Combining the message-passing paradigm with the global attention mechanism has emerged as an effective framework for learning over graphs. The message-passing paradigm and the global attention mechanism fundamentally generate node embeddings based on information aggregated from a node's local neighborhood or from the whole graph. The most basic and commonly used aggregation approach is to take the sum of information from a node's local neighbourhood or from the whole graph. However, it is unknown if the dominant information is from a node itself or from the node's neighbours (or the rest of the graph nodes). Therefore, there exists information lost at each layer of embedding generation, and this information lost could be accumulated and become more serious when more layers are used in the model. In this paper, we present a differential encoding method to address the issue of information lost. The idea of our method is to encode the differential representation between the information from a node's neighbours (or the rest of the graph nodes) and that from the node itself. The obtained differential encoding is then combined with the original aggregated local or global representation to generate the updated node embedding. By integrating differential encodings, the representational ability of generated node embeddings is improved. The differential encoding method is empirically evaluated on different graph tasks on seven benchmark datasets. The results show that it is a general method that improves the message-passing update and the global attention update, advancing the state-of-the-art performance for graph representation learning on these datasets.