Figure 1

Phylogenetic Networks. The figure shows two phylogenetic networks; the one on the left has only a single reticulate vertex and the one on the right has two reticulate vertices that are sisters to each other. Note that removing the edges (7, 9) and (7, 10) from the network on the right does not result in a tree where vertex 7 is a leaf. This shows that removing one incoming edge each per reticulate vertex does not necessarily produce a tree with the same leaf set as the network. The post-ordering and the pre-ordering of vertices of the network on the left are 1, 2, 8, 6, 3, 7, 5, 4, 0 and 0, 5, 6, 1, 8, 2, 7, 3, 4 respectively and for the network on the right, they are 1, 2, 9, 6, 3, 10, 7, 5, 4, 8, 0 and 0, 5, 6, 1, 9, 2, 7, 10, 3, 8, 4 respectively.