Background: The enhancer–promoter interaction (EPI) is a critical component of gene regulatory networks, playing a significant role in understanding the complexity of gene expression. Traditional EPI prediction methods focus on one-to-one interactions, neglecting more complex one-to-many and many-to-many patterns. To address this gap, we utilize graph neural networks to comprehensively explore all interaction patterns between enhancers and promoters, capturing complex regulatory relationships for more accurate predictions. Methods: In this study, we introduce a novel EPI prediction framework, GATv2EPI, based on dynamic graph attention neural networks. GATv2EPI leverages epigenetic information from enhancers, promoters, and their surrounding regions and organizes interactions into a network to comprehensively explore complex EPI regulatory patterns, including one-to-one, one-to-many, and many-to-many relationships. To avoid overfitting and ensure diverse data representation, we implemented a connectivity-based sampling method for dataset partitioning, which constructs graphs for each chromosome and assigns entire connected subgraphs to training or test sets, thereby preventing information leakage and ensuring comprehensive chromosomal representation. Results: In experiments conducted on four cell lines—NHEK, IMR90, HMEC, and K562—GATv2EPI demonstrated superior EPI recognition accuracy compared to existing similar methods, with a training time improvement of 95.29% over TransEPI. Conclusions: GATv2EPI enhances EPI prediction accuracy by capturing complex topological structure information from gene regulatory networks through graph neural networks. Additionally, our results emphasize the importance of epigenetic features surrounding enhancers and promoters in EPI prediction.