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.
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