On the same topics, this is Aaron David Fairbanks Bongard problem n.42. Try to write your solution (with a spoiler if you want). I'll give my solution under a spoiler in few hours.

For more info about Bongard problems in general take a look at my first messages:
https://mathstodon.xyz/@leonardom/116110015131667314
https://mathstodon.xyz/@leonardom/116110093951382315

#bongardproblem #mathpuzzle #puzzle #visualmath

@leonardom My guess would be that the set on the left consist of graphs which have at least one cycle that visits all nodes. The set on the right consists of graphs which do not have such a cycle.
@seanreid isn't this a cycle for you (from box 9)?
@leonardom no, what you've drawn will visit the center node twice
@seanreid so what you're referring to is a specific type of path/cycle (that has a specific name) :-)
Path (graph theory) - Wikipedia

@leonardom ooo this seems better suited- a Hamiltonian cycle perhaps?

https://en.wikipedia.org/wiki/Hamiltonian_path?wprov=sfti1

Hamiltonian path - Wikipedia

@leonardom pardon my ignorance on this topic, but this is fun guessing
@seanreid no need to apologize. These Bongard problems are means to learn. Your last answer was right.