SequenceGraph(L) returns a graph with the specified degree sequence L, if such a graph exists. It raises an exception otherwise.

To check if a graph with given degree sequence exists, use IsGraphicSequence.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$L≔\left[3\,2\,4\,2\,3\,4\,5\,7\right]$

$L≔\left[3\,2\,4\,2\,3\,4\,5\,7\right]$

$\mathrm{IsGraphicSequence}\left(L\right)$

$\mathrm{true}$

$G≔\mathrm{SequenceGraph}\left(L\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 8\; vertices\; and\; 15\; edges}$

$\mathrm{sort}\left(\mathrm{DegreeSequence}\left(G\right)\right)$

$\left[2\,2\,3\,3\,4\,4\,5\,7\right]$

Hakimi S., "On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph." I, Journal of SIAM, 10(3) (Sept 1962), pp. 496-506