  Phylogenetic networks are a generalization of phylogenetic trees allowing for
the representation of non-treelike evolutionary events such as hybridization.
Typically, such networks have been analyzed based on their `level', i.e. based
on the complexity of their 2-edge-connected components. However, recently the
question of how `treelike' a phylogenetic network is has become the center of
attention in various studies. This led to the introduction of \emph{tree-based
networks}, i.e. networks that can be constructed from a phylogenetic tree,
called the \emph{base tree}, by adding additional edges. While the concept of
tree-basedness was originally introduced for rooted phylogenetic networks, it
has recently also been considered for unrooted networks. In the present study,
we compare and contrast findings obtained for unrooted \emph{binary} tree-based
networks to unrooted \emph{non-binary} networks. In particular, while it is
known that up to level 4 all unrooted binary networks are tree-based, we show
that in the case of non-binary networks, this result only holds up to level 3.

Populations and Evolution;Combinatorics