I use local graph views far more than vault graph views, as I find the former to be a helpful way to organize notes and see which other pages referenced/are referenced by them, in case I need to expand and find more information.
Many of my notes are split between self-written organization notes and paper-specific notes, which I use for different tasks. While graph view has options to group by tag, it is annoying to need to reapply all grouping/graph settings each time I open a notes’ local graph.
Proposed solution
Allow modification of default local graph settings, in the same manner as global graphs.
Persistent Graph only functions for global graphs and not local ones. I suppose I could put the request to keep node settings for local graphs instead.