  We obtain results on the limiting distribution of the six-length of a random
functional graph, also called a functional digraph or random mapping, with
given in-degree sequence. The six-length of a vertex $v\in V$ is defined from
the associated mapping, $f:V\to V$, to be the maximum $i\in V$ such that the
elements $v, f(v), \ldots, f^{i-1}(v)$ are all distinct. This has relevance to
the study of algorithms for integer factorisation.
