Is there a shortest path algorithim that calculates the shortest route passing all available roads, ending where you started? This differs from the Travelling salesman problem as you need to pass through all roads between the cities, not just the cities. The traditional shortest path algorithims do not work because they only calculate the shortest distance between 2 points, and don't guarantee passing through all of the roads. Here is a vague map of my problem.
For a solution to be valid, it must pass through every road in between the points labeled.