  Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for
analyzing and processing graph data, typically apply frequency filtering via
Fourier transform to obtain representations with selective information.
Although research shows that spectral GCNNs can be enhanced by framelet-based
filtering, the massive majority of such research only considers undirected
graphs. In this paper, we introduce Framelet-MagNet, a magnetic framelet-based
spectral GCNN for directed graphs (digraphs). The model applies the framelet
transform to digraph signals to form a more sophisticated representation for
filtering. Digraph framelets are constructed with the complex-valued magnetic
Laplacian, simultaneously leading to signal processing in both real and complex
domains. We empirically validate the predictive power of Framelet-MagNet over a
range of state-of-the-art models in node classification, link prediction, and
denoising.
