Graph-level anomaly detection aims to identify abnormal graphs that exhibit deviant structures and node attributes compared to the majority in a graph set. One primary challenge is to learn normal patterns manifested in both fine-grained and holistic views of graphs for identifying graphs that are abnormal in part or in whole. To tackle this challenge, we propose a novel approach called Hierarchical Memory Networks (HimNet), which learns hierarchical memory modules -- node and graph memory modules -- via a graph autoencoder network architecture. The node-level memory module is trained to model fine-grained, internal graph interactions among nodes for detecting locally abnormal graphs, while the graph-level memory module is dedicated to the learning of holistic normal patterns for detecting globally abnormal graphs. The two modules are jointly optimized to detect both locally- and globally-anomalous graphs. Extensive empirical results on 16 real-world graph datasets from various domains show that i) HimNet significantly outperforms the state-of-art methods and ii) it is robust to anomaly contamination. Codes are available at: https://github.com/Niuchx/HimNet.

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