I have the same unrooted tree manipulated by different software resulting in different Newick files. I'm relatively sure that after the manipulation the tree remains unrooted and therefore should still be the same topology despite different branch lengths. But the problem is that can the same unrooted tree have different Newick forms? And if yes how can I rewrite the Newick files to convert them to look the same (except branch lengths)?
In this case (A,(C,D),B) is also the same? I had some confusions about adding support values to the arbitrary root. But now I think the root just doesn't have support value?
For bootstrapping, the value is attached to a branch, not to a node. For four leaves, there is only one bootstrapping value, on the branch between the (A,B) clade and the (C,D) clade. Or in the (A,(C,D),B) way, the only value is on the branch connecting the root and the parent of C and D. Generally, each binary unrooted tree with n leaves always has n-3 bootstrapping values.
No, that would have three descendants from the root node and would not be a binary tree any more. Though, (A,((C,D),B)) would be the same.
If the string represents an unrooted tree, (A,(C,D),B) is the exactly same as ((A,B),(C,D)). Actually some software intentionally put a trifurcation at the root to emphasize that this is an unrooted tree.