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.