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 Darcys law on an small-scale resistor network.
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