I know there are various ways to compute eigenvalues, and they are generally not very efficient for large matrices.
Graph Laplacians are symmetric and positive (except on the diagonal, which is negative). I see that this question and answer gives one way to decompose a symmetric matrix into an easier Eigen-problem. Is this the best way to find the eigenvalues of a matrix (specifically a graph Laplacian), or are there others that people use in practice? How about the largest K eigenvalues?