[hughesjj]

Yes, but in an UndirectedGraph you can do loops easy peasy. A->b->a->b etc. if you have a tree with a parent node, then the tree (A{children:[b], parent: null}, B{children:[], parent: A}) still may allow for this behavior (graph representation unions parent and children since a parent in tree parlence is basically 'incoming-edges' in graph parlence while children is 'outgoing-edges')

I was trying to find terminology for something Like 'all possible paths between these two nodes contain exactly one Hamiltonian sub-path' but I think that's a bit of a circular definition

All that said I'm running off 3 hours of sleep and about to recoup so that probably explains my non constructive comments here