The local graph is an amazing tool to see how notes connect. However, once you increase depth, it quickly becomes a bit overwhelming. There will always be notes (e.g. Daily Notes, Concepts, Meeting Notes) that might connect different topics, but you’re not actually looking for them. You can currently filter them out completely, but this also cuts off anything they might form a path to.
My personal use-case is an extreme example. My evergreen notes often have summary-style titles. As such, to make discovery of connections possible, I heavily rely on second order links through shared concepts or other “hooks” to find linked ideas. A lot of these hooks only connect to the center node, waiting to become useful in the future. For longer or broader notes clutter is a serious problem.
It could be super helpful if there ways to simplify the graph based on what you’re looking for. My dream example would be that from a new note I’ve just written, I set #Evergreen as a search goal, with e.g. depth 3. At that point, Obsidian would create the local graph it currently does, and then prune all paths that do not lead to a note tagged with #Evergreen in 3 steps or less, but preserve all paths that do. Then the local graph becomes much more actionable, only showing paths that lead somewhere, rather than only the obvious paths, or absolutely everything.
A (in my mind) smaller but related request, that would help my personal use case immensely already, would be if the “Existing Notes Only” would preserve paths leading to existing notes but grey out / hide non-existing nodes on the way.
To illustrate both requests, imagine I have a note [[Carbon Capture is the Future]], and a note [[Carbon Capture is Overpriced]], linked by a mention of [[Carbon Capture]]. I normally do not actually create [[Carbon Capture]]. The second note also mentions [[Expensive]] (just making things up). Toggling the Existing Notes Only with Depth 2 right now would break the link between these notes. Under the proposed, this link would be preserved, but the single link to [[Expensive]] would vanish.
Right now I mainly just stare at the local graph a lot, try to set colors to be smart, and refactor notes to not link to too many concepts (and subdivide concepts once too many notes link to them).