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

Abstract: We propose a network metric, edge proximity, ${\cal P}_e$, which demonstrates the importance of specific edges in a network, hitherto not captured by existing network metrics. The effects of removing edges with high ${\cal P}_e$ might initially seem inconspicuous but are eventually shown to be very harmful for networks. Compared to existing strategies, the removal of edges by ${\cal P}_e$ 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. ${\cal P}_e$ 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 ${\cal P}_e$ causes notable efficiency loss in U.S. and European power grid networks. ${\cal P}_e$ 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 ${\cal P}_e$ form the backbone of long food web chains. Finally, we scrutinize the potential of ${\cal P}_e$ in edge controllability dynamics of directed networks.