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The paper asks whether effective resistance in tissue-specific protein interaction networks can flag which protein-function predictions a graph neural network will get wrong. Because effective resistance on these networks is almost completely determined by inverse degree, the author strips out that degenerate component and tests whether the residual predicts per-node loss beyond standard uncertainty scores. The study concludes that a reproducible but tiny signal exists across 24 interactomes, and that degree degeneration strongly bounds how useful resistance can ever be on this class of biological graphs.
Protein function annotation needs to know which predictions to distrust, not only what a model predicts. We ask whether tissue-specific interaction structure carries that information. Our candidate signal is effective resistance, used previously to relieve over-squashing by rewiring. Across 24 tissue-specific interactomes it is dominated by inverse degree, and the degeneration deepens as the co-expression filtered network grows, with a Spearman correlation of -0.955. The residual departure from that limit exceeds degree-preserving null graphs in all 24 networks. Controlling for predictive entropy, degree, annotation cardinality, local structure and feature-only difficulty, the residual explains additional per-node loss in 19 of 24 held-out networks once a permutation floor is subtracted, at every depth, and the effect strengthens monotonically with depth. The increment reaches 0.37% of the variance the controls leave unexplained, 5.6 times a permutation floor, against 1.5 times when the model is retrained in a degree-preserving null world. Selective prediction improves negligibly. The signal is reproducible; degree degeneration bounds it.