There are a growing number of different research fields that concerned with analyzing network structures for community detection. To achieve the analysis, the partitioning of vertices into different clusters is a popular task in data mining. Though there had been a wide range of algorithms and methods that can deal with the discovery of the closest group for a vertex. In this paper, we aim to provide an adaption of the COP-kmean algorithm in the context of graph clustering. Traditionally, the algorithm integrates two constraints during the clustering process. These constraints guide a vertex to its nearest cluster centroid on each iteration. To generate the constraints, we specify them using the k-neighbors of each vertex. Then our implementation is provided to show the analysis on a real dataset.