I'm seeing seemingly contradictory information about this around. On the one hand, it seems that for undirected graphs, you need at least 3 nodes to make a cycle. On the other other, I've also seen people differentiate between trivial and non-trivial cycles.
Let's say in your directed graph you have two nodes A and B with an edge from A to B and an edge from B to A. Do you have a cycle (A, B)? And does it always count as a cycle, or would some people consider it a cycle and others not?
Also, let's say you traverse that directed graph and hit A before you hit B. Is the edge (B, A) a back edge?