# degree.sequence.game

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Percentile

##### 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 = NULL,
method = c("simple", "vl", "simple.no.multiple"), ...)
##### 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. By default this is NULL and an undirected graph is created.
method
Character, the method for generating the graph. Right now the simple, simple.no.multiple and vl methods are implemented.
...
Additional arguments, these are used as graph attributes.
##### Details

The simple method connects the out-stubs of the edges (undirected graphs) or the out-stubs and in-stubs (directed graphs) together. This way loop edges and also multiple edges may be generated. 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 simple.no.multiple method is similar to simple, but tries to avoid multiple and loop edges and restarts the generation from scratch if it gets stuck. It is not guaranteed to sample uniformly from the space of all possible graphs with the given sequence, but it is relatively fast and it will eventually succeed if the provided degree sequence is graphical, but there is no upper bound on the number of iterations. The vl method is a more sophisticated generator. The algorithm and the implementation was done by Fabien Viger and Matthieu Latapy. This generator always generates undirected, connected simple graphs, it is an error to pass 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 vl samples from the undirected, connected simple graphs unformly. See http://www-rp.lip6.fr/~latapy/FV/generation.html for details.

##### Value

• The new graph object.

##### concept

• Degree sequence
• Configuration model

erdos.renyi.game, barabasi.game, simplify to get rid of the multiple and/or loops edges.

##### Aliases
• degree.sequence.game
##### 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 0.6.5-2, License: GPL (>= 2)

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