  We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for
$N \le 26$ Majorana fermions with $q$-body interaction with $q=4,6,8$ for a
range of sparse parameter $k$. Using the peak of the Krylov complexity as a
probe, we find change in behavior as we vary $k$ for various $q$. We argue that
this captures the change from holographic to non-holographic behavior in the
sparse SYK-type models such that model is holographic for all $k \ge
k_{\text{min}}$. Our results also indicate that the Krylov complexity peak has
a holographic interpretation similar to the Lyapunov exponent.
