  We use methods from spectral graph theory to obtain bounds on the number of
incidences between $k$-planes and $h$-planes in $\mathbb{F}_q^d$ which
generalize a recent result given by Bennett, Iosevich, and Pakianathan (2014).
More precisely, we prove that the number of incidences between a set
$\mathcal{P}$ of $k$-planes and a set $\mathcal{H}$ of $h$-planes with $h\ge
2k+1$, which is denoted by $I(\mathcal{P},\mathcal{H})$, satisfies \[\left\vert
I(\mathcal{P},\mathcal{H})-\frac{|\mathcal{P}||\mathcal{H}|}{q^{(d-h)(k+1)}}\right\vert
\lesssim q^{\frac{(d-h)h+k(2h-d-k+1)}{2}}\sqrt{|\mathcal{P}||\mathcal{H}|}. \]
