Robustness asymmetry under edge failures: A unified framework based on structural controllability and power domination

Modern complex networks require effective mechanisms for network control and monitoring to ensure reliable operation under failures. Structural controllability and power domination provide fundamental frameworks for assessing these capabilities, yet a systematic comparison of their robustness under random failures remains limited. Unlike prior studies that typically examine structural controllability and power-domination-based monitoring separately, this work presents a unified framework for analyzing their robustness under identical edge-failure conditions in Erdős–Rényi random graphs. Using a simulation-based evaluation across a broad parameter space of network sizes, edge densities, and edge-survival probabilities, together with Monte Carlo estimation of the expected monitoring coverage and driver-node requirements under random edge failures, the analysis evaluates degradation through sensitivity, balance, and gap metrics. The results reveal a configuration-dependent robustness asymmetry, with structural controllability exhibiting its most pronounced relative vulnerability under sparse and severely degraded network conditions. Notably, following edge failures, the two frameworks are reevaluated through different structural mechanisms: the power dominating set is recomputed on the degraded network to determine the updated monitoring-node requirement, whereas the maximum matching is recomputed to determine the updated driver-node requirement for structural controllability. Network density also plays a critical role, with sparse networks exhibiting higher vulnerability and dense networks showing greater resilience. These findings indicate that, for the considered Erdős–Rényi random-network model under independent random edge failures, the stronger relative vulnerability of structural controllability is concentrated primarily in sparse and severely degraded network configurations.