Graph-based learning provides a useful approach for modeling data in classification problems. In this modeling scenario, the relationship between labeled and unlabeled data impacts the construction and performance of classifiers, and therefore a semi-supervised learning framework is adopted. We propose a graph classifier based on kernel smoothing. A regularization framework is also introduced, and it is shown that the proposed classifier optimizes certain loss functions. Its performance is assessed on several synthetic and real benchmark data sets with good results, especially in settings where only a small fraction of the data are labeled.