GRAPH PARTITIONING WITH EIGENVECTORS Panek, James Cheeger value Green's function Normalized Laplacian The Cheeger constant of a graph quantities how well a graph can be cut yield- ing two (typically) large vertex sets by a small edge cut. Lower and upper bounds have been developed using the eigenvalues and eigenvectors of the normalized Laplacian matrix of the graph. Here a classic sweep algorithm is studied using linear combinations of eigenvectors, specifically the columns of approximate discrete Green's functions. It is then shown, statistically on certain families of random graphs following a stochastic block model, that it is enough to use two eigenvalues and vectors to improve this classic algorithm's upper bound in most cases. M.S. in Applied Mathematics, May 2017 Ellis, Robert 2017 2017-05 Thesis application/pdf islandora:7521 http://hdl.handle.net/10560/4154 MATH / Applied Mathematics Illinois Institute of Technology en In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access