Clustering methods usually require to know the best number of clusters, or another parameter, e.g. a threshold, which is not ever easy to provide. This paper proposes a new graph-based clustering method called GBC which detects automatically the best number of clusters, without requiring any other parameter. In this method based on regions of influence, a graph is constructed and the edges of the graph having the higher values are cut according to a hierarchical divisive procedure. An index is calculated from the size average of the cut edges which self-detects the more appropriate number of clusters. The results of GBC for 3 quality indices (Dunn, Silhouette and Davies-Bouldin) are compared with those of K-Means, Ward's hierarchical clustering method and DBSCAN on 8 benchmarks. The experiments show the good performance of GBC in the case of well separated clusters, even if the data are unbalanced, non-convex or with presence of outliers, whatever the shape of the clusters.