Accurate recognition of human emotions from EEG signals plays a critical role in affective computing and human-computer interaction. However, existing methods face significant challenges in effectively capturing the sparse, dynamic, and energy-dependent characteristics of brain activity during emotional experiences. To address these challenges, we propose a novel framework, Spatial-Energy-Aware Dynamic Filtering with Sparse Graph Convolutions (SEASGC), which rethinks EEG graph modeling from three perspectives: (1) sparse graph construction to adaptively capture the essential functional relationships between brain regions, (2) dynamic and location-dependent filtering to model nonlinear interactions between EEG nodes, and (3) energy-aware feature aggregation to leverage energy changes as critical indicators of emotional intensity. By explicitly integrating these principles, SEASGC provides a more comprehensive representation of EEG signals for emotion recognition. Extensive experiments on benchmark EEG emotion datasets demonstrate that SEASGC achieves state-of-the-art performance, highlighting its effectiveness and generalizability in modeling the complex spatial-spectral dynamics of EEG signals.