I would like to know an algorithm to produce a graph decomposition into branches with rank in the following way:
Rank | path (or tree branch)
0 1-2
1 2-3-4-5-6
1 2-7
2 7-8
2 7-9
The node 1 would be the Root node and the nodes 6, 8 and 9 would be the end nodes. the rank of a branch should be given by the number of bifurcation nodes up to the root node. Let's assume that the graph has no loops.
I am electrical engineer, and perhaps this is a very standard problem, but so far I have only found the BFS algorithm to get the paths, and all the cut sets stuff.
I hope that my question is clear enough.
PS: should this question be in stack overflow?