Transport in networks with multiple sources and sinks

S. Carmi*, Z. Wu, S. Havlin, H. E. Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageAmerican English
Article number28005
JournalLettere Al Nuovo Cimento
Issue number2
StatePublished - 1 Oct 2008
Externally publishedYes


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