Post-Calibration Topology Drift Reveals Operator-Dependent Numerical Sensitivity in Quantized Graph Neural Networks

Post-training quantization (PTQ) is attractive for graph neural networks (GNNs), yet it is commonly evaluated on the same topology used for calibration. We study whether post-calibration topology drift changes the numerical discrepancy between a quantized GNN and its full-precision counterpart beyond the error already present on the calibration graph. We introduce Component-Preserving Degree-Preserving Rewiring (CP-DPR), a controlled intervention that changes neighborhood composition while preserving the node set, features, labels, model weights, edge count, exact node-wise degree sequence, and connected-component partition. We measure the baseline-adjusted excess logit divergence \(EQD_Z = QD_Z(A_\delta) - QD_Z(A_0)\). Experiments cover Cora, CiteSeer, PubMed, and Roman-empire; GCN and GraphSAGE; W8A8 and W4A4 simulated PTQ; five training seeds; and ten perturbation seeds per severity. At the strongest perturbation level, 10 of 12 external dataset–operator–precision settings exhibit positive excess divergence, with substantially larger absolute effects under W4A4. Roman-empire with GCN provides a consistent negative case that persists after validation-only model refinement. Activation diagnostics show negligible additional clipping in the dominant positive regimes and a stronger association with rounding mismatch. GraphSAGE further exposes an observer-blindness failure mode in which min–max calibration parameters remain unchanged despite internal activation-distribution motion. These results provide evidence that topology drift induces operator-dependent numerical sensitivity not captured by calibration-graph accuracy alone, while the evidence for operator dependence currently rests on one heterophilous benchmark.