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

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:10.5281/zenodo.22307723.

Authors 1

Van-Truong Le

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Official page: arxiv.org/abs/2609.11166
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
arXiv id: 2609.11166
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Categories: cs.LG
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
PDF: arxiv.org/pdf/2609.11166
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh

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34 min ago

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Authors: Van-Truong Le

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Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperWhen does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions
New paper: When does a spectral prior help graph learning? Connectivity-loss estimation under road-network disruptions
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Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	34 min ago	1

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