Maybee, John S.Olesky, D.D.van den Driessche, P.Wiener, G.2009-08-142009-08-1419872009-08-14http://hdl.handle.net/1828/1509We present a detailed account of various determinantal formulas in a graph-theoretic form involving paths and cycles in the digraph of the matrix. For cases in which the digraph has special local properties, for example a cutpoint or a bridge, we give particular formulas which are more efficient for computing the determinant than simply using the matrix representation. Applications are also given to characteristic determinants, general minors and cofactors.endigraphcycledeterminantminorcofactorTechnical Report