  A graph $G=(V,E)$ is said to be a \textit{$k$-threshold graph} with
\textit{thresholds} $\theta_1<\theta_2<...<\theta_k$ if there is a map $r: V
\longrightarrow \mathbb{R}$ such that $uv\in E$ if and only if $\theta_i\le
r(u)+r(v)$ holds for an odd number of $i\in [k]$. The \textit{threshold number}
of $G$, denoted by $\Theta(G)$, is the smallest positive integer $k$ such that
$G$ is a $k$-threshold graph. In this paper, we determine the exact threshold
numbers of cycles by proving
  \[ \Theta(C_n)=\begin{cases}
  1 & if\ n=3,
  2 & if\ n=4,
  4 & if\ n\ge 5,
  \end{cases}
  \]
  where $C_n$ is the cycle with $n$ vertices.
