This paper extends the theory of graphs associated with real rectangular matrices to include information about the signs of the elements. We show when signed row and column graphs can be defined for the matrix A. We also deduce conditions under which these graphs are balanced. This leads to a definition of the class of quasi-Morishima rectangular matrices A. It is shown that the Perron–Frobenius theorem applies to the matrices $AA^T $ and $A^T A$ when A is a quasi-Morishima matrix. Finally we examine the applications of our results to several classes of matrices occurring in energy economic models. All results in this paper are purely qualitative in character.