With recent advancements in non-invasive techniques for measuring brain activity, such as magnetic resonance imaging (MRI), the study of structural and functional brain networks through graph signal processing (GSP) has gained notable prominence. GSP stands as a key tool in unraveling the interplay between the brain's function and structure, enabling the analysis of graphs defined by the connections between regions of interest -- referred to as connectomes in this context. Our work represents a further step in this direction by exploring supervised contrastive learning methods within the realm of graph representation learning. The main objective of this approach is to generate subject-level (i.e., graph-level) vector representations that bring together subjects sharing the same label while separating those with different labels. These connectome embeddings are derived from a graph neural network Encoder-Decoder architecture, which jointly considers structural and functional connectivity. By leveraging data augmentation techniques, the proposed framework achieves state-of-the-art performance in a gender classification task using Human Connectome Project data. More broadly, our connectome-centric methodological advances support the promising prospect of using GSP to discover more about brain function, with potential impact to understanding heterogeneity in the neurodegeneration for precision medicine and diagnosis.