The first chapter of this book provides a brief treatment of  the basics of the subject. The other chapters deal with the various  decompositions of non-negative matrices, Birkhoff type theorems, the  study of the powers of non-negative matrices, applications of matrix  methods to other combinatorial problems, and applications of  combinatorial methods to matrix problems and linear algebra problems.    The coverage of prerequisites has been kept to a minimum.  Nevertheless, the book is basically self-contained (an Appendix  provides the necessary background in linear algebra, graph theory and  combinatorics). There are many exercises, all of which are accompanied  by sketched solutions.   Audience: The book is suitable for a graduate course as well as  being an excellent reference and a valuable resource for  mathematicians working in the area of combinatorial matrix theory.

Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3) PDF

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