Anomaly detection in directed dynamic graphs using Hermitian Laplacian spectral analysis

Dynamic graphs have become an important tool for characterizing interactions among entities and are widely used in fields such as finance, public health, and social network analysis. In many real-world settings, including capital flows, information diffusion, and epidemic spreading, the underlying networks are inherently directed. However, most existing anomaly detection methods for dynamic graphs do not explicitly incorporate edge directionality. Conventional adjacency and Laplacian matrices are not well suited to encoding directional information, which limits their ability to represent directed structures and may reduce detection accuracy. To address this limitation, we propose an anomaly detection method for directed dynamic graphs based on Hermitian Laplacian spectral analysis. The proposed framework constructs a spectral representation that preserves directional information and incorporates a temporal window mechanism to characterize structural variations over time, thereby enabling the identification of anomalous time points. We evaluate the method on synthetic data and on two real-world datasets, namely the UCI Message network and the global vaccine trade network. The results show that the proposed approach outperforms several baseline methods in detecting anomalous time points and more effectively captures anomalies associated with structural changes and directional heterogeneity. These findings indicate that the proposed framework provides both methodological and empirical advances for anomaly detection in directed dynamic graphs, while also offering useful insights into structural perturbations in complex systems.