Network permeability changes according to a quadratic power law upon removal of a single edge

TL;DR

This paper discovers an empirical quadratic power law describing how network permeability decreases when a single edge is removed, applicable to biological and regular lattice networks.

Contribution

It introduces a new empirical power law for network permeability reduction upon edge removal and provides a heuristic explanation based on resistor network mapping.

Findings

Permeability reduction follows a quadratic power law upon edge removal.

The power law applies to microvascular networks and regular lattices.

Heuristic argument based on Darcy's law explains the observed power law.

Abstract

We report an empirical power law for the reduction of network permeability in statistically homogeneous spatial networks upon removal of a single edge. We characterize this power law for plexus-like microvascular sinusoidal networks from liver tissue, as well as perturbed two- and three-dimensional regular lattices. We provide a heuristic argument for the observed power law by mapping arbitrary spatial networks that satisfies Darcy's law on an small-scale resistor network.