The human cerebral cortex features intricate, convoluted sulci forming a complex and variable geometry. Characterizing these variations in the sulcal patterns is critical for assessing cerebral structure abnormalities. However, the uniqueness of sulcal patterns in individuals poses challenges in dissociating abnormal from normal variations. In this study, we use deep graph representation learning models to analyze sulcal graphs from a population of 1090 healthy adults. We leverage sulcal graphs for encoding the surface geometry, combined with graph neural networks(GNNs) for predicting the gender of the subjects, and analyze the underlying variability. These methods show potential in offering valuable insights into biomarker discovery for neurological and psychiatric disorders, relying on structured representations of cortical geometry.