We describe an annealing procedure that computes the normalized N-cut of a weighted graph G. The first phase transition computes the solution of the approximate normalized 2-cut problem, while the low temperature solution computes the normalized N-cut. The intermediate solutions provide a sequence of refinements of the 2-cut that can be used to split the data to K clusters with 2 ≤ K ≤ N. This approach only requires specification of the upper limit on the number of expected clusters N, since by controlling the annealing parameter we can obtain any number of clusters K with 2 ≤ K ≤ N. We test the algorithm on an image segmentation problem and apply it to a problem of clustering high dimensional data from the sensory system of a cricket.