Split networks

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For a given set of taxa, and a set of splits S on the taxa, 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, then it can be represented by an unrooted phylogenetic tree and each edge in the tree corresponds to exactly one of the splits. More generally, S can always be represented by a split network,{{cite journal|last1=Bandelt|first1=Hans-Jürgen|last2= Dress|first2=Andreas W. M.| authorlink2=Andreas Dress|year=1992|title=A canonical decomposition theory for metrics on a finite set|journal=Advances in Mathematics|volume=92|pages=47–105|doi=10.1016/0001-8708(92)90061-o|doi-access=}} which is an unrooted phylogenetic network with the property that every split in S is represented by an array of parallel edges in the network.