Effective resistance, random walk and algorithms

Abstract

Efficiently determining the effective resistance of large-scale electrical networks is crucial for optimizing energy distribution and assessing network robustness. In this paper, we propose a novel approach that combines random walk simulations and advanced linear algebra techniques to compute the effective resistance of complex electrical networks. Our method leverages the concept of random walks to simulate the flow of current through the network, capturing its behavior under various conditions. Subsequently, we employ graph Laplacian-based linear algebra algorithms to analyze the resulting data, enabling accurate computation of the effective resistance. In our model, we aim to deploy these combined algorithm to develop a novel method to deal with such methods.