A novel matrix in chemistry is detour matrix, known in the formal graph theory since 1969 (F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969, p. 203). This matrix has been introduced in the chemical literature independently by two groups (O. Ivanciuc, A.T. Balaban, Comm. Math. Chem. 30 (1994) 141-152; D. Ami?, N. Trinajsti?, Croat. Chem. Acta 68 (1995) 53-62).
We will give the definition of the detour matrix and compared with the definition of the distance matrix. The computation of the detour matrix will be briefly outlined. Examples of graphs with identical detour matrices will be shown. We will consider three invariants of the detour matrix: the detour polynomial, the detour spectrum and the detour index. The detour spectrum and the detour index. The detour matrix and its invariants will be derived for special classes of graphs such as cycles and complete graphs.