  Suppose that $T$ is a stochastic matrix. We propose an algorithm for
identifying clusters in the Markov chain associated with $T$. The algorithm is
recursive in nature, and in order to identify clusters, it uses the sign
pattern of a left singular vector associated with the second smallest singular
value of the Laplacian matrix $I-T.$ We prove a number of results that justify
the algorithm's approach, and illustrate the algorithm's performance with
several numerical examples.
