I have hopped over from stackoverflow to get help on something that's more math-ey than I can handle :-)
Is there an algorithm that you can think of that would transform an (exhaustive) list of distances between X points into a graph with a minimum number of edges?
A B C D A x 5 6 8 B 5 x 4 1 C 6 4 x 3 D 8 1 3 x
I could easily just build 3 edges out of each node to create a working graph, but I am looking for an algorithm that reduces the number of edges by using some nodes as intermediaries where possible, instead of a fully interconnected graph.
Thanks and if this is too algorithmic and not mathematical enough, fell free to close the question.