This research presents detection algorithms that combine graph neural networks (GNNs), variational autoencoders (VAEs), permutation-invariant graph alignment, and spectral band-pass filtering to identify unusual patterns in graph-structured data. Detecting such irregularities is crucial in domains like finance, cybersecurity, healthcare, and fraud detection. The approach leverages GNNs to capture complex relationships between nodes, while VAEs provide a generative framework for analyzing the latent space. Spectral band-pass filtering further enhances the detection of deviations in graph spectral properties. These techniques enable the identification of anomalies at multiple levels nodes, edges, subgraphs, and entire graphs, in both static and dynamic datasets. Applied to real-world data, the methods effectively uncovered unexpected activities that diverge from normal patterns. Theoretical foundations were also explored to validate the techniques and clarify their capabilities. This work advances graph-based deep learning by integrating spectral analysis with generative modeling, offering promising results for detecting structural deviations in large and complex graph datasets.