Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a hammock network

TL;DR

This paper compares potential-based and recurrence relation methods for calculating point-to-point resistance in nearly rectangular hammock networks, highlighting their effectiveness and application to complex network topologies.

Contribution

It provides a comparative analysis of two main techniques for resistance calculation and applies them to a specific hammock network topology.

Findings

Potential and recurrence methods yield consistent resistance values.

The methods are effective for complex network topologies.

Application to hammock networks demonstrates practical utility.

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.