Title: Weakly Supervised Graph Clustering. Abstract: Graph Clustering, which clusters the nodes of a graph given its collection of node features and edge connections in an unsupervised manner, has long been researched in graph learning and is essential in certain applications. While this task is common, more complex cases arise in practice—can we cluster nodes better with some graph-level side information or in a weakly supervised manner as, for example, identifying potential fraud users in a social network given additional labels of fraud communities. This triggers an interesting problem which we define as Weakly Supervised Graph Clustering (WSGC). In this paper, we firstly discuss the various possible settings of WSGC, formally. Upon such discussion, we investigate a particular task of weakly supervised graph clustering by making use of the graph labels and node features, with the assistance of a hierarchical graph that further characterizes the connections between different graphs. To address this task, we propose Gaussian Mixture Graph Convolutional Network (GMGCN), a simple yet effective framework for learning node representations under the supervision of graph labels guided by a proposed consensus loss and then inferring the category of each node via a Gaussian Mixture Layer (GML). Extensive experiments are conducted to test the rationality of the formulation of weakly supervised graph clustering. The experimental results show that, with the assistance of graph labels, the weakly supervised graph clustering method has a great improvement over the traditional graph clustering method.