The Wiener sum index WS is a graph index defined for a graph on n nodes by WS = 1/2 sum_(i = 1)^n sum_(j = 1)^n (d)_(i j)/(Ω)_(i j), where (d)_(i j) is the graph distance matrix and (Ω)_(i j) is the resistance distance matrix. 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. The following table summarizes values of the Kirchhoff sum index for various special classes of graphs.

Balaban index | graph distance matrix | Kirchhoff sum index | resistance distance | Wiener index