Higher-education institutions store large academic records, but these data often remain administrative and provide limited support for model-based evaluation of graduation outcomes. In neural-network classification, method selection is important because Backpropagation and Radial Basis Function (RBF) networks learn through different mechanisms: Backpropagation iteratively adjusts weights by propagating error, whereas RBF represents data through distance-based responses around selected centres. Consequently, their accuracy, error balance, and computational time cannot be assumed to be equivalent for educational datasets and need to be compared under the same testing conditions. The comparison was intended to support method selection for the available alumni dataset rather than to propose an institution-wide deployment model. This study compared Backpropagation and RBF neural networks for retrospective classification of undergraduate alumni into Cum Laude and Non-Cum Laude groups and examined the predictive importance of the input variables. The dataset consisted of 824 alumni records from the Department of Mathematics, Universitas Negeri Makassar, with eight predictors: study programme, sex, admission route, study duration, tuition fee, graduated credits, age at entry, and final grade point average (GPA). After data cleaning, encoding, and Min-Max normalisation, the data were evaluated using a stratified 80:20 split, resulting in 659 training records and 165 test records. Twelve Backpropagation scenarios and twelve RBF scenarios were tested. Under the retained split and parameter grid, the best Backpropagation model used an 8-8-1 architecture and a learning rate of 0.01, achieving 98.79% accuracy and a 98.41% F1-score. The best RBF model used 40 centres and a spread of 0.8, achieving 87.88% accuracy and an 85.71% F1-score. RBF trained faster in the recorded Google Colab run, but Backpropagation produced fewer classification errors. Permutation importance showed that study duration (55.84%) and final GPA (35.17%) dominated the selected model. Because both variables are observed near graduation and are closely related to the administrative criteria for Cum Laude, the selected model should be interpreted as retrospective classification rather than early prediction.