Proximity in group inverses of M-matrices and inverses of diagonally dominant M-matrices

In this paper we connect, generalize, and broaden properties of matrices related to (i) the triangular inequality for mean first passage times in finite homogeneous ergodic Markov chains, (ii) the triangle inequality for proximities in Laplacian matrices of undirected weighted graphs, and (iii) the Metzler property of the column entrywise diagonal dominance of inverses of diagonally dominant M-matrices.