The resistance distance between vertices i and j of a graph G is defined as the effective resistance between the two vertices (as when a battery is attached across them) when each graph edge is replaced by a unit resistor (Klein and Randić 1993, Klein 2002). This resistance distance is a metric on graphs. Let Ω_(i j) be the resistance distance between vertices i and j in a connected graph G on n nodes, and define Γ = L + 1/n, where L is the Laplacian matrix of G and 1 is the unit n×n matrix.

Foster's theorems | Kirchhoff index | Kirchhoff sum index | resistance-equivalent graphs | resistor network | Wiener sum index