Who Gets the Risk? Unified Multiscale Optimal Transport for Graph Anomaly Detection

Label-free graph anomaly detection (GAD) aims to identify anomalous nodes without annotations. Yet anomaly patterns vary across graph domains, structures, and attribute regimes, making node-level evidence difficult to remain consistent across graphs. Moreover, existing methods typically map or aggregate label-free proxies into node scores that jointly determine risk positions and node assignment, leaving the valid scope of evidence implicit. To address these challenges, we propose Multiscale Optimal Transport for Graph Anomaly Detection (LORE), a unified framework designed for label-free graph anomaly detection. LORE reformulates graph anomaly detection as an evidence-guided risk allocation problem by constructing a graph-adaptive risk prior and incorporating label-free node evidence to establish the correspondence between node evidence and risk positions. It further leverages multiscale optimal transport to reassign risks across different granularities, thereby correcting initial anomaly rankings. We evaluate LORE on over 30 graphs. LORE achieves strong performance on primary benchmarks, scales favorably to large graphs, and mechanism analyses further support its evidence-guided risk-allocation design.