For alloy design involving atomistic models, the search for metastable and disordered crystal structures during structural sampling is unavoidable. The enormous complexity of alloy structural variability requires the use of computationally inexpensive surrogate models trained on physics-based simulation methods. In this study, we tested the performance of graph-based neural network surrogate models in predicting the energies and bulk moduli for model systems of solid solution alloy systems. Our study shows the capabilities and limitations of state-of-the-art GCNN surrogate models, by training them on data generated with EAM potentials to inform future, more computationally expensive DFT-based surrogate model development. As expected from previous reports , the surrogate-predicted energy shows good agreement with ground truth data for all composition ranges. However, the predictions from the surrogate model for the bulk modulus of the solid solution alloy model systems were less satisfactory and failed to provide a measure of ranking between them when averaged over the entire composition range. The performance is considerably improved when limiting the composition space to binary mixtures systems having one dominant component (Ni concentration lower than 0.2 and higher than 0.8) with an associated MAE of 1.9219 GPa. We attribute the difficulty of prediction bulk modulus for binary alloys with comparable Ni:Nb ratio (Ni concentration between 0.2 and 0.8) to high variations of the bulk modulus in this region, possibly due to the fact that the EAM-optimized crystal structures are often metastable and correspond only to local minima.