Transport in networks with multiple sources and sinks
Carmi, S.; Wu, Z.; Havlin, S.; Stanley, H. E.; Carmi, S.; Minerva Center and Department of Physics, Bar-Ilan University - Ramat Gan 52900, Israel; Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA; Wu, Z.; Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA; Havlin, S.; Minerva Center and Department of Physics, Bar-Ilan University - Ramat Gan 52900, Israel; Stanley, H. E.; Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
Журнал:
EPL (Europhysics Letters)
Дата:
2008-10-01
Аннотация:
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<sup>*</sup> 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.
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