Anomaly Edge Detection in Dynamic Graphs Based on Hyperbolic Graph Neural Networks

Dynamic graph anomaly edge detection aims to identify abnormal connection patterns emerging over time in graph structures. Existing methods primarily construct detection models based on Euclidean space, which suffers from embedding distortion due to the power-law distributions and hierarchical structural characteristics inherent in real-world networks. The representational capacity of Euclidean geometry is inherently limited by dimensionality, leading to suboptimal detection performance. This paper proposes a dynamic graph anomaly edge detection method based on hyperbolic graph neural networks, introducing hyperbolic geometry to capture graph hierarchies through its exponential expansion property. An improved hyperbolic graph neural network is proposed to significantly reduce the overhead of hyperbolic space mapping by folding inter-layer weight matrices. Additionally, a hyperbolic gated temporal convolution module is designed, which leverages dilated convolution to learn causal dependencies in historical evolutionary processes. Experiments conducted on four real-world datasets demonstrate that the proposed method outperforms existing baseline methods in both Euclidean and hyperbolic spaces.