Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures and topologies, and even outperforms supervised methods.

翻译：节点群集是分析网络的有力工具。 我们引入了一个图形神经网络框架, 以自我监督的方式为定向网络获取节点嵌入, 包括新颖的概率不平衡损失, 可用于网络群集。 在这里, 我们提出了直接流偏移措施, 与方向性密切相关, 以显示网络中的群集, 即使群集之间没有密度差异。 与文献中的标准方法相反, 定向性不被视为一种干扰, 而是包含主要信号。 DIGRAC 优化了不要求标签监督、不同于现有图形神经网络方法的集群定向流动不平衡, 并且可以自然地包含节点特征, 与现有的光谱方法不同。 关于合成数据的广泛实验结果, 以定向偏差区块模型的形式, 以及不同尺度上的真实世界数据, 表明我们的方法, 以流动不平衡为基础, 相对于文献中10种最先进的组合方法, 在定向图形群集中取得了最新的结果 。 DIGRAC 优化了定向流流偏向流动, 而不要求标签监督, 与现有的图形神经网络方法不同, 并可以自然纳入节点特征特征特征特征特征特征特征特征特征特征特征特征特征特征特征特征,, 。