  In this paper, we shall recall and arrange the relationship between
hyperbolic elements and parabolic subalgebras at first. And then, we shall
classify all the compatible parabolic subalgebras containing a $\tau$-stable
Borel subalgebra for complex symmetric pairs
$(\mathfrak{g},\mathfrak{g}^\tau)$, where $\tau$ is a involutive automorphism
of $\mathfrak{g}$.
