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We propose a network metric, edge proximity, ${\cal P}_e$, which demonstratesthe importance of specific edges in a network, hitherto not captured byexisting network metrics. The effects of removing edges with high ${\cal P}_e$might initially seem inconspicuous but are eventually shown to be very harmfulfor networks. Compared to existing strategies, the removal of edges by ${\calP}_e$ leads to a remarkable increase in the diameter and average shortest pathlength in undirected real and random networks till the first disconnection andwell beyond. ${\cal P}_e$ can be consistently used to rupture the network intotwo nearly equal parts, thus presenting a very potent strategy to greatly harma network. Targeting by ${\cal P}_e$ causes notable efficiency loss in U.S. andEuropean power grid networks. ${\cal P}_e$ identifies proteins with essentialcellular functions in protein-protein interaction networks. It pinpointsregulatory neural connections and important portions of the neural and brainnetworks, respectively. Energy flow interactions identified by ${\cal P}_e$form the backbone of long food web chains. Finally, we scrutinize the potentialof ${\cal P}_e$ in edge controllability dynamics of directed networks.

Slow poisoning and destruction of networks: Edge proximity and its implications for biological and infrastructure networks