Turbidity currents are complex multiphase flows whose dynamics depend on the interaction of several physical parameters, making high-fidelity numerical simulations computationally expensive. In this work, we propose a graph-based deep learning framework to efficiently model and predict the behavior of density currents under different settling velocities. The flow fields obtained from high-resolution numerical simulations are represented as graphs, in which nodes encode local flow information and edges capture spatial connectivity. A variational autoencoder based on Graph Convolutional Networks (GCN-VAE) is employed to learn compact latent representations of the flow while preserving essential physical features. These latent representations are used as inputs to a regression model that predicts the settling velocity. Different hyperparameters are applied to the autoencoder in order to analyze their impact on predictive performance. The model is trained and tested using datasets generated for multiple settling velocities (us), allowing the assessment of generalization capabilities across distinct flow regimes. The results demonstrate that the proposed approach is able to accurately reconstruct and predict key flow characteristics. The predictions obtained with the graph-based autoencoder model present a mean absolute percentage error (MAPE) of 0.426785, whereas the MLP-based model achieved a MAPE of 10.960471 and the CNN-based model achieved a MAPE of 7.483364. Overall, the proposed graph-based variational framework provides an efficient and flexible alternative model for density current simulations, reducing computational costs while maintaining satisfactory accuracy, and represents a promising tool for data-driven analysis of complex geophysical and environmental flows.