[danbruc]

IANAP and I don't know about Wolfram's ideas but some thoughts anyway. Graphs are incredible general, like sets, you can model almost everything with them and that looks like a bad thing to me if you want explanatory power.

The very few basic principles of relativity and quantum mechanics like the frame independence of the speed of light and unitarity put very strict constraints on possible theories, for example only particles with spin 0, 1/2, 1, 3/2 and 2 are possible. String theory on the other hand turned out to allow a ridicules large number - like 10 to the 500 - of different vacuum states and therefore you can have more or less whatever you want by fixing parameters in this way or another.

I may of course be totally wrong but that were my first thoughts, unless you can somehow derive a lot of constraints, using graphs to explain the universe seems a way to general idea to me. But again, I never read anything about Wolfram's ideas, at least nothing I can remember.