This paper presents a novel graph-based deep learning model for tasks involving relations between two nodes (edge-centric tasks), where the focus lies on predicting relationships and interactions between pairs of nodes rather than node properties themselves. This model combines supervised and self-supervised learning, taking into account for the loss function the embeddings learned and patterns with and without ground truth. Additionally it incorporates an attention mechanism that leverages both node and edge features. The architecture, trained end-to-end, comprises two primary components: embedding generation and prediction. First, a graph neural network (GNN) transform raw node features into dense, low-dimensional embeddings, incorporating edge attributes. Then, a feedforward neural model processes the node embeddings to produce the final output. Experiments demonstrate that our model matches or exceeds existing methods for protein-protein interactions prediction and Gene Ontology (GO) terms prediction. The model also performs effectively with one-hot encoding for node features, providing a solution for the previously unsolved problem of predicting similarity between compounds with unknown structures.