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.

我们提出了 Rayleigh Quotient Graph Neural Network (RQGNN)，这是第一个用于图级异常检测的谱 GNN，通过探索异常图的固有谱特征，显著提高了性能。