Theory of resistor networks: The two-point resistance

The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte