  To a given nonsingular triangular matrix A with entries from a ring, we
associate a weighted bipartite graph G(A) and give a combinatorial description
of the inverse of A by employing paths in G(A). Under a certain condition,
nonsingular triangular matrices A such that A and A^{-1} have the same
zero-nonzero pattern are characterized. A combinatorial construction is given
to construct outer inverses of the adjacency matrix of a weighted tree.
