The level set $G(n,m)$ comprises all unlabelled simple graphs of order $n$ and size $m$, and is partitioned into similarity classes, comprising all graphs with the same degree sequence. When graphs are ordered lexicographically by their signature, a unique numerical list of structural descriptors, the similarity classes of $G(n,m)$ occur in contiguous blocks; the ¯rst graph in each similarity class is its sentinel. The sentinel of the ¯rst similarity class in each $G(n,m)$ is determined, and shown to be the unique realization of its degree sequence. The degree sequence of the last similarity class in each $G(n,m)$ is also determined, as are the exact size range for which it has more than one realization, and the exact size range for which its sentinel has more than one component.
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