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 first graph in each similarity class is its sentinel. The sentinel of the first 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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