On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o

chapter 1|38 pages

Matrix Theory Preliminaries

chapter 2|52 pages

Graph Theory Preliminaries

chapter 3|28 pages

Introduction to Laplacian Matrices

chapter 4|54 pages

The Spectra of Laplacian Matrices

chapter 5|38 pages

The Algebraic Connectivity

chapter 7|78 pages

Bottleneck Matrices for Graphs

chapter 8|34 pages

The Group Inverse of the Laplacian Matrix