Segmentation is an important operation in image analysis. It is employed to extract interested objects from an image under test. Much research work has been performed and the optimal graph theoretic approach to data clustering is one of the promising methods. However, when the image size is large, the graph size is very large. As a result the graph becomes complex and its processing is computation demanding. In this paper, we propose to simplify the problem by pre-segmenting the image under test using an edge model before applying the optimal graph theoretic approach to data clustering. The experimental results show that the proposed method can efficiently segments an image with satisfactory results.