I've always seen cycles in graphs described as containing three or more vertices. I had a question posed to me today that I now pose to you: Is it valid to consider a pair of vertices connected by a single edge in an undirected graph to be a cycle?
More concretely, given the following undirected graph:
a---b \ / c | d
Obviously, (c, b, a, c) is a cycle. Is (c, d, c)? Why or why not?