  The cyclic graph of a group $G$ is the graph whose vertices are the
nonidentity elements of $G$ and whose edges connect distinct elements $x$ and
$y$ if and only if the subgroup $\langle x,y\rangle$ is cyclic. We obtain
information about the cyclic graph of $2$-Frobenius groups. The cyclic graph of
a $2$-Frobenius group is disconnected. In this paper, we determine the number
of connected components of the cyclic graph of any $2$-Frobenius group.
