Generalist Graph Anomaly Detection via a Spectral Vocabulary

Graph anomaly detection (GAD) methods are typically trained on individual graphs, limiting their ability to transfer anomaly knowledge across domains. Developing a generalist GAD model therefore requires representations that support transfer to unseen graphs. A fundamental challenge is the lack of a shared representation space across graphs that effectively leverages diverse graph data while generalizing across domains. To address this challenge, we introduce SV-GAD, a generalist GAD framework built on a shared "graph vocabulary". Our key insight is that spectral-energy statistics characterize how node signals vary with respect to graph structure through common measurements, providing a domain-agnostic representation across graphs. SV-GAD learns transferable anomaly patterns in the spectral space and leverages a mixture-of-experts architecture, where graph filters serve as specialized experts for different spectral behaviors. Extensive experiments across diverse GAD benchmarks demonstrate that SV-GAD effectively transfers anomaly knowledge to unseen graphs and consistently outperforms existing baselines in a zero-shot setting.