Breadth First Search (More of a Logic Question)

Hey guys, I'm having a logic block with a Breadth First Search using a queue.

Basically the way Breadth First Search works is that it expands all of the nodes one level at a time until it finds the result. I quickly whipped out a flash to demonstrate what I believe is the Breadth First Search.
http://www.nxsupport.com/dimava/bfs.swf

I wrote the code to do the algorithm, However if I just output the queue it shows all of the excess "potential" nodes and not just the direct route. For example, with the flash file linked above, it would show ABECGFC, instead of just ABCD.

I realise that I could trace back from the end to see which of the nodes D is connected to, then which of the nodes C is connected to, etc. But that wouldn't work out if there was more than one path with the same distance leading to the same destination.

Thanks,

Dimava