Impact statement: GCNs could be applied to a wide range of applications, including image segmentation [27], speech recognition [14], recommender system [17], point cloud [50, 24], traffic prediction [25] and many more [45]. Our method can help to expand the graph types from undirected to directed in the above application scenarios and obtain multi-scale features from the high-order hidden directed structure. For traffic prediction, our method can be used in map applications to obtain more fine-grained and accurate predictions. This requires users to provide location information, which has a risk of privacy leakage. The same concerns also arise in social network analysis [38], person re-ID [35] and NLP [49], which use graph convolutional networks as their feature extraction methods. Another potential risk is that our model may be adversarial attacked by adding new nodes or deleting existing edges. For example, in a graph-based recommender system, our model may produce completely different recommendation results due to being attacked. We see opportunities for research applying DiGCN to beneficial purposes, such as investigating the ability of DiGCN to discover hidden complex directed structure, the limitation of approximate method based on personalized PageRank and the feature oversmoothing problem in digraphs. We also encourage follow-up research to design derivative methods for different tasks based on our method.