







The weight of the subgraph is minimal, you don't care for the weight of the paths*. 
There is no backtracking in the construction. You've got a subset of the nodes, those are all candidates that may provide the next edge to be added. 
A B C A 0 1 0 B 1 0 2 Table (the "graph array") C 0 2 3 1 (A)(B) / /2 Graph / __(C) /  \___/ 3 