that, by using complex-valued matrices, the k clusters in a digraph can be well separated by angles in R

We thank all reviewers for their detailed and insightful reports. The result in Peng et al. [22] only holds for undirected graphs and Generalising their result into the setting of digraphs is a mathematically involved task. We thank R1 for recognising the conceptual contribution of introducing the flow ratio. DICUT problem, which is NP -hard (cf. We will add this in the final version.