# degree.sequence.game

##### Generate random graphs with a given degree sequence

It is often useful to create a graph with given vertex
degrees. This is exactly what `degree.sequence.game`

does.

- Keywords
- graphs

##### Usage

```
degree.sequence.game(out.deg, in.deg = numeric(0),
method = c("simple", "vl"), ...)
```

##### Arguments

- out.deg
- Numeric vector, the sequence of degrees (for undirected
graphs) or out-degrees (for directed graphs). For undirected graphs
its sum should be even. For directed graphs its sum should be the same
as the sum of
`in.deg`

. - in.deg
- For directed graph, the in-degree sequence.
- method
- Character, the method for generating the graph. Right
now the
simple andvl methods are implemented. - ...
- Additional arguments, these are used as graph attributes.

##### Details

The

This method is not adequate if one needs to generate simple graphs with a given degree sequence. The multiple and loop edges can be deleted, but then the degree sequence is distorted and there is nothing to ensure that the graphs are sampled uniformly.

THe `in.deg`

argument to it.
The algorithm relies on first creating an initial (possibly
unconnected) simple undirected graph with the given degree sequence
(if this is possible at all). Then some rewiring is done to make the
graph connected. Finally a Monte-Carlo algorithm is used to randomize
the graph. The

##### Value

- The new graph object.

##### concept

- Degree sequence
- Configuration model

##### See Also

`erdos.renyi.game`

, `barabasi.game`

,
`simplify`

to get rid of the multiple and/or loops edges.

##### Examples

```
## The simple generator
g <- degree.sequence.game(rep(2,100))
degree(g)
is.simple(g) # sometimes TRUE, but can be FALSE
g2 <- degree.sequence.game(1:10, 10:1)
degree(g2, mode="out")
degree(g2, mode="in")
## The vl generator
g3 <- degree.sequence.game(rep(2,100), method="vl")
degree(g3)
is.simple(g3) # always TRUE
## Exponential degree distribution
## Note, that we correct the degree sequence if its sum is odd
degs <- sample(1:100, 100, replace=TRUE, prob=exp(-0.5*(1:100)))
if (sum(degs) %% 2 != 0) { degs[1] <- degs[1] + 1 }
g4 <- degree.sequence.game(degs, method="vl")
all(degree(g4) == degs)
## Power-law degree distribution
## Note, that we correct the degree sequence if its sum is odd
degs <- sample(1:100, 100, replace=TRUE, prob=(1:100)^-2)
if (sum(degs) %% 2 != 0) { degs[1] <- degs[1] + 1 }
g5 <- degree.sequence.game(degs, method="vl")
all(degree(g5) == degs)
```

*Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)*