Non-symmetric finite networks: the two-point resistance

TL;DR

This paper derives an explicit formula for calculating the resistance between two nodes in non-symmetric networks, significantly improving efficiency in electronic circuit fault analysis by leveraging eigenvector properties.

Contribution

It introduces a novel explicit formula for two-point resistance in non-symmetric networks, enabling faster analysis in complex circuit systems.

Findings

Formula accurately computes resistance in example networks

Reduces analysis time in electronic circuit fault detection

Demonstrates effectiveness with circuit network examples

Abstract

An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved repeatedly. Analysis time can be greatly reduced by utilization of the obtained formula. The presented approach is based on the "mutual orthogonality" of the full system of left and right-hand eigenvectors of a diagonalizable matrix L. Some examples are given that demonstrate the accuracy of the approach on circuit networks.