table of contents NeighborNet is a novel method for phylogenetic analysis that is currently being … 
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Preliminaries

and put
for all x, y ∈ X. A distance function d is called circular if there exits a circular split weight function ω such that d = d_{ω}. An ordering Θ of X is said to be compatible with d if there exists ω such that d = d_{ω }and Ϭ_{ω }⊆ Ϭ_{Θ. }Note that the representation of a circular distance function d is unique, i.e., if d = and d = for circular split weight functions ω_{1 }and ω_{2 }then ω_{1 }= ω_{2 }holds [10].
Circular distances were introduced in [10] and have been further studied in, for example, [12] and [13]. Just as any treelike distance function on X can be uniquely represented by a phylogenetic tree [[11], ch. 7], any circular distance function d can be represented by a planar phylogenetic network such as the one pictured in Figure 1[14]. The program SplitsTree [9] allows the automatic generation of such a network for d by computing a circular split weight function ω with d = d_{ω}.
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