# Morphological organization of point-to-point transport in complex networks

## TL;DR

This paper explores the universal structural organization of point-to-point transport in complex scale-free networks, revealing a tree-cluster-tree pattern that results in a power-law current distribution with an exponent of -2.

## Contribution

It uncovers a universal structural pattern in complex networks that explains the distribution of transport currents, independent of network specifics.

## Key findings

- Transport structures form a tree-cluster-tree pattern.
- Current distribution follows a power law with exponent -2.
- The pattern is universal across different network types.

## Abstract

We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied, selects two tree-like structures, one emerging from the source and the other converging to the drain. These trees merge into a large cluster of the remaining nodes that is found to be quasi-equipotential and thus presents almost no resistance to transport. Such a global "tree-cluster-tree" structure is universal and leads to a power law decay of the currents distribution. Its exponent, $-2$, is determined by the multiplicative decrease of currents at successive branching points of a tree and is found to be independent of the network connectivity degree and resistance distribution.