Transport in networks with multiple sources and sinks

TL;DR

This paper analyzes how the number of sources and sinks affects electrical current and flow in complex networks, revealing optimal points and the impact of bottlenecks on transport efficiency.

Contribution

It provides analytical formulas for current and flow between multiple sources and sinks, highlighting how increasing n influences network transport and identifying optimal configurations.

Findings

Increasing n improves total transport for small n

Bottlenecks reduce efficiency for large n

Optimal n* exists for flow transport

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.