), consistent with empirical supply chain network studies [16] . Table 1 presents the comprehensive network characteristics and structural properties.

Figure 1 presents the network topology with nodes colored by systemic importance and sized by revenue. The visualization reveals clear tier-based clustering with high-importance nodes distributed across all tiers, though concentrated in the supplier tier.

The systemic importance analysis identifies 296 suppliers (59.2% of the network) as systemically important based on a threshold of 0.2. The mean systemic importance score across all nodes is 0.267, with scores ranging from near-zero to 0.560. This distribution indicates significant concentration of systemic risk among a subset of suppliers, validating the “too-central-to-fail” concept in supply chain contexts.

Table 2 presents the detailed distribution of systemic importance across supply chain tiers and risk categories.

Financial fragility analysis reveals overall network robustness with mean financial fragility of 0.330. Only 1 node (0.2%) exhibits high financial vulnerability (fragility > 0.7), while 47 nodes (9.4%) show moderate vulnerability (0.5 - 0.7).

The correlation between systemic importance and financial fragility is 0.657, indicating that structurally important suppliers tend to exhibit higher financial vulnerability.

Figure 2 shows the distribution of key risk metrics across all network nodes, revealing the heterogeneous risk profile of the supply chain network.

Figure 3 presents the complete correlation structure among risk metrics.

The spillover coefficient ${\text{Θ}}_{ij}$ from sector $i$ to sector $j$ quantifies the expected contagion transmission strength through the following formulation:

(5)

where:

The coefficient captures both direct connections and weighted economic importance, normalized to ensure comparability across sector pairs. Values range from 0 (no spillover) to 1 (complete transmission).

Cross-sector spillover analysis reveals asymmetric contagion patterns between supply chain tiers, reflecting the hierarchical nature of supply chain relationships and financial dependencies. Table 3 presents the complete spillover coefficient matrix, quantifying directional contagion strengths between all supply chain tiers calculated using the above methodology.

The strongest contagion pathway operates from suppliers to manufacturers (0.234), reflecting the upstream dependency structure characteristic of supply chains. Secondary contagion occurs from manufacturers to retailers (0.187), indicating effective transmission of disruptions through the manufacturing tier. Direct supplier-to-retailer spillovers are more limited (0.098), suggesting that manufacturer intermediation plays a crucial role in supply chain resilience.

Figure 4 visualizes these spillover relationships with statistical significance indicators.

Monte Carlo simulations across 1000 independent runs provide comprehensive statistical characterization of network resilience under random failure scenarios. Table 4 summarizes the complete distribution of failure outcomes and tail risk characteristics.

The simulations demonstrate moderate network resilience with mean failure rates of 5.4% under random shocks. Figure 5 presents the distribution of failure rates and their relationship with cascade propagation dynamics.

Targeted attack simulations reveal significant vulnerability to strategic node removal, demonstrating that informed adversarial targeting can achieve substantially greater network disruption than random failures.

Attack Simulation Metrics Definitions

To clarify the metrics used in targeted attack analysis, two primary measures quantify network vulnerability under strategic node removal. Max Impact, expressed as a percentage, represents the maximum proportion of network nodes that fail either directly or through cascades when a single critical node is removed under each targeting strategy. This metric captures worst-case single-node failure impact and provides insight into the network’s vulnerability to targeted disruption. Nodes to 50% Damage measures the minimum number of nodes that must be sequentially removed following the targeting strategy to cause 50% of the network to fail through direct removal and cascade effects. Lower values for this metric indicate higher network vulnerability and reduced resilience to systematic attacks.

These metrics differ fundamentally from the Monte Carlo analysis results, which showed a 5.4% mean failure rate, for several important reasons. First, Monte Carlo simulations select failed nodes randomly based on financial fragility probabilities, while targeted attacks strategically select the most critical nodes according to specific network characteristics. Second, the 5.4% figure represents the average outcome across 1000 random scenarios, whereas Max Impact captures the worst-case outcome from targeted removal of the single most critical node. Third, random failures typically affect peripheral nodes with limited network influence, while targeted attacks focus on highly connected or systemically important nodes that serve as critical infrastructure for network functionality.

Table 5 presents comprehensive results from targeted attack simulations using these metrics.

High-degree attacks prove most effective, achieving 3.2% maximum network failure through targeting of highly connected nodes. This finding validates the importance of major suppliers in network stability and supports degree-based regulatory prioritization.

Figure 6 shows progressive attack results under different targeting strategies.

Liquidity crisis simulations with severity parameter 0.4 demonstrate cascading financial contagion affecting 42.2% of the network through payment delays and working capital stress. Table 6 presents detailed analysis of liquidity crisis propagation dynamics.

The propagation exhibits classic contagion dynamics with peak transmission in Round 3 (12.1% new infections) before gradual convergence to equilibrium after 8 rounds. Figure 7 illustrates the temporal dynamics of crisis propagation.

Network resilience analysis evaluates the system’s capacity to maintain functionality under various failure scenarios through comprehensive connectivity assessment and structural robustness evaluation.

Percolation analysis conducts systematic examination of network connectivity degradation patterns through progressive node removal [34] . This involves progressive random node removal while monitoring the largest connected component size, characterizing continuous fragmentation behavior and connectivity decline patterns across the removal spectrum.

The percolation simulation protocol removes nodes randomly at incremental rates from 0% to 80% in 10% intervals. For each removal fraction, 50 independent simulations are conducted to ensure statistical reliability.

The percolation analysis reveals systematic connectivity decline characterized by gradual rather than abrupt fragmentation behavior. Key findings include: The network exhibits smooth, continuous connectivity degradation without sharp transition points. Even at 80% node removal, the largest connected component retains 18.3% of the original network. Connectivity loss follows approximately linear patterns across the removal spectrum. The supply chain network demonstrates no identifiable percolation threshold where connectivity collapses abruptly.

The calculated network resilience score of 0.20 indicates moderate overall robustness, as shown in Table 7 . This score reflects the network’s capacity to maintain partial functionality across a wide range of disruption scenarios while acknowledging vulnerability to extensive node removal.

The percolation analysis shown in Figure 8 establishes that supply chain networks exhibit resilience through distributed connectivity rather than threshold-based robustness, with significant implications for risk management and system design.

These analyses provide quantitative foundations for systematic supply chain regulation based on network structure and systemic risk assessment. The identification of 296 systemically important suppliers (59.2% of the network) establishes clear regulatory prioritization criteria analogous to systemically important financial institutions.

The asymmetric spillover patterns revealed in this work’s cross-sector analysis support tier-differentiated regulatory approaches. Enhanced oversight requirements should focus on supplier-manufacturer relationships (spillover coefficient 0.234), while targeted resilience standards should address manufacturing nodes serving as critical contagion intermediaries. Direct supplier-retailer regulations can be calibrated to lower intensity given limited spillover effects (0.098).

Financial adequacy standards should incorporate our composite fragility index, with enhanced requirements for suppliers exhibiting both high systemic importance and financial vulnerability. The strong correlation (0.657) between these measures suggests that structurally critical suppliers often face elevated financial risks, warranting integrated oversight approaches.

Stress testing requirements should mandate regular assessment using our multi-scenario framework, including Monte Carlo failure analysis, targeted attack simulations, and liquidity crisis propagation testing. Regulatory stress testing should utilize scenario severities calibrated to our empirical findings: 95th percentile Monte Carlo outcomes (7.0% failure rates) for base scenarios and targeted attack severities (3.2% failure rates) for adverse scenarios.

Early warning systems should monitor the network centrality measures and financial fragility indicators identified in the analysis of this work. Regulatory triggers should activate when suppliers exceed systemic importance thresholds (SI > 0.2) combined with deteriorating financial conditions (FF > 0.5), enabling proactive intervention before systemic events materialize.

International coordination frameworks should address cross-border supply chain dependencies using our spillover analysis methodology. Regional regulatory harmonization should focus on suppliers and manufacturers, given their dominant role in international contagion transmission, while retailer regulations can maintain greater national flexibility.

This study makes several theoretical and methodological contributions to supply chain risk analysis. The adaptation of financial systemic risk models to operational networks provides the first comprehensive framework for quantitative supply chain systemic risk assessment. The integration of DebtRank methodology with supply chain dependencies creates novel metrics for identifying “too-central-to-fail” suppliers based on rigorous network analysis.

The composite financial fragility index, combining debt ratios, liquidity stress, working capital pressure, and concentration risk, provides a comprehensive vulnerability assessment tool calibrated to supply chain operational characteristics. The multi-scenario stress testing framework advances supply chain risk methodologies by incorporating probabilistic analysis, strategic attack assessment, and financial contagion simulation in an integrated analytical approach.

The asymmetric spillover analysis reveals tier-specific contagion patterns that challenge assumptions of uniform risk transmission in supply chains. The findings demonstrate that supplier-manufacturer relationships drive primary contagion, while manufacturer-retailer transmission creates secondary effects, supporting theoretical models of hierarchical risk propagation in production networks.

Network resilience analysis using percolation theory provides quantitative characterization of supply chain connectivity degradation patterns, advancing understanding of gradual decline behavior in complex operational systems. The identification of asymmetric resilience patterns (high random failure robustness, moderate targeted attack vulnerability) and continuous degradation characteristics contributes to theoretical understanding of distributed network vulnerability in supply chain contexts.

Several limitations constrain the interpretation and generalization of this work’s findings. The synthetic network approach enables comprehensive methodological development but requires empirical validation using real-world supply chain data. Future research should apply the framework to industry-specific networks to validate theoretical predictions and calibrate model parameters to empirical relationships.

The static network analysis assumes fixed supplier relationships and dependencies, while real supply chains exhibit dynamic adaptation and supplier substitution capabilities. Dynamic extensions incorporating adaptive responses, supplier diversification strategies, and network evolution would enhance analytical realism and policy relevance.

The behavioral assumptions underlying our models assume rational responses to financial stress and operational disruptions. Future research should incorporate behavioral biases, coordination failures, and strategic gaming that may alter contagion dynamics and resilience outcomes in practice.

Geographic and political risk factors receive limited treatment in the work’s current framework. Incorporating geopolitical risk, natural disaster exposure, and regional economic dependencies would enhance the framework’s applicability to contemporary supply chain challenges, including trade conflicts and climate change impacts.

Empirical validation across different industries, regions, and economic conditions represents a critical next step for framework development. Longitudinal studies examining supply chain evolution and stress event outcomes would provide essential calibration data for regulatory implementation.