In the end you have to examine the arguments in some order. By deciding the order you are reducing work for the reader in finding a pleasant traversal of the graph.
Maybe you're increasing the work by deciding an order. I've testing this approach several times of actually laying out complex arguments graphviz-style and watching people's eyes as they review it. Everyone seems to traverse the graph differently, depending on which parts challenge them.
Toulmin's model (data, warrant,backung,claim,rebuttal) reminds us that arguments are generally expressed with qualifiers and rebuttals rather than asserted as absolutes. This lets the reader know how to take the reasoning, how far it is meant to be applied,
I think there is certainly room to present graphs replete with pleasant and unpleasant traversals highlighted. It should also be possible to deconstruct misleading traversals.
