This work demonstrates the accuracy and transferability of graph neural network models to accurately predict the DFT-relaxed properties (i.e., formation energies) of a crystal structure that has been mapped onto an idealized lattice/interstitial representation. It shares the advantages of the CE method in that (1) only a small number of DFT training examples are needed (∼100s) to obtain meV/atom MAEs in up to quinary composition spaces and (2) model inputs are derived from a trivialto-generate representation of the relaxed crystal structure. Therefore, one can then rapidly and accurately compute energetics of hundreds of thousands of random alloy configurations that may be needed to converge thermodynamic property predictions. At the same time, we showed how the CGCNN approach employing an identical, low-complexity architecture and identical hyperparameters can accurately predict configurational energetics in diverse materials for diverse applications. This removes the need for manual tuning of the CE method when transitioning between problems of varying complexity.