When Can Graph Conformal Sets Transfer? Selective Diagnostics Under Unlabeled Topology Shift

Unlabeled graph topology can reveal shift but cannot universally certify conformal coverage: observable-equivalent target environments may have different label conditionals and arbitrarily different miscoverage. We turn this identifiability limit into a selective transfer criterion over a declared family of graph-environment shifts. From labeled calibration environments, TOPOTRANSFER fits a cross-fitted monotone envelope from topology–representation discrepancy to excess miscoverage, conformalizes its environment-level residual, and returns a validity decision only inside calibrated support. On GOOD-Cora topology shift, TOPOTRANSFER reaches 0.89 violation AUROC with a 5.6% false-certificate rate at 74.9% acceptance; SNAPS reaches 0.72, 16.8%, and 86.4%, respectively. The support and envelope ablations show that graph observables become useful only after environment-level calibration, yielding a non-vacuous selective decision within the reported environment family rather than an unconditional topology-shift score.