Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD configuration for corresponding flow characteristics. Convolutional Neural Network (CNN) is one of the most popular algorithms used to extract and identify flow features. However its use, without any additional flow field interpolation, is limited to the simple domain geometry and regular meshes which limits its application to real industrial cases where complex geometry and irregular meshes are usually used. Aiming at the aforementioned problems, we present a Graph Neural Network (GNN) based model with U-Net architecture to identify the vortex in CFD results on unstructured meshes. The graph generation and graph hierarchy construction using algebraic multigrid method from CFD meshes are introduced. A vortex auto-labeling method is proposed to label vortex regions in 2D CFD meshes. We precise our approach by firstly optimizing the input set on CNNs, then benchmarking current GNN kernels against CNN model and evaluating the performances of GNN kernels in terms of classification accuracy, training efficiency and identified vortex morphology. Finally, we demonstrate the adaptability of our approach to unstructured meshes and generality to unseen cases with different turbulence models at different Reynolds numbers.