In Obsidian, the local graph has real uses, but the global one is mostly to see structure in your notes and look cool on social media.
I was researching and prototyping a graph like Obsidian's before Obsidian came out, based on the ideas in "how to take smart notes"
https://www.youtube.com/watch?v=a6yUA46ek6M
I believe the direction of UI I was exploring there has more than what graphs currently have, although I didn't have the time to build it out and I saw that the site has been offline for a while.
It was a working tool though.