In this paper we propose a new method for choosing the number of clusters and the most appropriate eigenvectors, that allow to obtain the optimal clustering. To accomplish the task we suggest to examine carefully properties of adjacency matrix eigenvectors: their weak localization as well as the sign of their values. The algorithm has only one parameter — the number of mutual neighbors. We compare our method to several clustering solutions using different types of datasets. The experiments demonstrate that our method outperforms in most cases many other clustering algorithms.