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.
