A computer program for calculating the graph-theoretical detour matrix is introduced, which uses the topological symmetry of a graph to minimize path-tracing. The high performance of the program allows one to treat graphs of the complexity of fullerenes (e.g., C ₆₀). A more logical definition of the detour matrix and the detour index ω than is presently in use is proposed. Index ω is probed as a descriptor for boiling points of acyclic and cyclic alkanes. The detour index in combination with the Wiener index W is more useful than Hosoya's Z index for regression of the boiling points of a large sample of compounds containing all acyclic and cyclic alkanes with known boiling points from methane up to polycyclic octanes.