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

Matrix Theory Preliminaries. Graph Theory Preliminaries. Introduction to Laplacian Matrices. Algebraic Connectivity. The Fiedler Vector and Bottleneck Matrices for Trees. Bottleneck Matrices for Graphs. The Group Inverse of the Laplacian Matrix.