The gravity of an edge.

We describe a methodology for characterizing the relative structural importance of an arbitrary network edge by exploiting the properties of a -shortest path algorithm. We introduce the metric , measuring how often an edge occurs in any possible network path, as well as -Gravity, a lower bound based on paths enumerated while solving the -shortest path problem. The methodology is demonstrated using Granovetter's original network examples as well as the well-known Florentine families of the Italian Renaissance and the Krebs 2001 terrorist networks.