Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Collecting diverse results into a single volume, this self-contained book highlights the importance and utility of the group inverses of M-matrices in several application areas. The authors emphasize the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. They show how group inverses offer valuable insight into each of these areas.