Question: ```
                      L->|
  A -> B              ^  |
  |__> C -> D-> G->X--|  |
       K    |_> T  |  |_>Z
       |___________|

```

I hope this small drawing helps convey what I'm trying to do.

I have a list of 7,000 locations, each with an undefined, but small number of doors. Each door is a bridge between both locations.

Referencing the diagram above, how would I go about finding the quickest route through the doors to get from A to Z?

I don't need full on source, just psuedo code would be fine.

Obviously you can take A -> B ->C -> D -> G -> X -> L -> Z, 
but the shortest route is A -> B -> C -> K -> X -> Z.

Answer: 
Represent your locations as nodes and the doors as edges in a graph. Then apply some rather standard [shortest path algorithm(s)](http://en.wikipedia.org/wiki/Shortest_path_problem) and you're done.
Look up [Pathfinding](http://en.wikipedia.org/wiki/Pathfinding) algorithms on Wikipedia. You basically build up a series of nodes and connections between them, and the algorithm works through them finding a way from the start to a goal.