An attributed graph is denoted by G=(V,E,F) where V is the set of vertices, E is the set of edges, and F={a 1 , a 2 , …, a m } is the set of m attribute associated with vertices in for describing vertex properties. Each vertex v i ? V and attributes a j , is associated with a value val(v i ,v j ). Data clustering is an unsupervised division method to extract a significant relationship between the given data. In the graph clustering problem the aim is to allocated within each vertex to a clusters such that within each cluster the connection is dense or similar and vertices features are similar and homogeneous. Also, the connection between clusters are spares.