  The random reversal graph offers new perspectives, allowing to study the
connectivity of genomes as well as their most likely distance as a function of
the reversal rate. Our main result shows that the structure of the random
reversal graph changes dramatically at $\lambda_n=1/\binom{n+1}{2}$. For
$\lambda_n=(1-\epsilon)/\binom{n+1}{2}$, the random graph consists of
components of size at most $O(n\ln(n))$ a.s. and for
$(1+\epsilon)/\binom{n+1}{2}$, there emerges a unique largest component of size
$\sim \wp(\epsilon) \cdot 2^n\cdot n$!$ a.s.. This "giant" component is
furthermore dense in the reversal graph.
