Localization of Electrical Flows
Data Structures and Algorithms
2017-08-08 v1 Discrete Mathematics
Abstract
We show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a random edge is . This is a consequence of a more general result which shows that the spectral norm of the entrywise absolute value of the transfer impedance matrix of a graph is . This result implies a simple oblivious routing scheme based on electrical flows in the case of transitive graphs.
Cite
@article{arxiv.1708.01632,
title = {Localization of Electrical Flows},
author = {Aaron Schild and Satish Rao and Nikhil Srivastava},
journal= {arXiv preprint arXiv:1708.01632},
year = {2017}
}