  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.
