EEG is a non-invasive tool to study complex activity of neurons, but traditional signal processing techniques typically process individual EEG channels separately and fail to adequately model spatial and functional relationships between brain regions. In this paper, we introduce a Graph Signal Processing Graph Attention Network (GSP – GAT) framework for the EEG-based neural pattern discovery and classification. Multichannel EEG signals are preprocessed, segmented and displayed as functional connectivity graphs, where electrodes are nodes and the relationship between channels are weighted edges. Global, local, and multiscale spatial–spectral characteristics are extracted using the graph Fourier Transform, graph spectral energy analysis, graph filtering and graph wavelet analysis. Through comparative and ablation analyses, we show the potential advantages of explicit graph signal representations and attention-based graph learning over regular machine learning, deep learning and standalone graph-based methods. Comparative and ablation analyses illustrate the potential benefits of combining explicit graph signal representations with attention-based graph learning, compared to regular machine learning, deep learning and standalone graph-based methods. The proposed framework is an effective and comprehensible approach to neural pattern discovery and has the potential to be applied in brain–computer interfaces, cognitive-state recognition, neurological assessment, seizure analysis, and other intelligent systems that rely on EEG.