  The Preisach graph is a directed graph associated with a permutation
$\rho\in{\cal S}_N$. We give an explicit bijection between its vertices and
increasing subsequences of $\rho$ with the property that the length of a
subsequence equals to the degree of nesting of the corresponding vertex inside
a hierarchy of cycles and sub-cycles of the graph. As a consequence, the
nesting degree of the Preisach graph equals the length of the longest
increasing subsequence.
