  Phylogenetic networks are becoming increasingly popular in phylogenetics
since they have the ability to describe a wider range of evolutionary events
than their tree counterparts. In this paper, we study Markov models on
phylogenetic networks and their associated geometry. We restrict our attention
to large-cycle networks, networks with a single undirected cycle of length at
least four. Using tools from computational algebraic geometry, we show that the
semi-directed network topology is generically identifiable for Jukes-Cantor
large-cycle network models.
