Edge Failures Hit Network Controllability Hardest in Sparse Graphs

When links fail in a complex network, how badly is the ability to steer the system damaged compared with the ability to monitor it? A new simulation study in PLOS One addresses that question by putting two established network frameworks, structural controllability and power domination, through identical random edge-failure conditions and measuring how each degrades.

Structural controllability concerns the minimum set of driver nodes needed to steer a network’s dynamics, determined through maximum matching, while power domination concerns the minimum set of monitoring nodes needed to observe the whole network. Earlier work typically examined these two capabilities separately. The new study instead analyzes them within a unified framework, applying the same edge-failure scenarios to both in Erdős–Rényi random graphs.

The researchers used a simulation-based evaluation across a broad parameter space of network sizes, edge densities, and edge-survival probabilities. Monte Carlo estimation was employed to quantify the expected monitoring coverage and driver-node requirements as edges were randomly removed. Degradation was assessed through sensitivity, balance, and gap metrics, offering a systematic comparison of how the two frameworks respond to the same damage.

After failures, the two frameworks were reevaluated through different structural mechanisms. The power dominating set was recomputed on the degraded network to determine the updated monitoring-node requirement, whereas the maximum matching was recomputed to determine the updated driver-node requirement for structural controllability.

The results reveal a configuration-dependent robustness asymmetry between the two frameworks. Structural controllability showed its most pronounced relative vulnerability under sparse and severely degraded network conditions, while power domination proved comparatively more resilient in those regimes.

Network density emerged as a critical factor. Sparse networks exhibited higher vulnerability to edge failures, whereas dense networks showed greater resilience for both capabilities. The asymmetry favoring monitoring over control was therefore not universal but concentrated in specific structural regimes.

The authors note that these findings apply to the considered Erdős–Rényi random-network model under independent random edge failures.

Subject of Research: Robustness of structural controllability and power domination in random networks under edge failures

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

Article References: Alwasel, B. (2026). Robustness asymmetry under edge failures: A unified framework based on structural controllability and power domination. PLOS One, 21(10), e0361399. https://doi.org/10.1371/journal.pone.0361399

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0361399

Keywords: structural controllability, power domination, network robustness, edge failures, Erdős–Rényi random graphs, driver nodes, monitoring nodes, maximum matching, network density, Monte Carlo simulation, complex networks, Robustness