Can an undirected graph cycle have only two vertices? 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?
once this doubt occurred to me. It seams trivial, but when I am on doubt I always look for strong definitions, so this is what I found.

I will cite the definition of cycle in the book of Diestel, Graph Theory [http://www.flooved.com/reader/3447?no-redirect#16]

Page 8: "If $P=x_0 ... x_{k-1}$ is a path and $k \geq 3$, then the graph $C:=P+x_{k-1}x_0$
is called a cycle."

Thus $cdc$ is not a cycle because $cd$ is not a path with more than two vertices.

But what about $cdcdc$? It would be a path if $cdcd$ would. However, according Diestel definition of path (page 6) all vertices of a path are different.
once this doubt occurred to me. It seams trivial, but when I am on doubt I always look for strong definitions, so this is what I found.

I will cite the definition of cycle in the book of Diestel, Graph Theory [http://www.flooved.com/reader/3447?no-redirect#16]

Page 8: "If $P=x_0 ... x_{k-1}$ is a path and $k \geq 3$, then the graph $C:=P+x_{k-1}x_0$
is called a cycle."

Thus $cdc$ is not a cycle because $cd$ is not a path with more than two vertices.

But what about $cdcdc$? It would be a path if $cdcd$ would. However, according Diestel definition of path (page 6) all vertices of a path are different.