A Simple Method for Computing Resistance Distance

Abstract

The resistance distance rij between two vertices vi and Vj of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any edge is unity. We show how rij can be computed from the Laplacian matrix L of the graph G: Let L(i) and L(i, j) be obtained from L by deleting its i-th row and column, and by deleting its i-th and j-th rows and columns, respectively. Then rij = detL(i, j)/detL(i).