> I have a theory that intelligence is not so much about the knowledge of facts but about the relations between those facts (more about the edges than the nodes)

Indeed, I have reached a similar conclusion. For me, the brain is a huge pattern-matching machine, therefore it needs to have patterns to be able to match anything, that's where the knowledge comes in. In addition, the more "patterns" it has, the faster it works. And it can come up with new patterns (and infer their relationships) on its own.

I have noticed that many people that are perceived as "slow" or "dumb" are just unfamiliar with concepts, no matter how trivial they seem. So their brains have to work overtime to try to understand something that is "intuitive" for others - probably something everyone struggled with at some point of their lives, perhaps as children.

I wish I could have data to back this up, but I only have anecdotal evidence.