Este artigo propõe um framework de computação física que combina um modelo conjunto de grafos aleatórios exponenciais temporais e um algoritmo aprimorado de Motter-Lai para avaliar a evolução estrutural e quantificar o limiar de resiliência de ecossistemas de economia digital sob falhas em cascata.
Artigo de investigação
Evolução Estrutural e Resiliência de Ecossistemas de Economia Digital: Uma Abordagem Conjunta via Modelo de Grafos Aleatórios Exponenciais Temporais e Estrutura Motter-Lai
Neste artigo
Resumo
Resumo
Os métodos existentes de análise estática ignoram a evolução estrutural de topologias de redes complexas e as falhas em cascata induzidas pela redistribuição local de carga, levando a vieses na avaliação da resiliência de ecossistemas da economia digital. Para quantificar com precisão o limiar de resiliência do sistema, este artigo propõe um framework de computação física que combina um Modelo Temporal de Grafos Aleatórios Exponenciais (TERGM) conjunto e um algoritmo Motter-Lai aprimorado (TERGM-ML). Este framework utiliza a Estimação da Máxima Verossimilhança por Cadeias de Markov de Monte Carlo (MCMC-MLE) para modelar efeitos estruturais endógenos e reconstruir a trajetória de evolução temporal da topologia real da rede, superando as limitações das referências estáticas. Posteriormente, com base na centralidade dos nós e em sua capacidade física não linear, uma regra de redistribuição de tráfego dependente da capacidade remanescente dos vizinhos é acionada ao ocorrer um ataque deliberado, rastreando todo o processo de desintegração do sistema causado pela propagação de sobrecarga local. Simulações comparativas multimodelo mostram que, após a introdução de um mecanismo duplo de evolução temporal e realocação dinâmica, o limiar crítico de remoção de nós que desencadeia um colapso global da eficiência de transmissão em um cenário de ataque deliberado baseado na centralidade de intermediação é de 12,41% ± 0,63%, significativamente maior do que a referência estática de escala livre (7,85% ± 0,42%, p < 0,001).
Introdução
Com a profunda integração da tecnologia da informação global, o ecossistema da economia digital evoluiu gradualmente para um sistema de rede complexo, transnacional, entrelaçado e altamente interdependente1,2. A pesquisa sobre a evolução estrutural e os limites de resiliência desse sistema possui grande importância estratégica para garantir a operação estável da macroeconomia e a segurança da indústria digital. No entanto, diante da reconfiguração da paisagem econômica global e da ocorrência frequente de choques externos assimétricos, a vulnerabilidade topológica em rede exibida pelo ecossistema da economia digital tornou-se proeminente3,4. Os métodos existentes de econometria macroeconômica e análises estatísticas estáticas frequentemente tratam as relações internas do sistema como combinações lineares de variáveis, falhando em revelar as leis de transição de fase dinâmica em resposta a riscos extremos sob a perspectiva do encadeamento microtopológico5,6,7.
Para superar essas limitações, foi desenvolvido um framework de computação física com um modelo conjunto de grafos aleatórios exponenciais temporais (TERGM)8,9 e um algoritmo Motter-Lai aprimorado, com o objetivo de resolver os problemas técnicos associados à discreção temporal, suposições sobre compartilhamento de carga e desacoplamento de arquiteturas na pesquisa existente10. Esse framework preenche as lacunas matemáticas entre as interações em nível micro e a falha de um sistema inteiro em nível macro, ao medir o limite de resiliência do ecossistema da economia digital quando submetido a ataques assimétricos planejados. O framework de computação integrado construído neste estudo não apenas melhora o mecanismo de inferência matemática da resiliência da evolução de redes complexas, mas também fornece uma base matemática altamente reprodutível para prevenir crises de interrupção de redes globais na era digital.
Protocolo
The protocol consists of four sequential computational stages that transform empirical panel data into a quantified resilience threshold for the digital economy ecosystem.
Temporal topology evolution via TERGM
The first stage executes topology evolution using the Temporal Exponential Random Graph Model with Markov Chain Monte Carlo Maximum Likelihood Estimation. The empirical longitudinal panel dataset ICT-DE500, which represents digital economy entities over the 2018–2023 observation period, is imported into the system environment, and entity index numbers are aligned across different time steps to construct a vertically directed graph sequence. The parameter update step size is fixed at 0.01, and the initial 10,000 MCMC iterations are discarded as the burn-in period to achieve stationary distribution. The ICT-DE500 dataset is constructed from Crunchbase global corporate investment and merger records spanning 2018 to 2023, with entities filtered to include only those operating in the Information and Communication Technology and Digital Economy sectors. In this constructed network, nodes represent individual digital economy entities (i.e., enterprises and investment institutions), and directed edges represent the unweighted binary capital flows via investment or merger and acquisition (M&A) events. These financial interactions serve as logical pathways for modeled load propagation, as equity dependencies and capital flows create direct risk transmission channels; financial distress in one node forces liquidity redistribution and asset devaluation that directly propagate to its topologically connected partners. The 500 core entities are selected based on the highest network centrality ranking and most active interaction records during the observation period. Annual edge slices are extracted for each of the six years. To ensure strict temporal alignment of entity index numbers and unify matrix dimensions (N = 500) for the TERGM estimation, isolated nodes with degree zero in any given year's slice were retained as temporarily inactive entities rather than being structurally removed. TERGM convergence is assessed by monitoring the MCMC-MLE parameter trajectories for all endogenous structural coefficients, including edge density, reciprocity, and geometrically weighted edgewise shared partnership. The chain is declared converged when all parameter trajectories exhibit stable oscillation around their respective mean values without directional drift after the 10,000-step burn-in threshold. After parameter convergence, the system performs 10,000 sequential Gibbs sampling iterations to model endogenous effects such as star hub tendencies, generating continuous time-aligned topologies that represent the network's macroscopic structural evolution.
To formally define the generation process, the mathematical specification of the TERGM models the conditional probability of observing the target network topology Gt at macro-time step t, given the preceding network Gt-1, as
Here, θ is the core parameter vector controlling the structural evolution, h(Gt, Gt-1) is the network's sufficient statistics vector quantifying the endogenous structural terms described previously (i.e., edge density, reciprocity, and geometrically weighted edgewise shared partnership), and c(θ, Gt-1) is the partition function ensuring probability normalization. For the subsequent nonlinear cascading-failure simulations, a final stable network realization from the generated prior sequence G1:T is extracted to serve as the initial topological substrate. Crucially, because macroeconomic structural evolution operates on a vastly longer timescale (macro-time steps, t) than instantaneous local cascading failures, the network topology does not continue to evolve via TERGM mechanisms during the cascade simulation. Instead, topological changes during the rapid micro-cascade time steps (τ) are exclusively driven by the deliberate node removals and subsequent overload-induced secondary failures.
Physical capacity calibration and load initialization
The second stage performs physical capacity calibration for all nodes in the outputted network topology matrix sequence. The total degree and directed betweenness centrality for every node are extracted, with a small constant of 10-8 introduced in betweenness centrality calculations to avoid division by zero caused by local network discreteness. The initial service load Li(0) is mapped to all network nodes using a nonlinear power-law equation
where ki is the normalized total degree, Bi is the normalized directed betweenness centrality, λ is the equilibrium weight factor (fixed at 0.5 to ensure equal weighting), and β is the load allocation index constrained within the range of 1.0 to 1.5. The physical carrying capacity limit Ci for each node is established by applying a system-level capacity tolerance hyperparameter α (ranging from 0.1 to 0.5) to build the physical redundancy boundary against shocks
The lower bound α = 0.1 represents a minimal redundancy scenario where nodes possess only 10% spare capacity above their baseline load, while the upper bound α = 0.5 corresponds to a high-redundancy configuration with 50% spare capacity. Intermediate values α = 0.2, 0.3, and 0.4 are also employed in the bivariate sensitivity analysis to construct the full orthogonal parameter space with the load heterogeneity exponent β. The load allocation index β is constrained within the range of 1.0 to 1.5, where β = 1.0 produces a linear load distribution and β = 1.5 generates a highly polarized load concentration toward high-centrality nodes. The equilibrium weight factor λ is fixed at 0.5 to ensure equal contribution from degree and betweenness centrality in the initial load calculation. The core parameter settings for the time-series evolution and cascading failure simulations are summarized in Table 1.
Nonlinear cascading dynamics under deliberate attacks
The third stage implements nonlinear cascading dynamics under deliberate attack conditions. The simulation initiates a deliberate attack by locking and forcibly removing the core node set in descending order of betweenness centrality, thereby disrupting the initial topology protection of the digital ecosystem to test dynamic stress at micro-cascade time steps. The load reallocation engine is triggered to reroute overflow flow constrained by the real-time remaining physical capacity of neighboring nodes, with a sink term of 10-8 introduced to simulate digital asset overflow when commercial pathways are completely blocked. A node is declared failed when its transient load exceeds its physical capacity, and this overload verification executes in parallel across all active nodes to update the binary survival state function. The deliberate attack targets nodes in strictly descending order of betweenness centrality, with each attack step removing exactly one node from the surviving active set. The load redistribution weight 
assigned from a failed node i ∈ Fτ to a surviving neighbor j ∈ Aτ at micro-time step τ is computed as
where 
represents the remaining physical capacity of neighbor j, Gij is the topological adjacency indicator, Aτ is the active surviving node set, and 
= 10-8 prevents division by zero. Based on these weights, the instantaneous load scale 
of surviving nodes is synchronously transitioned
Subsequently, the secondary failure-state update is verified via a binary survival function 
:
A node is declared failed (
) when its transient load exceeds its capacity, updating the failure set Fτ+1. The cascade reaches steady state when Fτ+n = ∅, indicating that no additional nodes have failed in the current micro-time step and all surviving nodes operate within their capacity boundaries.
The cascading loop continues until no additional nodes fail, marking the arrival at a secondary steady state where the cascade potential is fully dissipated.
System resilience evaluation and threshold identification
The fourth stage evaluates system resilience by monitoring the macro-disintegration rate of the digital ecosystem graph. The relative scale of the largest connected component derived from surviving nodes is continuously extracted to plot the phase transition decay curve over the fraction of removed nodes. The global transmission efficiency E(τ) is calculated to quantify the connectivity of the surviving topology
where N is the initial total number of nodes (a constant), Aτ is the set of surviving active nodes, and 
is the directed shortest geodesic distance from node i to j at the current step. The critical transition threshold is then identified by monitoring the mutation of the first derivative of this efficiency function with respect to the removal ratio. This threshold is determined as the point at which the first derivative attains its minimum value, indicating the steepest decline in transmission efficiency. The critical resilience threshold is calculated by numerically differentiating the global transmission efficiency E(τ) with respect to the node removal ratio f using a second-order central difference scheme. The first derivative trajectory dE/df is smoothed with a moving average window of five consecutive data points to reduce Monte Carlo sampling noise while preserving the location of the steepest descent. The critical threshold fc is selected as the removal ratio at which the smoothed first derivative attains its global minimum value, corresponding to the point of maximum decay rate in transmission efficiency. This selection criterion is applied consistently across all simulation scenarios and baseline models. The reported threshold value of 12.41% ± 0.63% represents the mean and standard deviation computed from 100 independent Monte Carlo simulations with different random seeds, ensuring statistical robustness of the phase transition localization.
Simulation configurations and baseline implementations
To ensure fully reproducible simulations, random seeds were sequentially assigned (integers 1 through 100) prior to each Monte Carlo iteration. The topological evolution and statistical modeling were executed using R with the tergm package, while the nonlinear cascading simulations were implemented in Python using the NetworkX library. Furthermore, for the comparative deep learning baseline, the GCN-Attack model was implemented using PyTorch Geometric. It was constructed with a standard two-layer Graph Convolutional Network architecture (hidden dimension of 64), and trained using the Adam optimizer with a learning rate of 0.01 for 200 epochs to ensure rigorous and consistent experimental control across baseline evaluations.
Resultados
The overall execution logic and data flow of the proposed physical computation framework are illustrated in Figure 1. As the framework executes, the microscopic thermal characteristics of local overflow load redistribution and the nonlinear evolution of node degree distributions are captured (overviewed in Figure 2 and Figure 3, with dynamic details described below. The subsequent sections map the simulation outcomes directly to the protocol stages.
Temporal topology evolution via TERGM
Figure 4 visually deconstructs the spatial topology and community structure of the ICT-DE500 core network, highlighting the distribution of high-betweenness nodes targeted in deliberate attack simulations. The goodness-of-fit test confirms that the generated network topology effectively models the temporal evolution of real ecosystems, successfully avoiding gradient explosion or traps of local optimality after the 10,000-step burn-in period. Figure 5 presents the MCMC-MLE parameter convergence diagnostic trajectories and the geodesic distance goodness-of-fit. Figure 5A shows that the three core parameters representing edge density θ₁, mutuality θ₂, and geometrically weighted edgewise shared partnership θ₃ all terminate their large directional drift after crossing the 10,000-step burn-in threshold, with expected means converging and stabilizing near the horizontal baseline. Figure 5B demonstrates that the empirical observations of shortest geodesic distances fall robustly within the overall distribution boundaries of 1,000 independent network realizations. These realizations were extracted using a thinning interval of 10 from the 10,000 sequential Gibbs sampling iterations to minimize autocorrelation, confirming the reliability of the topology generation base. The specific MCMC-MLE parameter estimates, standard errors, and statistical significance for endogenous structural effects across the observation years are detailed in Table 2.
The temporal evolution of macroscopic topological structure is quantified in Figure 6. The network density steadily increased from 0.015 to 0.035 between 2018 and 2023, while the average clustering coefficient rose from 0.22 to 0.37, highlighting a significant density-cluster divergence phenomenon. The density rises most sharply between 2020 and 2021, fluctuating from 0.021 to 0.029, whereas the clustering coefficient reaches a local peak of approximately 0.31 in 2020 and subsequently drops to approximately 0.29 despite rapid density growth in 2021. This divergence reveals the adaptive evolution mechanism under macroeconomic cycle fluctuations, where risk-avoidance grouping in 2020 drives local clustering, while massive new cross-border connections in 2021 temporarily dilute the close-knit community structure.
Physical capacity calibration and load initialization
The bivariate sensitivity analysis in Figure 7 examines the joint effect of physical capacity redundancy and load polarization on the phase transition trajectory of the largest connected component. Across the nine orthogonal combinations of capacity tolerance α and load heterogeneity β, the array of panels shows that increasing α and decreasing β both delay network collapse. Under the polarized load scenario with β = 1.5 and minimal redundancy α = 0.1 in Figure 7A, the critical collapse threshold is approximately fc = 0.08. Raising α to 0.5 in Figure 7C shifts the inflection point rightward to fc ≈ 0.23. Under the balanced load scenario with β = 1.0 and α = 0.1 in Figure 7G, the threshold remains robust at fc ≈ 0.18, and at the optimal combination α = 0.5 and β = 1.0 in Figure 7I, the threshold extends significantly to fc ≈ 0.38. These results demonstrate that load balancing produces a greater marginal gain in resilience than capacity expansion alone.
Nonlinear cascading dynamics under deliberate attacks
As introduced in the framework overview, the microscopic thermal characteristics of local overflow load redistribution following the initial cascade failure are shown in Figure 2, and the nonlinear evolution of node degree distribution across three typical micro-time steps is presented in Figure 3.
System resilience evaluation and threshold identification
The critical transition threshold for global transmission efficiency is located at 12.41% ± 0.63% node removal during a targeted attack. In the context of the 500-node network, this proportion corresponds to the targeted removal of approximately 62 core hub nodes. This threshold marks the efficiency-collapse point (i.e., the onset of the steepest decline in transmission efficiency) rather than a complete topological disconnection. Figure 8 presents the three-dimensional evolution surface of global efficiency E(τ) over removal ratio and peak network load in Figure 8A, and the two-dimensional cross-section with numerical differentiation in Figure 8B. When the removal ratio f is below 0.10, E(τ) remains above 0.8 and the first derivative oscillates in a shallow region. The minimum of the first derivative trajectory identifies the critical transition threshold, with Figure 8B displaying a single-run cross-section at fc = 12.0% that is highly consistent with the statistical mean from 100 independent Monte Carlo simulations.
Simulation configurations and baseline implementations
The proposed model significantly outperforms the static and deep learning baselines under targeted attack scenarios. However, under random failure conditions, the Static BA-ML baseline exhibits a higher survival threshold (49.12%) compared to the TERGM-ML model (46.28%). It is important to note that the comparison with the Static BA-ML model serves as a distinct topological benchmark rather than a strictly controlled ablation, as the Barabási-Albert generative mechanism fundamentally differs from the ERGM framework. Figure 9 displays the raincloud plot of cascade propagation peak velocities across four model architectures. The Static BA-ML baseline shows a median peak velocity of approximately 49.7 nodes per step, with extreme batches approaching 140. The SNA-Cascading and GCN-Attack models have medians of approximately 35.6 and 23.9, respectively. The TERGM-ML model exhibits the strongest convergence with a median of 13.2 nodes per step, almost eliminating extreme collapses exceeding 40. Table 3 summarizes the critical thresholds and statistical significance for all models. These comparisons clarify that while the TERGM-ML framework demonstrates superior structural resilience to targeted asymmetric shocks, the observed performance differences reflect the joint influence of distinct underlying topologies, temporal evolution, and capacity-aware redistribution, rather than being solely attributable to isolated mechanism ablations.
DATA AVAILABILITY:
The raw data used in this study are derived from the Crunchbase global corporate investment and merger database, publicly accessible via the Kaggle platform at https://www.kaggle.com/datasets/justinas/startup-investments. The processed ICT-DE500 subset, consisting of 500 entities with annual edge matrices for the period 2018–2023 and node attribute data including degree and betweenness centrality, along with the TERGM estimation and convergence diagnostic scripts, the cascading failure simulation code with the improved Motter-Lai algorithm, and the complete dependency specifications, have been deposited in a publicly accessible GitHub repository at https://github.com/moonmoon1189/digital-economy-resilience-complex-networks.
Figure 1: Temporal topology evolution and nonlinear cascade physical computation framework. This figure illustrates the overall execution logic and data flow, including topology evolution, physical capacity calibration, nonlinear cascading, and resilience evaluation stages for identifying the critical transition threshold. Please click here to view a larger version of this figure.
Figure 2: Thermal diagram of the microscopic evolution of nonlinear load redistribution and local cascade overload. The figure illustrates the dynamic thermal characteristics of the local redistribution of overflow load after the initial cascade failure from micro-time step 0 to step 5. Please click here to view a larger version of this figure.
Figure 3: Scatter plot of nonlinear evolution of node degree distribution during cascading failure. The figure presents the evolution trajectory of the node degree distribution of the system at three typical micro-time steps (0, 3, 6). Please click here to view a larger version of this figure.
Figure 4: Spatial topology, community structure, and deliberate attack target distribution of the ICT-DE500 core network. The figure visually deconstructs the highly nonlinear macroscopic topology and microscopic node attributes of the core network, highlighting star hubs and vulnerable sources. Please click here to view a larger version of this figure.
Figure 5: Goodness-of-fit test of Markov Chain Monte Carlo parameter diagnostic trajectory and geodesic distance. (A) This panel shows the diagnostic trajectory of MCMC-MLE parameter estimation across iterations, while panel (B) displays the goodness-of-fit test of the shortest geodesic distance. Please click here to view a larger version of this figure.
Figure 6: Joint distribution of macro-topological feature parameters in time series evolution. The figure shows the changing trend of macro-topological parameters, specifically network density and average clustering coefficient, for the digital economy ecosystem between 2018 and 2023. The shaded regions around the trend lines represent the 95% confidence intervals derived from 100 independent Monte Carlo simulations. Please click here to view a larger version of this figure.
Figure 7: Array plot of phase transition decay for bivariate sensitivity to capacity tolerance and load heterogeneity. (A–I) These panels display the phase transition trajectories across various orthogonal combinations of capacity tolerance and load heterogeneity. Please click here to view a larger version of this figure.
Figure 8: Joint profile of global transmission efficiency in three dimensions and cross-sectional critical transition threshold. Panel (A) constructs the three-dimensional spatial evolution of global transmission efficiency, and panel (B) extracts the two-dimensional cross-sectional critical transition threshold (i.e., the efficiency-collapse point) localization using numerical differentiation. Please click here to view a larger version of this figure.
Figure 9: Heterogeneous distribution of cascade propagation peak evolution velocity in raincloud plot. The figure comprehensively displays the heterogeneous probability density distribution of the cascade propagation peak velocities of four models during secondary disaster outbreaks. Please click here to view a larger version of this figure.
| Parameter | Variable & Range | Constraint & Justification |
| Network Scale | N=500 | Fixed size of the extracted ICT-DE500 empirical network subset. |
| Centrality Weight | λ=0.5 | Anchored baseline ensuring equal weighting for degree and betweenness. |
| Load Allocation Index | β∈[1.0,1.5] | Non-linear exponent controlling initial business load heterogeneity. |
| Capacity Tolerance | α∈[1.0,1.5] | System-level redundancy ratio defining the upper bound of physical capacity. |
| MCMC Burn-in Period | >10,000 steps | Mandatory initial iterations discarded to achieve stationary distribution. |
| Gibbs Sampling Iterations | >10,000 steps | Sequential sampling steps to generate time-aligned network topologies. |
Table 1: Core parameter settings for time-series evolution and cascading failure physical simulations. The table defines the core parameters, including network scale, centrality weight, load allocation index, capacity tolerance, and Markov Chain Monte Carlo (MCMC) iterations.
| Observation Year | Edge Density (θ1) Estimate | Edge Density (θ1) Std.Error | Mutuality (θ2) Estimate | Mutuality (θ2) Std.Error | GWESP (θ3) Estimate | GWESP (θ3) Std.Error | Significance |
| 2018 | -6.35 | 0.12 | 1.95 | 0.08 | 1.25 | 0.05 | *** |
| 2019 | -6.15 | 0.11 | 1.98 | 0.09 | 1.35 | 0.06 | *** |
| 2020 | -6.05 | 0.14 | 2.15 | 0.1 | 1.55 | 0.07 | *** |
| 2021 | -5.85 | 0.13 | 1.9 | 0.09 | 1.3 | 0.06 | *** |
| 2022 | -5.75 | 0.12 | 2.05 | 0.08 | 1.42 | 0.05 | *** |
| 2023 | -5.65 | 0.11 | 2.1 | 0.07 | 1.48 | 0.05 | *** |
Table 2: TERGM parameter estimates for endogenous structural effects across observation years (2018–2023). The table reports the Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) parameter estimates, standard errors, and statistical significance for edge density, mutuality, and geometrically weighted edgewise shared partnership across the six annual observation periods. ***p < 0.001. Standard errors are reported next to parameter estimates.
| Model Architecture | Temporal Evolution Mechanism | Dynamic Reallocation Mechanism | Critical Threshold (Targeted Attack) | Critical Threshold (Random Failure) | Statistical Significance (p-value) |
| TERGM-ML | Yes | Yes | 12.41% ± 0.63% | 46.28% ± 1.75% | Reference Baseline |
| Static BA-ML | No | Yes | 7.85% ± 0.42% | 49.12% ± 1.88% | p < 0.001 *** |
| SNA-Cascading | Yes | No | 8.93% ± 0.55% | 37.54% ± 1.42% | p = 0.003 ** |
| GCN-Attack (SOTA Baseline) | Implicit | Implicit | 10.76% ± 0.81% | 43.15% ± 2.05% | p = 0.021 * |
Table 3: Comparison of core mechanism ablation and multimodel architecture resilience boundary. The table details the critical thresholds and statistical test results for system resilience of time-series graphs and improved Motter-Lai (TERGM-ML) and three baseline models under both deliberate attack and random failure scenarios. Values are reported as mean ± standard deviation based on 100 independent Monte Carlo simulations. Targeted attack refers to the sequential removal of nodes based on descending betweenness centrality. Statistical significance evaluates the difference in the Targeted attack threshold between the respective baseline model and the proposed framework using an independent two-sample t-test (*p < 0.05, **p < 0.01, ***p < 0.001).
Discussão
O quadro proposto de computação física em cascata, que combina gráficos conjuntos de séries temporais e o modelo aprimorado de Motter-Lai (TERGM-ML), alivia efetivamente as limitações de caixa-preta dos modelos tradicionais puramente baseados em dados na previsão de resiliência. Este quadro fundamenta-se nos modelos gráficos aleatórios exponenciais introduzidos por Wasserman e Pattison11 e no quadro de ataque baseado em cascata originalmente desenvolvido por Motter e Lai12, estendendo ambos para abordar dinâmicas temporais e restrições locais de capacidade. Esse paradigma acopla fortemente a evolução topológica endógena real com os limites de suporte de carga das microentidades, introduzindo uma lógica seletiva de fluxo baseada em restrições de limites de capacidade física local. O mecanismo de evolução temporal segue as especificações do TERGM para modelagem de redes dinâmicas13,14, e a estratégia de alocação de capacidade está alinhada aos princípios de projeto de redundância em redes para mitigação de falhas em cascata15,16.
Uma etapa crítica do protocolo é o mecanismo ideal de rerroteamento do fluxo comercial subjacente com base na capacidade disponível dos vizinhos, substituindo a suposição irrealista de "distribuição média" no modelo tradicional de Motter-Lai. A suposição de redistribuição uniforme do modelo padrão de Motter-Lai tem sido criticada em estudos recentes sobre resiliência de infraestrutura por negligenciar restrições heterogêneas de capacidade dos nós6,10. Os resultados atuais indicam que a rede comunitária em malha fechada subjacente possui um efeito físico definido de amortecimento sobre picos de carga em excesso, suprimindo efetivamente a propagação em cascata e atrasando significativamente a desintegração da transição de fase na eficiência global de transmissão. O modelo TERGM-ML apresenta o limiar crítico mais alto para ataques deliberados, atingindo 12,41% ± 0,63%, o que reflete a capacidade de amortecimento da arquitetura de rede endógena e reduz o risco global de avalanche induzido por um único ponto de excesso de carga. O aumento do limiar crítico de 7,85% para 12,41% decorre de dois mecanismos sinérgicos. O mecanismo de evolução temporal gera estruturas comunitárias em malha fechada e laços recíprocos ausentes em redes estáticas livres de escala. Essas comunidades restringem espacialmente a propagação da sobrecarga, forçando a carga em excesso a percorrer múltiplos caminhos intracomunidade antes de alcançar regiões distantes, com cada etapa de travessia dissipando uma fração da carga transitória por meio da absorção pelos nós vizinhos. O mecanismo de redistribuição dinâmica direciona a carga em excesso exclusivamente para vizinhos com capacidade remanescente positiva ΔCj(τ) > 0, evitando a distribuição uniforme que rapidamente esgota a redundância local no modelo padrão de Motter-Lai. As comunidades em malha fechada fornecem a estrutura topológica que torna o roteamento com base na capacidade eficaz, enquanto o roteamento com base na capacidade evita a saturação prematura dos enlaces internos da comunidade. Esse acoplamento explica por que o framework combinado supera a linha de base estática em mais de 4 pontos percentuais no limiar crítico. Esse valor de limiar é consistente com as previsões teóricas para redes livres de escala sob ataques direcionados17 e com os comportamentos de transição de fase de percolação observados em sistemas complexos18.
Apesar desses avanços, existem limitações no método. Limitadas pelas fronteiras observacionais existentes, as extrapolações atuais dependem fortemente de cortes centralizados e completos da topologia global, e suas janelas de tempo de amostragem discretizadas não conseguem capturar com precisão perturbações de impedância que variam em microescala de tempo provocadas por oscilações externas e súbitas de alta frequência no ambiente. Essas limitações refletem os desafios identificados em revisões recentes sobre métricas de resiliência para sistemas ciberfísicos e modelagem de falhas em cascata sob condições dinâmicas19,20. Pesquisas e aplicações futuras podem avançar em direção a arquiteturas descentralizadas, concentrando-se na exploração de mecanismos dinâmicos adaptativos de compensação de resiliência com base em colaboração distribuída entre múltiplos agentes em condições de jogos com informação incompleta. A abstração em grafo de camada única e a atribuição global de parâmetros representam limitações centrais da estrutura atual. Estudos em redes de múltiplas camadas demonstraram que as interdependências entre camadas de interação podem amplificar ou atenuar a propagação em cascata de maneiras que modelos de camada única não conseguem representar. A atribuição global da tolerância de capacidade α e do expoente de alocação de carga β abstrai a heterogeneidade específica das entidades em margens de capacidade e sensibilidades à carga. Três extensões merecem investigação em trabalhos futuros: substituir a topologia de camada única por uma representação de múltiplas camadas que distinga fluxos de capital, licenciamento tecnológico e prestação de serviços como camadas separadas com dependências entre camadas; calibrar parâmetros específicos de capacidade e carga a partir de dados operacionais em nível empresarial; e migrar de cortes topológicos centralizados para arquiteturas multiagente descentralizadas, nas quais os nós tomam decisões adaptativas de redistribuição com base em sinais observáveis localmente. Estudos recentes em redes de múltiplas camadas demonstraram que as interdependências entre camadas distintas de interação podem amplificar ou atenuar a propagação em cascata de maneiras que modelos de camada única não conseguem capturar.
Divulgações
Os autores declaram não haver conflitos de interesses. Nenhuma ferramenta de inteligência artificial generativa (IA) foi utilizada na criação, geração ou modificação de quaisquer elementos gráficos.
Contribuições dos Autores:
F.Y. e Y.Z. conceberam e projetaram o estudo. F.Y. realizou as simulações computacionais, analisou os dados e redigiu o manuscrito original. Y.Z. supervisionou a pesquisa, forneceu orientação teórica e revisou criticamente o manuscrito por conteúdo intelectual importante. Todos os autores revisaram e aprovaram o manuscrito final.
Agradecimentos
Os autores não receberam apoio de nenhuma organização para o trabalho submetido.
Materiais
| Nome | Empresa | Número de catálogo | Comentários |
|---|---|---|---|
| CPU AMD EPYC 7742 | Advanced Micro Devices | 7742 | Processador de alto desempenho para percorrer estruturas de grafos e recálculos de caminhos mais curtos. |
| Base de Dados Crunchbase | Kaggle | investimentos-em-startups | Investimento corporativo global e M&Um registro de rede utilizado como base de rede global. |
| CUDA 11.6 | NVIDIA | versão 11.6 | Plataforma de aceleração de hardware utilizada para operações de tensor no modelo de referência GCN. |
| NetworkX 2.8 | Desenvolvedores do NetworkX | versão 2.8 | Biblioteca de análise de redes complexas utilizada para a extração de parâmetros de grafos e busca de caminhos. |
| NumPy | Desenvolvedores do NumPy | N/A | Estrutura de kernel matemático que garante lógica determinística e elimina deriva numérica. |
| GPU NVIDIA RTX 3090 | NVIDIA | RTX 3090 | Processador gráfico utilizado para acelerar cálculos de tensores na linha de base de aprendizado profundo. |
| Python 3.9 | Fundação Python Software | versão 3.9 | Ambiente de execução subjacente para o framework principal compilado e executado. |
| PyTorch 1.12 | Meta AI | versão 1.12 | Biblioteca de aprendizado profundo utilizada para calcular gráficos e propagação direta no modelo de referência. |
| R | / | versão 4.2.2 | / |
| pacote statnet | O Projeto statnet | N/A | Pacote avançado de expansão estatística utilizado para redes dinâmicas multinível TERGM MCMC-MLE. |
| pacote tergm | / | versão 4.2.0 | / |
| Ubuntu 22.04.1 LTS | Canônico | 22.04.1 LTS | Configuração do sistema operacional do servidor que hospeda a matriz computacional multithread. |
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