Let me give you a concrete example. I can’t post screenshots due to the presence of confidential client information, but I don’t think I’ll need to.
I make heavy use of “daily notes.” But not just “daily” notes. I also have a “monthly note” and every daily note links back to the monthly note. With a local graph, I get an otherwise unavailable view of my entire month–I see every day and because I have the local graph set to 2 links deep, I can also see, at a glance, what I did each day. In other words, the local graph provides me an incredibly useful overview and navigation point of my activities over the past month. While I haven’t done so, I could also create weekly notes for an added bit of organization.
I don’t know of any other feature that would provide this type of functionality. The above analysis also applies to, e.g., a client note, giving me an overview of what’s going on with that client. It is actually quite wonderful.
(EDIT: I’m going to see about screenshots, I’ll just do some gaussian fuzzing to protect the innocent…)
I think I may be a bit late to the party, but I would also find this feature HUGELY useful: I am using devonthink as a Zettelkasten way of curating ideas over time (I wanted to post links but not allowed, just google it then! ). I love that you forward- and backward-link notes. The whole point of method is to create small notes for ideas that link and grow over time, then when you need to write a piece, you look at your notes, and follow the links. Having a visualization of the graph would be extremely powerful in this context.
The method is quite simple: one creates a mini note for singleton idea, and link it to related ideas, creating over time a web of ideas. When the time comes to write a paper, it is then only a matter of following the trail of ideas. (https://en.wikipedia.org/wiki/Zettelkasten)