Handbook of Linear Algebra, 2nd Edition

Chapter 40

Digraphs and Matrices

Jeffrey L. Stuart

Pacific Lutheran University

Directed graphs, often called digraphs, have much in common with graphs, which were the subject of the previous chapter. While digraphs are of interest in their own right, and have been the subject of much research, this chapter focuses on those aspects of digraphs that are most useful to matrix theory. In particular, it will be seen that digraphs can be used to understand how the zero-nonzero structure of square matrices affects matrix products, determinants, inverses, and eigenstructure. Basic material on digraphs and their adjacency matrices can be found in many texts on graph theory, nonnegative matrix theory, or combinatorial matrix theory. For all aspects of ...