Transport in networks with multiple sources and sinksS. 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.
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