  Recent work by Arpin, Chen, Lauter, Scheidler, Stange, and Tran counted the
number of cycles of length $r$ in supersingular $\ell$-isogeny graphs. In this
paper, we extend this work to count the number of cycles that occur along the
spine. We provide formulas for both the number of such cycles, and the average
number as $p \to \infty$, with $\ell$ and $r$ fixed. In particular, we show
that when $r$ is not a power of $2$, cycles of length $r$ are
disproportionately likely to occur along the spine. We provide experimental
evidence that this result holds in the case that $r$ is a power of $2$ as well.
