Cycle Graph of Order 2 is Multigraph

Theorem

Let $C_2$ denote the cycle graph of order $2$.

Then $C_2$ is a multigraph.

Proof

By definition, the vertex set of $C_2$ is doubleton, $\set {v_1, v_2}$, say.

By definition of cycle graph, there is a circuit $v_1 v_2 v_1$.

That is:

there exists an edge which is incident to $v_1$ and $v_2$

there exists an edge which is incident to $v_2$ and $v_1$

That is, there are $2$ edges which are both incident to $v_1$ and $v_2$

Hence the result by definition of multigraph.

$\blacksquare$