  The Burge correspondence yields a bijection between simple labelled graphs
and semistandard Young tableaux of threshold shape. We characterize the simple
graphs of hook shape by peak and valley conditions on Burge arrays. This is the
first step towards an analogue of Schensted's result for the RSK insertion
which states that the length of the longest increasing subword of a word is the
length of the largest row of the tableau under the RSK correspondence.
Furthermore, we give a crystal structure on simple graphs of hook shape. The
extremal vectors in this crystal are precisely the simple graphs whose degree
sequence are threshold and hook-shaped.
