The traffic assignment problem is one of the significant components of traffic flow analysis for which various solution approaches have been proposed. However, deploying these approaches for large-scale networks poses significant challenges. In this paper, we leverage the power of heterogeneous graph neural networks to propose a novel end-to-end surrogate model for traffic assignment, specifically user equilibrium traffic assignment problems. Our model integrates an adaptive graph attention mechanism with auxiliary "virtual" links connecting origin-destination node pairs, This integration enables the model to capture spatial traffic patterns across different links, By incorporating the node-based flow conservation law into the overall loss function, the model ensures the prediction results in compliance with flow conservation principles, resulting in highly accurate predictions for both link flow and flow-capacity ratios. We present numerical experiments on urban transportation networks and show that the proposed heterogeneous graph neural network model outperforms other conventional neural network models in terms of convergence rate and prediction accuracy. Notably, by introducing two different training strategies, the proposed heterogeneous graph neural network model can also be generalized to different network topologies. This approach offers a promising solution for complex traffic flow analysis and prediction, enhancing our understanding and management of a wide range of transportation systems.