Cycles in revealed preference data are often interpreted as fundamental units of choice-theoretic inconsistency. We fully characterize the manner in which the structure of a choice environment can lead to non-trivial dependence relations between cyclic choice patterns in data. We show that for any finite data set, while there may not be a unique maximal independent collection of choice cycles that explain the entirety of the inconsistency, the size of any such collection of cycles is well-defined. We utilize this to provide a means of controlling for the influence of experimental structure in the construction of inconsistency indices for choice data.