Volume 84, Number 2, October 2008
Article Number 28005
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 14 October 2008
EPL, 84 (2008) 28005
DOI: 10.1209/0295-5075/84/28005

Transport in networks with multiple sources and sinks

S. Carmi1, 2, Z. Wu2, S. Havlin1 and H. E. Stanley2

1   Minerva Center and Department of Physics, Bar-Ilan University - Ramat Gan 52900, Israel
2   Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA

received 19 May 2008; accepted in final form 9 September 2008; published October 2008
published online 14 October 2008

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.

89.75.Hc - Networks and genealogical trees.
05.60.Cd - Classical transport.
02.50.-r - Probability theory, stochastic processes, and statistics.

© EPLA 2008