  We define the \emph{occurrence graph} $G_p(\pi$) of a pattern $p$ in a
permutation $\pi$ as the graph with the occurrences of $p$ in $\pi$ as vertices
and edges between the vertices if the occurrences differ by exactly one
element. We then study properties of these graphs. The main theorem in this
paper is that every \emph{hereditary property} of graphs gives rise to a
\emph{permutation class}.
