title: Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a 'hammock' network.
abstract: Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. Here, these methods are compared and used to determine the resistance distances between any two nodes of a network with topology of a hammock.
authors.affiliation: Department of Mathematics, Royal Holloway College , University of London , Egham, Surrey TW20 0EX, UK.
authors.forename: John W
authors.initials: JW
authors.lastname: Essam
authors.affiliation: Applied Mathematics Research Centre , Coventry University , Coventry CV1 5FB, UK ; Yerevan Physics Institute , Alikhanian Brothers 2 , 375036 Yerevan, Armenia.
authors.forename: Nikolay Sh
authors.initials: NSh
authors.lastname: Izmailyan
authors.affiliation: Applied Mathematics Research Centre , Coventry University , Coventry CV1 5FB, UK.
authors.forename: Ralph
authors.initials: R
authors.lastname: Kenna
authors.affiliation: Department of Physics , Nantong University , Nantong 226019, People's Republic of China.
authors.forename: Zhi-Zhong
authors.initials: ZZ
authors.lastname: Tan
keywords: hammock; resistance; resistor network