Here, we propose the Graph Regularizable Assessment Metric (GRAM), a customizable tool for evaluating the quality of generated brain graphs. Current geometric deep learning methods often lack robust quantification techniques for assessing the synthetic brain graphs integrity. GRAM addresses this gap by proportionally combining a set of existing graph metrics to establish a linear correlation between distortions’ levels and metric values of ground-truth graphs. To evaluate the performance of our model, we generated a synthetic dataset of structural brain connectomes which was derived from an existing dataset and used to simulate a set of predicted connectomes from a generative model with controlled levels of distortions. Our results show that GRAM outperforms single metrics in quantifying the distortion between generated and original graphs. This approach is a significant step towards establishing a universal graph quality index for graph-based predictive studies.