Many times when information is being represented, we find it useful to do so like this:
With a similar structure (leaving out the distances, or replacing them by something else), we could represent many other situations, like an underground network, or a network of pipes (where a number might give the diameter), or a railway map, or an indication for which cities are linked by flights, or ferries. Even if we assume it's a network of paths or roads, the numbers needn't give a distance: They might be an indication for how long it takes to cover the distance in question on foot, so up a steep hill an equal distance would take longer than on even ground.
There is more to be done with such a picture of a situation than just
reading off which place is directly connected with another place: For
example, we can ask ourselves whether there is a way of getting from 
to 
at all, or which the shortest way is. And then there is the
famous `Travelling Salesman Problem', which asks to find the shortest
way through the structure which visits each city precisely once.