Edmonds branching algorithm

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Can anyone in very simple terms explain what is and how to perform the Edmunds Branching algorithm.

So far I know you need to have a spanning tree rooted at r (a set of n-1 edges containing paths from r to every vertex.

And for every node you need to be taking the largest input.

I cannot find anywhere a simple "step by step", on where to begin if you don't have an named node r, how to proceed, what edges to delete and replace, when to stop... If anyone can explain using very simple terminology, I would be extremely grateful. I added a picture with an example for reference. enter image description here

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