Comment by ColinWright

In the version I'm discussing, both parties already know the graph, so your point (B) seems irrelevant. The interrogator needs to know the graph in order to specify an edge (and to know that they've done so), so I'm not sure of the precise version you are thinking of.

Put point (A) is relevant ... certainly each call only provides a small amount of additional confidence, so a lot of calls might be required. Even so, the system seems sound to me, and I'd appreciate any details of ways in which it is not.

See also my comment here: https://news.ycombinator.com/item?id=46121137

That gives more detail of the setup, and how it can be implemented digitally.