"Cyclicity" vs. "cyclicality"

There is no difference between the two words.

In Merriam-Webster Unabridged (subscription required), the definition of cyclicality refers to the definition of cyclicity, meaning that they are effectively the same word, sharing the same definition:

cyclicity, n. : the quality or state of being cyclic

The fact that the definition of cyclicality refers to cyclicity tends to imply that cyclicity is the preferred form:

Candy sales demonstrate a monthly cyclicity.

Using a sentence construction which forces you to use words that are unfamiliar is a bad decision, and using more familiar words is a better choice.

I can see that candy sales are cyclical. People are buying on average more at the beginning of the month than at the end of the it.

To me cyclicity describes whether or not something has cycles, whereas cyclicality describes whether it is composed of cycles.

So in the first case, I expect the structure to merely contain a cycle (so it's not completely free of cycles), whereas in the second, I expect cycles to be a notable or even defining characteristic of the structure.

In your example, the proper word would be cyclicity, since the presence of cycles is an attribute that happened to exist, rather than being a fundamental part of what you're describing.