We extend the work of Wu and Small who introduced symmetry-adapted basis defect patterns (BDPs) for systematic analysis of the effects of random static energy disorder (diagonal or off-diagonal) on the excitonic level structure of cyclic C-n arrays of chromophores. Examples include the B850 and B875 rings of bacteriochlorophyll (BChl) molecules associated with the LH2 and LH1 antenna complexes of purple bacteria for which, so far, n = 8, 9, and 16. Calculation of the localization/extendedness (chromophore occupation number) patterns and participation numbers of the exciton levels reveals that the effects of random disorder on the exciton levels that contribute to the critically important B850 or B875 absorption band can be understood in terms of a single BDP of e(1) symmetry ("hidden correlation" effect). This is a consequence of the structures of the complexes, the complexes falling in the weak disorder regime and the strict symmetry selection rules that govern the couplings between zero-order exciton levels by BDPs. The above finding greatly simplifies computational studies on the effects of random disorder on the spectroscopic properties of the above bands. Our results show that interpretation of electric field (Stark) effects on the B850 and B875 absorption bands must include the effects of energy disorder. Similarities and differences between the effects of diagonal and off-diagonal energy disorder are discussed as is the relevance of oar findings to the superradiant properties of the LH complexes.