Chromosome aberrations are large-scale illegitimate rearrangements of the genome. They are indicative of DNA damage and informative about damage processing pathways. Despite extensive investigations over many years, the mechanisms underlying aberration formation remain controversial. New experimental assays such as multiplex fluorescent in situ hybridyzation (mFISH) allow combinatorial "painting" of chromosomes and are promising for elucidating aberration formation mechanisms. Recently observed mFISH aberration patterns are so complex that computer and graph-theoretical methods are needed for their full analysis. An important part of the analysis is decomposing a chromosome rearrangement process into "cycles." A cycle of order n, characterized formally by the cyclic graph with 2n vertices, indicates that n chromatin breaks take part in a single irreducible reaction. We here describe algorithms for computing cycle structures from experimentally observed or computer-simulated mFISH aberration patterns. We show that analyzing cycles quantitatively can distinguish between different aberration formation mechanisms. In particular, we show that homology-based mechanisms do not generate the large number of complex aberrations, involving higher-order cycles, observed in irradiated human lymphocytes.