  In a previous work, we gave a metric on the class of semibinary tree-sibling
time consistent phylogenetic networks that is computable in polynomial time; in
particular, the problem of deciding if two networks of this kind are isomorphic
is in P. In this paper, we show that if we remove the semibinarity condition
above, then the problem becomes much harder. More precisely, we proof that the
isomorphism problem for generic tree-sibling time consistent phylogenetic
networks is polynomially equivalent to the graph isomorphism problem. Since the
latter is believed to be neither in P nor NP-complete, the chances are that it
is impossible to define a metric on the class of all tree-sibling time
consistent phylogenetic networks that can be computed in polynomial time.
