Before revision:  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:  Such measuresnaturally also lead to characterizations of tree-based for unrooted phylogenetic networks, with a range of proximity measures. These measures also provide characterisations of tree-based networks. One measure in particular, related to the nearest neighbour interchange operation, allows us to define the notion of ``tree-based rank''. This provides a subclassification within the tree-based networks themselves, identifying those networks that are ``very'' tree-based. Finally, we prove results relating tree-based networks in the settings of rooted and unrooted phylogenetic networks, showing effectively that an unrooted network is tree-based if and only if it can be made a rooted tree-based network by rooting it and orienting the edges appropriately .