Use this if you are using igraph from R
is_degseq
checks whether the given vertex degrees (in and
outdegrees for directed graphs) can be realized by a graph. Note that the
graph does not have to be simple, it may contain loop and multiple edges.
For undirected graphs, it also checks whether the sum of degrees is even.
For directed graphs, the function checks whether the lengths of the two
degree vectors are equal and whether their sums are also equal. These are
known sufficient and necessary conditions for a degree sequence to be valid.
is_degseq(out.deg, in.deg = NULL)
out.deg 
Integer vector, the degree sequence for undirected graphs, or the outdegree sequence for directed graphs. 
in.deg 

A logical scalar.
Tamas Nepusz ntamas@gmail.com and Szabolcs Horvat szhorvat@gmail.com
Z Kiraly, Recognizing graphic degree sequences and generating all realizations. TR201111, Egervary Research Group, H1117, Budapest, Hungary. ISSN 15874451 (2012).
B. Cloteaux, Is This for Real? Fast Graphicality Testing, Comput. Sci. Eng. 17, 91 (2015).
A. Berger, A note on the characterization of digraphic sequences, Discrete Math. 314, 38 (2014).
G. Cairns and S. Mendan, Degree Sequence for Graphs with Loops (2013).
Other graphical degree sequences:
is_graphical()
g < sample_gnp(100, 2/100) is_degseq(degree(g)) is_graphical(degree(g))