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.

翻译：假设$T$是一个随机矩阵。 我们建议使用一种算法来识别与$T美元相关的Markov链条中的集群。 算法具有递归性质, 为了识别集群, 它使用左单向量的标记模式, 与拉普拉西亚矩阵的第二个最小单向值相关。 我们证明了一些结果, 证明算法的方法是正确的, 并以几个数字例子来说明算法的性能 。