Attributed graph clustering (AGC) is an important problem in graph mining as more and more complex data in real-world have been represented in graphs with attributed nodes. While it is a common practice to leverage both attribute and structure information for improved clustering performance, most existing AGC algorithms consider only a specific type of relations, which hinders their applicability to integrate various complex relations into node attributes for AGC. In this paper, we propose GRACE, an extended graph convolution framework for AGC tasks. Our framework provides a general and interpretative solution for clustering many different types of attributed graphs, including undirected, directed, heterogeneous and hyper attributed graphs. By building suitable graph Laplacians for each of the aforementioned graph types, GRACE can seamlessly perform graph convolution on node attributes to fuse all available information for clustering. We conduct extensive experiments on 14 real-world datasets of 4 different graph types. The experimental results show that GRACE outperforms the state-of-the-art AGC methods on the different graph types in terms of clustering quality, time, and memory usage.

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