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 in
conspicuous 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.
Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or graphlets.
We analyze the simplest case, attachment of the three node V-graphlet, where, with probability alpha, we attach a peripheral node of the graphlet, and with probability (1-alpha), we attach the central node. Our analytical results and simulations show that tuning alpha produces a wide range in degree distribution and degree assortativity, achieving assortativity values that capture a diverse set of many real-world systems. We introduce a fifteen-dimensional attribute vector derived from seven well-known network properties, which enables comprehensive comparison between any two networks. Principal Component Analysis (PCA) of this attribute vector space shows a significantly larger coverage potential of real-world network properties by a simple extension of the above model when compared against a classic model of network growth.
