In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a chemical graph (Plavšić et al. 1993).
Particular topological indices include the Balaban index,
Harary index, molecular
topological index, and Wiener index. Unless otherwise
stated, hydrogen atoms are usually ignored in the computation of such indices as
organic chemists usually do when they write a benzene ring as a hexagon (Devillers
and Balaban 1999, p. 25).
"The" topological index of a graph index defined by
Devillers, J. and Balaban, A. T. (Eds.). Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands:
Gordon and Breach, p. 31, 1999.Plavšić, D.; Nikolić,
S.; Trinajstić, N.; and Mihalić, Z. "On the Harary Index for the Characterization
of Chemical Graphs." J. Math. Chem.12, 235-250, 1993.Schultz,
H. P. "Topological Organic Chemistry. 1. Graph Theory and Topological Indices
of Alkanes." J. Chem. Inf. Comput. Sci.29, 227-228, 1989.Schultz,
H. P.; Schultz, E. B.; and Schultz, T. P. "Topological Organic
Chemistry. Part 2. Graph Theory, Matrix Determinants and Eigenvalues, and Topological
Indices of Alkanes." J. Chem. Inf. Comput. Sci.30, 27-29, 1990.
is the adjacency matrix, 
is the graph distance
matrix, and 
denotes the determinant of the matrix
addition (Devillers and Balaban 1999, p. 31).
