# is.degree.sequence

##### Degree sequences of graphs

These functions decide whether a sequence (or two, if the graph is directed) of integers can be realized as vertex degrees by a graph or simple graph.

- Keywords
- graphs

##### Usage

```
is.degree.sequence (out.deg, in.deg = NULL)
is.graphical.degree.sequence (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 undireted graphs, it should be`NULL`

. For directed graphs it specifies the in-degrees.

##### Details

`is.degree.sequence`

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.

`is.graphial.degree.sequence`

determines whether the given vertex
degrees (in- and out-degrees for directed graphs) can be reliazed in a
simple graph, i.e. a graph without multiple or loop edges.

##### Value

- A logical scalar.

##### concept

Degree sequence

##### References

Hakimi SL: On the realizability of a set of integers as degrees of the
vertices of a simple graph. *J SIAM Appl Math* 10:496-506, 1962.
PL Erdos, I Miklos and Z Toroczkai: A simple Havel-Hakimi type algorithm
to realize graphical degree sequences of directed graphs.
*The Electronic Journal of Combinatorics* 17(1):R66, 2010.

##### Examples

```
g <- erdos.renyi.game(100, 2/100)
is.degree.sequence(degree(g))
is.graphical.degree.sequence(degree(g))
```

*Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)*