Fluctuations and redundancy in optimal transport networks

TL;DR

This paper explores how allowing flow fluctuations in optimal transport networks leads to structures with loops, contrasting the traditional tree-like optimal networks under stationary flow assumptions, with implications for natural network formation.

Contribution

It demonstrates that non-stationary flows result in loop-containing hierarchical networks, expanding understanding of optimal network structures beyond classical tree models.

Findings

Optimal networks with flow fluctuations contain loops.

Transitions between network topologies depend on problem parameters.

Natural networks like leaf venation may be shaped by flow variability.

Abstract

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are trees. It is shown here that this result is contingent on the assumption of a stationary flow through the network. When time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops. The transitions between different network topologies as the parameters of the problem vary are examined. These results may have strong implications for the structure and formation of natural networks, as is illustrated by the example of leaf venation networks.