Before revision:  Importantly, the results and algorithms in this paper still hold true for some non-binary phylogenetic networks and this generalization gives a partial answer to an open question from Pons, Semple, and Steel.
After revision:  Importantly, the results and algorithms in this paper still hold true for a special class of rooted non-binary phylogenetic networks and this generalization gives a partial answer to an open question from Pons, Semple, and Steel.