Example

In the following graph, we have an example of a weighted and directed map. This map represents a zoo train where each node represents a station and each edge is a part of the track. Zoo guests can get on and off wherever they desire.

This graph is weighted as guests must pay the associated fee for each part of the track. Our example train also has a one way direction in most cases. The exception to this is the entrance/exit to the aquarium, this part of the track can go either direction.

In this graph, we also have a couple of loops. This would allow for zoo-guests to ride the train around an expansive exhibit such as the elephants or giraffes.

One possible way to tour the zoo for a guest starting at the entrance could be: aquarium, primates, big cats, antelope, giraffes, loop around the giraffes, elephants, aquarium, then exit. Their total payment for just the train would be $14.