This article introduces the unrooted analog of level-k networks, a special kind of abstract network to visualize conflicts between phylogenetic trees which may correspond to such exchanges, and gives an equivalence theorem between circular split systems and un rooted level-1 networks.Expand

It is argued that galled networks (a generalization of galled trees) provide a good trade-off between level of generality and tractability and solve the problem of computing an optimal rooted phylogenetic network from a set of clusters.Expand

A new visualisation which displays more information: the tree cloud, which shows the most frequent words of the text, where the size reflects the frequency, but the words are arranged on a tree to reflect their semantic proximity according to the text.Expand

The structure oflevel-k networks, and how they can be decomposed into level-k generators, is studied, and a polynomial time algorithm is provided which takes as input the set of level- k generators and builds theSet of level-(k + 1) generators.Expand

This paper proposes “horizontal” moves that ensure that every network of a certain complexity can be reached from any other network of the same complexity, and “vertical” Moves that ensure reachability between networks of different complexities that are robust to the fact that networks with higher complexity usually allow a better fit with the data.Expand

The NP-completeness proof of recognizing 2- Interval graphs is extended to the recognition of balanced 2-interval graphs, and instances that show that all inclusions are strict are provided.Expand

Clust&See, a Cytoscape plugin dedicated to the identification, visualization and analysis of clusters extracted from networks, provides the ability to apply three different, recently developed graph clustering algorithms to networks and to visualize the obtained partition as a quotient graph.Expand

Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees,… Expand

A quadratic-time algorithm for this problem for binary nearly-stable phylogenetic networks is developed and it is shown that the number of reticulations in a reticulation visible or nearly stable phylogenetic network is bounded from above by a function linear in theNumber of taxa.Expand

To identify network classes on which the problem is polynomial time solvable, this work introduces two classes of networks by generalizations of tree-child networks through vertex stability, namely nearly stable networks and genetically stable networks.Expand