So far, in the field of data mining, people have achieved a variety of algorithms of clustering. And the most widely used is K-means clustering algorithm. But the main problem of K-means is the initial center selection problem. In this paper, a method is proposed to determine the initial K centers of the K-means algorithm through the relationship matrix and the Degree Centrality. Compared with the traditional algorithm, the proposed algorithm can get the better clustering result. Experimental results have proved the validity and feasibility of this algorithm.