Review for NeurIPS paper: Higher-Order Spectral Clustering of Directed Graphs

Summary and Contributions: The paper considers a graph clustering on directed graphs. The authors introduce a new notion of clustering objective denoted by flow ratio. For any ordered partition of vertex set V into k pairwise disjoint subset (S0, ..., Sk-1), the flow ratio of the partition is sum of the average flow (i.e. The optimal clustering is the partitioning of V that maximizes the flow ratio among all possible partitions. The authors represent the directed graph using the Hermitian adjacency matrix.