Algebraic aspects of the normalized Laplacian

Abstract

Spectral graph theory looks at the interplay between the structure of a graph and the eigenvalues of a matrix associated with the graph. Many interesting graphs have rich structure which can help in determining the eigenvalues associated with a particular graph matrix. This survey looks at some common techniques in working with and determining the eigenvalues associated with the normalized Laplacian matrix, in addition to some algebraic applications of these eigenvalues.