Abstract
Constructing rooted phylogenetic networks from rooted phylogenetic trees has become an important problem in molecular evolution. So far, many methods have been presented in this area, in which most efficient methods are based on the incompatible graph, such as the CASS, the LNETWORK, and the BIMLR. This paper will research the commonness of the methods based on the incompatible graph, the relationship between incompatible graph and the phylogenetic network, and the topologies of incompatible graphs. We can find out all the simplest datasets for a topology G and construct a network for every dataset. For any one dataset 𝒞, we can compute a network from the network representing the simplest dataset which is isomorphic to 𝒞. This process will save more time for the algorithms when constructing networks.
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