In biomedical and neurodegenerative disorders, accurate and early disease identification remains challenging due to the scarcity of labeled data and the complexity of imaging patterns. To address these challenges, we introduce ARMA-C3, a unified unsupervised and semi-supervised graph learning framework for node classification based on contrastive learning and graph-cut regularization to learn structurally meaningful and discriminative representations. By modeling samples or images as graph nodes and exploiting inter-sample relationships, the proposed framework captures subject-level dependencies that conventional machine learning methods typically overlook. We conduct extensive binary classification experiments across five clinically relevant datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI), the Neuroimaging in Frontotemporal Dementia (NIFD) dataset, and three medical imaging benchmarks (BreastMNIST, PneumoniaMNIST, and a liver ultrasound dataset). Experimental results demonstrate that ARMA-C3 achieves competitive and frequently superior performance compared to classical clustering techniques, state-of-the-art machine learning models, and existing graph-based deep learning approaches across multiple evaluation settings, particularly under limited supervision and severe class imbalance. The proposed framework further demonstrates robust representation learning and strong cross-modal generalization across diverse biomedical imaging modalities.