Graph-level anomaly detection has gained significant attention as it finds many applications in various domains, such as cancer diagnosis and enzyme prediction. However, existing methods fail to capture the underlying properties of graph anomalies, resulting in unexplainable framework design and unsatisfying performance. In this paper, we take a step back and re-investigate the spectral differences between anomalous and normal graphs. Our main observation shows a significant disparity in the accumulated spectral energy between these two classes. Moreover, we prove that the accumulated spectral energy of the graph signal can be represented by its Rayleigh Quotient, indicating that the Rayleigh Quotient is a driving factor behind the anomalous properties of graphs. Motivated by this, we propose Rayleigh Quotient Graph Neural Network (RQGNN), the first spectral GNN for graph-level anomaly detection, providing a new perspective on exploring the inherent spectral features of anomalous graphs. Specifically, we introduce a novel framework that consists of two components: the Rayleigh Quotient learning component (RQL) and Chebyshev Wavelet GNN with RQ-pooling (CWGNN-RQ). RQL explicitly captures the Rayleigh Quotient of graphs and CWGNN-RQ implicitly explores the spectral space of graphs. Extensive experiments on 10 real-world datasets show that RQGNN outperforms the best rival by 6.74% in Macro-F1 score and 1.44% in AUC, demonstrating the effectiveness of our framework.

翻译：图级异常检测因其在癌症诊断和酶预测等多个领域的应用而备受关注。然而，现有方法未能捕捉图异常的内在特性，导致框架设计缺乏可解释性且性能欠佳。本文重新审视异常图与正常图之间的谱差异。我们的主要观察显示，这两类图在累积谱能量上存在显著差异。此外，我们证明图信号的累积谱能量可通过其雷利商表示，表明雷利商是图异常特性的驱动因素。受此启发，我们提出雷利商图神经网络（RQGNN），这是首个用于图级异常检测的谱图神经网络，为探索异常图的内在谱特征提供了新视角。具体而言，我们引入了一个由两部分组成的新颖框架：雷利商学习组件（RQL）和带RQ池化的切比雪夫小波图神经网络（CWGNN-RQ）。RQL显式捕获图的雷利商，而CWGNN-RQ隐式探索图的谱空间。在10个真实数据集上的大量实验表明，RQGNN在Macro-F1分数上比最佳对手高出6.74%，在AUC上高出1.44%，证明了我们框架的有效性。