Integrating uncertainty quantification and ML for network robustness study: From metrics to surfaces

Network robustness, defined as a system's capacity to retain functionality under failures or attacks, is conventionally studied using synthetic models such as Erdös-Rényi (ER), Barabási-Albert (BA), and Holme-Kim (HK). However, model parameters are often chosen arbitrarily, neglecting their influence on robustness metrics. This study integrates forward uncertainty quantification and machine learning to quantify parameter impact on measures —natural connectivity (NC), global efficiency (GE), algebraic connectivity (AC), spectral radius (SR), average path length (APL), and effective graph conductance (C). We analyse how these metrics vary across model configurations by constructing response surfaces based on influential parameters. Some key findings reveal distinct parameter dominance: in ER models, the number of nodes (n) and edge probability (p1) govern NC, AC, and SR, while p1 predominantly shapes GE, APL, and C. For BA models, n and attachment edges variably influence all metrics. In KH models, n and random edge additions drive all robustness metrics with minimal impact from triangle-formation probability. The derived robustness surfaces offer practical tools for network design: identifying critical vulnerability thresholds, optimising topologies and benchmarking architectures for resilience.