Metrics for classes of semi-binary phylogenetic networks using μ-representations

Phylogenetic networks are useful in representing the evolutionary history of taxa. In certain scenarios, one requires a way to compare different networks. In practice, this can be rather difficult, except within specific classes of networks. In this paper, we derive metrics for the class of orchard networks and the class of strongly reticulation-visible networks, from variants of so-called μ-representations, which are vector representations of networks. For both network classes, we impose degree constraints on the vertices, by considering semi-binary networks.