Prove that any directed cycle in the graph of a partial order must only involve one node So I have the question:

Prove that any directed cycle in the graph of a partial order must only involve one node.

So I know that a partial order must be transitive, antisymmetric, and reflective, but from there I am pretty lost. I also know that any path of one or more edges from a node to itself is a directed cycle, but from there I am having trouble connecting everything.

I kind of need help as to where to start thinking, and the first step as to how to answer this question.
I'm assuming your partial orders are of the type "$a \leq b$" rather than of the type "$a &lt; b$", though the proof is very similar to both cases. Each edge $a \to b$ in the graph corresponds to an inequality $a \leq b$. Now suppose you had a triangle $a \to b \to c \to a$. Such a triangle would imply
$$a \leq b \leq c \leq a, $$
which has some implications since $\leq$ is a partial order. The case of longer (or shorter) cycles is similar.