Network Permeability Changes According To A Quadratic Power Law Upon Removal Of A Single Edge

We report a phenomenological 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 satisfy Darcy's law on a small-scale resistor network.