Graph clustering is an important task of discovering the underlying structure in a network. Well-known methods such as the normalized cut and modularity-based methods are developed in the past decades. These methods may be called non-overlapping because they assume that a vertex belongs to one community. On the other hand, overlapping methods such as CPM, which assume that a vertex may belong to more than one community, have been drawing attention as the assumption fits the reality. We believe that existing overlapping methods are overly simple for a vertex located at the border of a community. That is, they lack careful consideration on the edges that link the vertex to its neighbors belonging to different communities. Thus, we propose a new graph clustering method, named RoClust, which uses three different kinds of roles, each of which represents a different kind of vertices that connect communities. Experimental results show that our method outperforms state-of-the-art methods of graph clustering.