We propose a network metric, edge proximity, ${\mathcal{P}}_e$, which demonstrates the importance of specific edges in a network, hitherto not captured by existing network metrics. The effects of removing edges with high ${\mathcal{P}}_e$ might initially seem inconspicuous but are eventually shown to be very harmful for networks. Compared to existing strategies, the removal of edges by ${\mathcal{P}}_e$ leads to a remarkable increase in the diameter and average shortest path length in undirected real and random networks till the first disconnection and well beyond. ${\mathcal{P}}_e$ can be consistently used to rupture the network into two nearly equal parts, thus presenting a very potent strategy to greatly harm a network. Targeting by ${\mathcal{P}}_e$ causes notable efficiency loss in U.S. and European power grid networks. ${\mathcal{P}}_e$ identifies proteins with essential cellular functions in protein-protein interaction networks. It pinpoints regulatory neural connections and important portions of the neural and brain networks, respectively. Energy flow interactions identified by ${\mathcal{P}}_e$ form the backbone of long food web chains. Finally, we scrutinize the potential of ${\mathcal{P}}_e$ in edge controllability dynamics of directed networks.

• Received 3 October 2014

DOI:https://doi.org/10.1103/PhysRevE.91.022807