Graph navigation with C#

Question

I having a bit of a quandry trying to come up with a good algorithm to navigate the following graph.

alt text http://www.archimedesinc.biz/images/StackOverflow/Tree.jpg

If a user chooses "Table 21" as a starting point, I need to be able to get the path to any other table from that starting table.

EX: If the user chooses "Table 21" as a start and then adds a value from "Table 8", I need to create the following path "Table 21 -> Table 12 -> Table 9 -> Table 6 -> Table 8", all of the weights between the tables are the same.

I seem to have forgotten my skills in dealing with directed graphs, and can't think of a good algorithm. I'm not asking for a solution, but just a push in the right direction.

Thank you!

Answer 1

Breadth-first search will find a shortest path: http://en.wikipedia.org/wiki/Breadth-first_search

Answer 2

Since you said the edges are all of the same weight, Dijkstra's algorithm (my usual first choice for this sort of thing) will just degrade to breadth first search so I suggest using that for simplicity.