Before revision:  Tree-based networks can be viewed as a natural generalization of rooted binary phylogenetic trees because they are merely trees with additional arcs, and in defining those networks, a certain kind of spanning trees called subdivision trees plays an essential role .
After revision:  Tree-based networks can be viewed as a natural generalization of rooted binary phylogenetic trees because they are merely trees with additional arcs, and in defining those networks, a certain kind called "subdivision trees" play an essential role .