When does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions

The paper investigates how graph neural networks can quickly estimate the loss of algebraic connectivity after multiple road-link disruptions, comparing learned corrections to first‑order Fiedler sensitivity with analytical baselines. Experiments on synthetic failures and real OpenStreetMap data across six countries show that residual GCN and GraphSAGE models reduce mean absolute error for spatial and targeted failures, while second‑order perturbation offers minimal improvement. The study also demonstrates that sparse scaling allows the approach to scale to 20,000 nodes and that the spectral residual acts as a domain‑sensitive inductive bias for connectivity screening.

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