  Hybridization networks are representations of evolutionary histories that
allow for the inclusion of reticulate events like recombinations,
hybridizations, or lateral gene transfers. The recent growth in the number of
hybridization network reconstruction algorithms has led to an increasing
interest in the definition of metrics for their comparison that can be used to
assess the accuracy or robustness of these methods. In this paper we establish
some basic results that make it possible the generalization to tree-child time
consistent (TCTC) hybridization networks of some of the oldest known metrics
for phylogenetic trees: those based on the comparison of the vectors of path
lengths between leaves. More specifically, we associate to each hybridization
network a suitably defined vector of `splitted' path lengths between its
leaves, and we prove that if two TCTC hybridization networks have the same such
vectors, then they must be isomorphic. Thus, comparing these vectors by means
of a metric for real-valued vectors defines a metric for TCTC hybridization
networks. We also consider the case of fully resolved hybridization networks,
where we prove that simpler, `non-splitted' vectors can be used.
