A contemporary application of this seemingly esoteric branch of mathematics is, of course, the Internet. Routers located throughout the World Wide Web need to constantly and instantly compute the fastest possible route for the data packets that make up your e-mail, telnet sessions, and pr0n downloads through an incredibly complex network of wires and fiber optics. The formulas they use are part of a classic graph theory problem: finding the shortest route from point A to point B across a graph.
Part of the "Math is good for more than just balancing your checkbook" project