Random Walks, Conductance, and Resistance for the Connection Graph Laplacian
Discrete Mathematics
2023-08-22 v2
Abstract
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of Dirichlet-type and Poisson-type problems on connection graphs. Additionally, we delve into random walks, taking into account both node transitions and vector rotations. This approach introduces novel concepts of effective conductance and resistance matrices for connection graphs, capturing mean rotation matrices corresponding to random walk transitions. Thereby, it provides new theoretical insights for network analysis and optimization.
Keywords
Cite
@article{arxiv.2308.09690,
title = {Random Walks, Conductance, and Resistance for the Connection Graph Laplacian},
author = {Alexander Cloninger and Gal Mishne and Andreas Oslandsbotn and Sawyer Jack Robertson and Zhengchao Wan and Yusu Wang},
journal= {arXiv preprint arXiv:2308.09690},
year = {2023}
}