DIGRAC: Digraph Clustering with Flow Imbalance.

Node clustering is a powerful tool in the analysis of networks. Here, we introduce a graph neural network framework with a novel scalable Directed Mixed Path Aggregation(DIMPA) scheme to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss. The method is end-to-end in combining embedding generation and clustering without an intermediate step. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. In particular, we leverage the recently introduced cut flow imbalance measure, which is tightly related to directionality; cut flow imbalance is optimized without resorting to spectral methods or cluster labels. Experimental results on synthetic data, in the form of directed stochastic block models and real-world data at different scales, demonstrate that our method attains state-of-the-art results on directed clustering, for a wide range of noise and sparsity levels, as well as graph structures.