Graph-unravelling puzzle game

Play it here!

I present a game that shows two arrangements of one simple graph. Your task is to drag around vertices on either arrangement, until they're obviously equivalent.

The game starts with a graph of four vertices. It gets harder in each round, by adding more vertices. "New graph" gives a different graph with the same number of vertices.

All the graphs are randomly generated. They will usually be planar, based on the number of edges given, but that's not guaranteed.

There are some possible variations and improvements:

• subtly change one graph, or not, and make the task be to judge if they're equivalent
• guarantee planarity, then make the task be to fully unravel just one form
• don't guarantee planarity, then make the task be to fully unravel the graph (proving it planar) or identify a Kuratowski graph (proving it non-planar)
• implement a way to drag multiple vertices in tandem, such as for multi-touch screens
• add a button to rotate one or the other entire arrangement
• match up vertices more permissively, as by something based on force-directed rendering or counting edge crossings

You may implement some of those, or demand it from me, but I call the game Done for now.