This volume aims to gather information from both those who work on linear algebra problems in which combinatorial or graph-theoretical analysis is a major component and those that work on combinatorial or graph-theoretical problems for which linear algebra is a major tool. The fifteen papers in this volume span a wide cross-section of past and current research in the field. Specific topics covered in the papers include matrix problems and results in symbolic dynamics, block-triangular decompositions of mixed matrices, algebraic and geometric properties of Laplacian matrices of graphs, the use of eigenvalues in combinatorial optimization, perturbation effects on rank and eigenvalues, and polynomial spaces. This book should be of interest to researchers in linear algebra, combinatorics and graph theory, and to anyone who wishes to get a glimpse of this fascinating area.