Integer generalized inverses of incidence matrices

AbstractGraphical procedures are used to characterize the integral {1}- and {1, 2}-inverses of the incidence matrix A of a digraph, and to obtain a basis for the space of matrices X such that AXA = 0. These graphical procedures also produce the Smith canonical form of A and a full rank factorization of A using matrices with entries from {-1, 0, 1}. It is also shown how the results on incidence matrices of oriented graphs can be used to find generalized inverses of matrices of unoriented bipartite graphs