Wave equation based algorithm for distributed eigenvector computation

We propose a novel distributed algorithm to compute eigenvectors and eigenvalues of the graph Laplacian matrix L. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of L. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to eigenvector computation and derive convergence rates. We also demonstrate its utility on a distributed estimation example.