Localization of Electrical Flows [chapter]

Aaron Schild, Satish Rao, Nikhil Srivastava
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
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 O(log 2 n). 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 O(log 2 n). This result implies a simple oblivious routing scheme based on electrical flows in the case of transitive graphs.
doi:10.1137/1.9781611975031.103 dblp:conf/soda/SchildRS18 fatcat:if36wfailvfflbmgkfv7fw4lba