Before revision:  Therefore, measures are needed to quantify how close a non-tree-based network is to being tree-based . Such measuresnaturally also lead to characterizations of tree-based networks, and some measures for this purpose have recently been introduced both for binary and non-binary rooted phylogenetic networks .
After revision:  Therefore, measures are needed to quantify how close a non-tree-based network is to being tree-based , or very far. In this paper, we formalise the notion of proximity to tree-based networks, and some measures for this purpose have recently been introduced both for binary and non-binary rooted phylogenetic networks .