  We prove that Nakhleh's latest dissimilarity measure for phylogenetic
networks is a metric on the classes of tree-child phylogenetic networks, of
semi-binary time consistent tree-sibling phylogenetic networks, and of
multi-labeled phylogenetic trees. We also prove that it distinguishes
phylogenetic networks with different reduced versions. In this way, it becomes
the dissimilarity measure for phylogenetic networks with the strongest
separation power available so far.
