[Haskell-beginners] operations on cyclic data structures

I'm new to haskell and functional programming in general. One of the things I've tried to wrap my brain around is dealing with cyclic immutable data structures like the half-edge data structure. First, how would an experienced haskeller design their data structures to perform an operation on this structure? I've implemented this structure with mutable structures in c++ but when when I've asked about cyclic structures I'm pointed to research papers which overwhelm my experience in immutable data structures like those in haskell. Also how efficient could this structure be if only a small portion of the mesh is updated? Would the entire mesh need to be rebuilt? Thanks.