Transport in networks with multiple sources and sinks
Discrete Mathematics
2008-11-17 v2 Disordered Systems and Neural Networks
Abstract
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for small n, increasing n improves the total transport in the network, while for large n bottlenecks begin to form. For the case of flow, this leads to an optimal n* above which the transport is less efficient. For current, the typical decrease in the length of the connecting paths for large n compensates for the effect of the bottlenecks. We also derive an expression for the average flow as a function of n under the common limitation that transport takes place between specific pairs of sources and sinks.
Keywords
Cite
@article{arxiv.0805.1567,
title = {Transport in networks with multiple sources and sinks},
author = {Shai Carmi and Zhenhua Wu and Shlomo Havlin and H. Eugene Stanley},
journal= {arXiv preprint arXiv:0805.1567},
year = {2008}
}