From Single- to Multi-relation: Relation Inconsistency Modeling for Unsupervised Graph Anomaly Detection

Graph anomaly detection (GAD) in this work aims to identify anomalous nodes whose behavioral patterns deviate from those of the majority of normal nodes. However, most existing GAD methods are developed for single-relation graphs and cannot directly capture the diverse relational semantics prevalent in real-world systems. Current multi-relation approaches, in turn, largely overlook *cross-relation behavioral inconsistency* as an informative signal of anomalies. To bridge this gap, we identify two complementary forms of relation inconsistency: *explicit inconsistency*, manifested as structural connectivity shifts across relations, and *implicit inconsistency*, revealed by divergent reconstruction patterns. Based on this insight, we propose RelIn-GAD, an architecture-agnostic, plug-and-play module that extends unsupervised reconstruction-based single-relation detectors to multi-relation settings. RelIn-GAD employs global-to-local relation weighting to adaptively aggregate relation-wise reconstruction evidence, and a dual-inconsistency mechanism that distinguishes anomaly-related disparities from benign relational diversity. The resulting inconsistency signal further adapts the node-wise training objective, while explicit structural inconsistency provides a gated correction to reconstruction-based anomaly scoring. Extensive experiments on four real-world datasets and seven backbones demonstrate the broad effectiveness of RelIn-GAD, yielding average relative improvements of up to 36.29% in AUROC and 108.89% in AUPRC, while achieving strong performance against eighteen state-of-the-art baselines.