The vapor pressures (<em>p</em><sub>vap</sub>) of organic molecules play a crucial role in the partitioning of secondary organic aerosol (SOA). Given the vast diversity of atmospheric organic compounds, experimentally determining <em>p</em><sub>vap</sub> of each compound is unfeasible. Machine Learning (ML) algorithms allow the prediction of physicochemical properties based on complex representations of molecular structure, but their performance crucially depends on the availability of sufficient training data. We propose a novel approach to predict <em>p</em><sub>vap</sub> using group contribution-assisted graph convolutional neural networks (GC<sup>2</sup>NN). The models use molecular descriptors like molar mass alongside molecular graphs containing atom and bond features as representations of molecular structure. Molecular graphs allow the ML model to better infer molecular connectivity compared to methods using other, non-structural embeddings. We achieve best results with an adaptive-depth GC<sup>2</sup>NN, where the number of evaluated graph layers depends on molecular size. We present two vapor pressure estimation models that achieve strong agreement between predicted and experimentally-determined <em>p</em><sub>vap</sub>. The first is a general model with broad scope that is suitable for both organic and inorganic molecules and achieves a mean absolute error (MAE) of 0.67 log-units (R<sup>2</sup>=0.86). The second model is specialized on organic compounds with functional groups often encountered in atmospheric SOA, achieving an even stronger correlation with the test data (MAE=0.36 log-units, R<sup>2</sup>=0.97). The adaptive-depth GC<sup>2</sup>NN models clearly outperform existing methods, including parameterizations and group-contribution methods, demonstrating that graph-based ML techniques are powerful tools for the estimation of physicochemical properties, even when experimental data are scarce.