A breath of knowledge/science/maths at El Reg! Bravo!
I'm fascinated by these newfangled graph engines. We used to have a CODASYL networked database back in the 70s that handled a lot of the cases that Neo4J/etc. does now - not as slickly of course.
Another problem for the yanks: Which state do you have to start from if you want to form a path that only visits every state once? There are several solutions so it's best to think of a commonality between all the solutions. (https://www.cs.cmu.edu/~bryant/boolean/maps.html).