Edges in real-world graphs are typically formed by a variety of factors and carry diverse relation semantics. For example, connections in a social network could indicate friendship, being colleagues, or living in the same neighborhood. However, these latent factors are usually concealed behind mere edge existence due to the data collection and graph formation processes. Despite rapid developments in graph learning over these years, most models take a holistic approach and treat all edges as equal. One major difficulty in disentangling edges is the lack of explicit supervisions. In this work, with close examination of edge patterns, we propose three heuristics and design three corresponding pretext tasks to guide the automatic edge disentanglement. Concretely, these self-supervision tasks are enforced on a designed edge disentanglement module to be trained jointly with the downstream node classification task to encourage automatic edge disentanglement. Channels of the disentanglement module are expected to capture distinguishable relations and neighborhood interactions, and outputs from them are aggregated as node representations. The proposed DisGNN is easy to be incorporated with various neural architectures, and we conduct experiments on $6$ real-world datasets. Empirical results show that it can achieve significant performance gains.