KU-GAD: Rethinking Semi-Supervised Graph Anomaly Detection with Known–Unlabeled Discrimination

Semi-supervised graph anomaly detection (GAD) typically has access to only a small set of verified normal nodes, while anomaly labels remain unavailable. Existing methods infer anomaly information indirectly through normality modeling or surrogate signals, leaving unclear whether the observed unlabeled population can provide direct supervision for anomaly ranking. In this work, we revisit this setting from a population perspective and show that, under a fixed representation and representative normal sampling, the optimal known-unlabeled discrimination score preserves the anomaly-to-normal likelihood-ratio ordering. Based on this insight, we propose KU-GAD, a theory-guided framework for estimating anomaly ranking scores from multi-scale graph representations. Since anomalies may arise from different structural contexts, KU-GAD constructs normal-calibrated multi-hop graph responses to capture anomaly evidence across propagation scales. A hop-sequence Transformer is then employed to adaptively aggregate these responses and produce anomaly scores optimized by the known-unlabeled objective. Extensive experiments on seven graph anomaly detection benchmarks demonstrate the effectiveness of KU-GAD, with further analyses validating the importance of graph context, calibration, and normal-reference quality.