This sounds broadly sensible. It's basically a classic normalised relational design, which is as perfect as alligators or sewing needles, but with extracted supertables for nodes and edges.

I would challenge the idea that you need these supertables, though. What those allow you to do is to write graph queries which are generic (polymorphic?) over multiple kinds of node and edge. So as well as "find me all the people who are friends with my friends", you can write "find me all the people who are friends with my friends, or who have been to a place i've been, or who own a thing i own" without using a union. Do you actually need to write queries like that?

There are two downsides to the supertables. Firstly, more complexity, although it's a minor, or at least constant-factor, amount. Secondly, a loss of type safety. If your edges are defined in a supertable, then the columns which point to the ends of the edge have to be foreign keys to the node supertable. That means they can be any type of node; there's no way to constrain particular kinds of edge to connecting particular kinds of node. That seems like a considerable drawback to me.