HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration

For graph node classification, calibrated class probabilities are need when confidence scores, usually the maximum predicted class probability, are used to rank prediction, defer uncertain nodes to human review or control risk. Existing post-hoc calibrators either apply one global temperature or use graph-awared modules without a derived strctural form. We study node-level calibration for graph node-classification problem under structural heterogeneity. Our first results show that a logit-only temperature rule is insufficient when nodes with identical logits but different local homophily require different optimal temperatures. We then analyze a population-concentration contextual stochastic block model with Gaussian features and a one-layer linear GCN. Under equidistant class means, the Bayes posterior over class-template scores is a temperature-scaled softmax whose inverse temperature is governed by homophily-dependent signal strength. In the positive-signal homophilic regime, the resulting temperature decreases approximately with normalized local homophily. This law motivates Homophily-aware Temperature Scaling (HoTS), a simple post-hoc calibrator that assigns each node a positive scalar temperature from entropy-based logit concentration and estimated local homophily. HoTS has three parameters, preserving class, and learn the strength of the structural correction from calibraion data. Across 18 node-classification benchmarks, two GNN backbones, and eight calibration baselines, HoTS achieves the best mean Expected Calibration Error (ECE) of $4.66\%$, the best average rank, and the strongest confidence ranking in selective classification.