  Phylogenetic networks are a generalization of phylogenetic trees that allow
for the representation of non-treelike evolutionary events, like recombination,
hybridization, or lateral gene transfer. In a recent series of papers devoted
to the study of reconstructibility of phylogenetic networks, Moret, Nakhleh,
Warnow and collaborators introduced the so-called {tripartition metric for
phylogenetic networks. In this paper we show that, in fact, this tripartition
metric does not satisfy the separation axiom of distances (zero distance means
isomorphism, or, in a more relaxed version, zero distance means
indistinguishability in some specific sense) in any of the subclasses of
phylogenetic networks where it is claimed to do so. We also present a subclass
of phylogenetic networks whose members can be singled out by means of their
sets of tripartitions (or even clusters), and hence where the latter can be
used to define a meaningful metric.
