Euler 857 - please clarify the notion of a cycle

[FritzF]

To me, the notion of "cycle" is unclear in this problem.
I do not see the difference between the second case on the top row vs the second case on the bottom row.

[FritzF]

I withdraw the question, assuming that cycles are meant to go through at least 3 vertices.

[__ngn__]

assuming that cycles are meant to go through at least 3 vertices

A 2-cycle always satisfies the condition for beauty, as it can only be made of the two arrows in a blue-red multi-edge. But, I guess, the second sample graph in the bottom row has more cycles, consisting of 3 vertices: the red-green-brown cycle and the blue-brown-green cycle. Those don't satisfy the condition.

If this interpretation is correct, it may be more clear if green and brown edges are described as "bidirectional" instead of "undirected".