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

We propose a network metric, edge proximity, 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 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 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. 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 P(e) causes notable efficiency loss in U.S. and European power grid networks. 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 P(e) form the backbone of long food web chains. Finally, we scrutinize the potential of P(e) in edge controllability dynamics of directed networks.