We have presented a GCNN model to predict the formation energy and the bulk modulus for the Ni-Nb solid solution binary alloy as a function of the atomic crystal lattice structure. The numerical results describe the predictive performance of the GCNN model on an open-source dataset for model systems of a binary Ni-Nb solid solution alloy , which spans a large variety of irregular crystal structures, each obtained as the result of a topology optimization starting from regular BCC, FCC, and HCP supercells. For each of the optimized crystal geometries, the formation energy and the bulk modulus as a prototypical elastic property are provided. Our PyTorch-based architecture that implements GCNN models, called HydraGNN, allows to flexibly switch between different graph convolutional layers implemented in PyTorch-Geometric that perform different message passing policies to aggregate information across adjacent nodes in the graph, and perform a cross-comparison. The PNAConv graph convolutional layer clearly outperforms the CGConv graph convolutional layer in all cases in terms of accuracy. The HydraGNN model using the PNAConv convolutional layer shows robustness in accurately predicting the formation energy over the diverse set of optimized lattice structures, which shows the potential of GCNN models of playing a pivotal role as effective surrogate models in alloy design, since accurately estimating the formation energy is needed to identify the ensemble of stable crystal structures at a given chemical composition. We found that a radius cut-off larger than 5 Å significantly improves the predictive performance of the surrogate model for the prediction of the formation energy. The HydraGNN performance for predicting the bulk modulus seems less dependent on the cutoff radius, as large structural variations and number of local minima in intermediate concentration ranges between 0.2 and 0.8 of element composition dramatically increase.