This paper introduces the use of per-class regularization hyperparameters in Gabriel graph-based binary classifiers. We demonstrate how the quality index used for regularization behaves both in the margin region and in the presence of outliers, and how incorporating this regularization flexibility can lead to solutions that effectively eliminate outliers while training the classifier. We also show how it can address class imbalance by generating higher and lower thresholds for the majority and minority classes, respectively. Thus, rather than having a single solution based on fixed thresholds, flexible thresholds expand the solution space and can be optimized through hyperparameter tuning algorithms. Friedman test shows that flexible thresholds are capable of improving Gabriel graph-based classifiers.