Let $G$ be an undirected graph, seen as a network of 1 Ohm resistors.As explained by this article (or stated on Wikipedia), the effective resistance between any two vertices can be obtained by taking the pseudo-inverse of the Laplacian matrix $L$ of $G$.Are there any efficient ways to compute this? Say I am only interested about the effective resistance between a given pair of vertices, in a large graph. I would be interested in the computational complexity of computing that resistance, or any approximation strategy, any preprocessing (lighter than computing the whole matrix) that would make these queries more efficient.In other words, I am looking for literature about the problem with a computational perspective.
Computing the effective resistance between two vertices in a large graph
complexity theory;graph theory