Page-Relative Local-Graph Filtering
Right now, you can only filter the local graph globally – the filter applies to all pages.
I’d find it useful if there was an option to also filter the local graph for individual pages separately such that, when I visit different pages, different filters are automatically applied.
How this could work
On a page, in the local graph menu, there is an option to add a local search field underneath the global search field. The local search field overrides the global one – while the local field is active, the global one is disabled for that page. Every time you visit the page, the local filter is automatically applied.