Accurate recognition of human emotional states is critical for effective human-machine interaction. Electroencephalography (EEG) offers a reliable source for emotion recognition due to its high temporal resolution and its direct reflection of neural activity. Nevertheless, variations across recording sessions present a major challenge for model generalization. To address this issue, we propose EGDA, a framework that reduces cross-session discrepancies by jointly aligning the global (marginal) and class-specific (conditional) distributions, while preserving the intrinsic structure of EEG data through graph regularization. Experimental results on the SEED-IV dataset demonstrate that EGDA achieves robust cross-session performance, obtaining accuracies of 81.22%, 80.15%, and 83.27% across three transfer tasks, and surpassing several baseline methods. Furthermore, the analysis highlights the Gamma frequency band as the most discriminative and identifies the central-parietal and prefrontal brain regions as critical for reliable emotion recognition.