When does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions
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Computer Science > Machine Learning
arXiv:2609.11166 (cs)
[Submitted on 10 Sep 2026]
Title:When does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions
Authors:Van-Truong Le
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Abstract:Rapid evaluation of many simultaneous road-link disruptions requires a practical compromise between exact spectral recomputation and local approximation. We estimate relative algebraic-connectivity loss after multi-edge deletion using graph neural networks (GNNs) that learn a bounded correction to a first-order Fiedler sensitivity. The study considers independent, spatially clustered, and edge-betweenness-targeted failures, with graph-disjoint synthetic splits and zero-shot transfer to 13 OpenStreetMap (OSM) areas in six countries. GCN, GraphSAGE, and edge-aware MPNN backbones are compared with analytical baselines. In expanded OSM tests, residual GCN improves spatial-failure MAE by 0.0391 (95% hierarchical interval 0.0151-0.0662), while residual GraphSAGE improves targeted-failure MAE by 0.0257 (0.0095-0.0446). Second-order perturbation improves first-order MAE by only 0.0028-0.0053. Correction slopes decrease under targeted transfer, indicating residual shrinkage around systematic prior error. Leave-one-country-out OSM-to-OSM transfer is mixed: residual GCN improves targeted-failure MAE by 0.0622 (0.0169-0.1153) but worsens the spatial point estimate. Sparse scaling extends to 20,000 nodes and separates one-time spectral setup from amortized screening cost. These results characterize the spectral residual as a useful but domain-sensitive inductive bias for structural connectivity screening. Code, cached networks, and reproducibility artifacts are archived at doi:https://doi.org/10.5281/zenodo.22307723.
| Comments: | 24 pages, 7 figures, 7 tables. Code and data: doi:https://doi.org/10.5281/zenodo.22307723 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.11166 [cs.LG] |
| (or arXiv:2609.11166v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.11166
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled When does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions, by Van-Truong Le
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