degree.sequence.game {igraph} | R Documentation |
It is often useful to create a graph with given vertex
degrees. This is exactly what degree.sequence.game
does.
degree.sequence.game(out.deg, in.deg = numeric(0), method = c("simple", "vl"), ...)
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” and “vl” methods are implemented. |
... |
Additional arguments, these are used as graph attributes. |
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 “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.
The new graph object.
Gabor Csardi csardi@rmki.kfki.hu
erdos.renyi.game
, barabasi.game
,
simplify
to get rid of the multiple and/or loops edges.
## 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)