The inherent symmetry in traffic flow patterns plays a fundamental role in urban transportation systems. This study proposes a Dynamic Graph Convolutional Recurrent Adaptive Network (DGCRAN) for traffic flow prediction, leveraging symmetry principles in spatial–temporal dependencies. Unlike conventional models relying on static graph structures that often break real-world symmetry relationships, our approach introduces two key innovations respecting the dynamic symmetry of traffic networks: First, a Dynamic Graph Convolutional Recurrent Network (DGCRN) is proposed that preserves and adapts to the time-varying symmetry in node associations, and an Adaptive Graph Convolutional Network (AGCN) that captures the symmetric and asymmetric patterns between nodes. The experimental results on PEMS03, PEMS04, and PEMS08 datasets demonstrate that DGCRAN maintains superior performance symmetry across metrics: reducing MAE, RMSE, and MAPE by average margins of 12.7%, 10.3%, and 14.2%, respectively, compared to 15 benchmarks. Notably, the model achieves maximum MAE reduction of 21.33% on PEMS08, verifying its ability to model the symmetric and asymmetric characteristics in traffic flow dependencies while significantly improving prediction accuracy and generalization capability.