sentences:  It partitions points into two sets formula_9 based on the eigenvector formula_10 corresponding to the second-smallest eigenvalue of the symmetric normalized Laplacian defined as
  
  A mathematically equivalent algorithm  takes the eigenvector corresponding to the largest eigenvalue of the random walk normalized adjacency matrix formula_12.Knowing the eigenvectors, partitioning may be done in various ways, such as by computing the median formula_13 of the components of the second smallest eigenvector formula_10, and placing all points whose component in formula_10 is greater than formula_13 in formula_17, and the rest in formula_18.The algorithm can be used for hierarchical clustering by repeatedly partitioning the subsets in this fashion.