My mistake was thinking that he was proposing something about the nature of physical reality. Ie. that physical reality was literally a network of interconnected nodes at its fundamental level. Something along the lines of macroscopic -> atomic -> sub atomic -> wolfram-nodal. A la, string theory, et. al.
From the replies here, I gather this has nothing to do with physical reality.. he's not describing how this nodal network might be implemented in reality... just that it must be, because the predictions come out correctly.
It's "nothing" as far as we're concerned but despite being intangible, despite being nothing, it has rules and laws that govern matter that traverses it just like every other part of our universe. So what is space itself? What is it composed of? You can't take a quick step outside of the universe to get a look under the hood because you are part of the universe. You can only talk about it in terms of it's rules and behavior–in the abstract.
If we get fundamental enough, we can go below geometry, into algebra.
For a less abstract example, what's the radius of an electron in modern physics?
No, no, no! These graphs are meant to be more fundamental than spacetime. They can change in the sense that there are algebraic rules for stepping them from one state to another, but this step isn't in our time. Our space and time should be generated by operating on these graphs (let's say "stepping" them, as long as we remember that it's not a time-step in our spacetime, but just an algebraic operation).
EDIT> I should say that this whole idea is a model. The question of whether a model is real or not independent of the system being modeled is a philosophical one that we can't really do justice to in an HN comment thread.
It isn't as if there is an actual line connecting two dots across space.
It's just, there's a set of "points" (there doesn't need to be any things about these "points" other than that they are distinct. You could think of them as urelements I guess.), and another set of "edges", which are each a set of two elements from the first set.
A pair of "points" are "connected" by an "edge" iff the set comprised of those two "points" is in the second set.
This doesn't need a notion of space to work, unless you need like, an idea of space to have collections of things. So unless "the collection of odd numbers" needs an idea of space, then graphs don't need space.