Is this a partially ordered set?

Question

I was wondering if partially ordered sets could have loops in their diagrams. For example isn't the $S=\{1,2,3\}$ and relation $R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(3,1)\}$ a partially ordered set that has a cycle? $R$ is reflexive, antisymmetric and transitive.

Answer 1

Transitivy fails for your relation $R$.

As for loops on the diagram, that is not possible due to transitivy, that should become apparent from the algorithm to draw diagrams I describe in this answer.