Hi @bdj68, welcome to the Supernotes Community! 
Regarding the graph view, it should already appear almost the same between sessions if no changes have been made to the hierarchy. However, it does not currently store any modifications you make, such as moving nodes around, as you’ve noticed.
While it could be useful to implement this feature, it might not be practical for most hierarchies since they tend to change frequently. And would really only apply to rare static hierarchies that remain unchanged over time.
Thanks for sharing your thoughts, if anyone would like this please like Ben’s post above. A possible alternative is the Tabletop Whiteboard View, as discussed in this thread 