The concept of a quasi-median network is a generalization of the concept of a

median network In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertex (graph theory), vertices ''a'', ''b'', and ''c'' have a unique ''median'': a vertex ''m''(''a'',''b'',''c'') that belongs to shortest pat ...

that was introduced to represent multistate characters. Note that, unlike median networks, quasi-median networks are not

split networks For a given set of taxa like X, and a set of splits S on X, usually together with a non-negative weighting, which may represent character changes distance, or may also have a more abstract interpretation, if the set of splits S is compatible, the ...

. A quasi-median network is defined as a

phylogenetic network A phylogenetic network is any graph used to visualize evolutionary relationships (either abstractly or explicitly) between nucleotide sequences, genes, chromosomes, genomes, or species. They are employed when reticulation events such as hybrid ...

, the node set of which is given by the quasi-median closure of the condensed version of M (let M be a

multiple sequence alignment Multiple sequence alignment (MSA) may refer to the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evolutio ...

of DNA sequences on X) and in which any two nodes are joined by an edge if and only if the sequences associated with the nodes differ in exactly one position. The quasi-median closure is defined as the set of all sequences that can be obtained by repeatedly taking the quasi-median of any three sequences in the set and then adding the result to the set.

References

Phylogenetics Computational phylogenetics Bioinformatics algorithms Bioinformatics {{bioinformatics-stub