The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, i.e. the minimal number of rearrangements needed to transform one genome into another. We interpret this distance in topological terms and relate it to the random matrix theory. Namely, the number of genomes at a given 2-break distance from a fixed one (the Hultman number) is represented by a coefficient in the genus expansion of a matrix integral over the space of complex matrices with the Gaussian measure. We study generating functions for the Hultman numbers and prove that the 2-break distance distribution is asymptotically normal.