creator Panek, James advisor Ellis, Robert 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. Submitted by Erma Thomas (thomase@iit.edu) on 2017-11-03T21:29:58Z No. of bitstreams: 1 etdadmin_upload_498502.zip: 894203 bytes, checksum: c180624e47dce3fdab60ef5d9ed5b1f4 (MD5) Made available in DSpace on 2017-11-03T21:29:58Z (GMT). No. of bitstreams: 1 etdadmin_upload_498502.zip: 894203 bytes, checksum: c180624e47dce3fdab60ef5d9ed5b1f4 (MD5) Previous issue date: 2017-05 M.S. in Applied Mathematics, May 2017 2017 2017-05 http://hdl.handle.net/10560/4154 en Cheeger value Green's function Normalized Laplacian Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department