The Kirchhoff index K f, also simply called the resistance and denoted R , of a connected graph G on n nodes is defined by K f = 1/2 sum_(i = 1)^n sum_(j = 1)^n (Ω)_(i j), where (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. Precomputed values for many graphs are implemented in the Wolfram Language as GraphData[g, KirchhoffIndex].

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

GraphData

Gustav Kirchhoff