Check if a degree sequence is valid for a multi-graph

is_degseq() checks whether the given vertex degrees (in- and out-degrees 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.

Usage

is_degseq(out.deg, in.deg = NULL)

Arguments

out.deg

Integer vector, the degree sequence for undirected graphs, or the out-degree sequence for directed graphs.

in.deg

NULL or an integer vector. For undirected graphs, it should be NULL. For directed graphs it specifies the in-degrees.

Value

A logical scalar.

References

Z Király, Recognizing graphic degree sequences and generating all realizations. TR-2011-11, Egerváry Research Group, H-1117, Budapest, Hungary. ISSN 1587-4451 (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).

See also

Other graphical degree sequences: is_graphical()

Author

Tamás Nepusz ntamas@gmail.com and Szabolcs Horvát szhorvat@gmail.com

Examples

g <- sample_gnp(100, 2 / 100)
is_degseq(degree(g))
#> [1] TRUE
is_graphical(degree(g))
#> [1] TRUE