barabasi.game {igraph} | R Documentation |
The BA-model is a very simple stochastic algorithm for building a graph.
barabasi.game(n, power = 1, m = NULL, out.dist = NULL, out.seq = NULL, out.pref = FALSE, zero.appeal = 1, directed = TRUE, time.window = NULL)
n |
Number of vertices. |
power |
The power of the preferential attachment, the default is one, ie. linear preferential attachment. |
m |
Numeric constant, the number of edges to add in each time
step This argument is only used if both out.dist and
out.seq are omitted or NULL. |
out.dist |
Numeric vector, the distribution of the number of
edges to add in each time step. This argument is only used if the
out.seq argument is omitted or NULL. |
out.seq |
Numeric vector giving the number of edges to add in each time step. Its first element is ignored as no edges are added in the first time step. |
out.pref |
Logical, if true the total degree is used for calculating the citation probability, otherwise the in-degree is used. |
zero.appeal |
The ‘attractiveness’ of the vertices with no adjacent edges. See details below. |
directed |
Whether to create a directed graph. |
time.window |
Integer constant, if given only edges added in the
previous time.window time steps are counted as the basis of
preferential attachment. |
This is a simple stochastic algorithm to generate a graph. It is a discrete time step model and in each time step a single vertex is added.
We start with a single vertex and no edges in the first time step. Then we add one vertex in each time step and the new vertex initiates some edges to old vertices. The probability that an old vertex is chosen is given by
P[i] ~ k[i]^alpha + a
where k[i] is the in-degree of vertex i in the
current time step (more precisely the number of adjacent edges of
i which were not initiated by i itself) and
alpha and a are parameters given by the
power
and zero.appeal
arguments.
The number of edges initiated in a time step is given by the m
,
out.dist
and out.seq
arguments. If out.seq
is
given and not NULL then it gives the number of edges to add in a
vector, the first element is ignored, the second is the number of
edges to add in the second time step and so on. If out.seq
is
not given or null and out.dist
is given and not NULL then it is
used as a discrete distribution to generate the number of edges in
each time step. Its first element is the probability that no edges
will be added, the second is the probability that one edge is added,
etc. (out.dist
does not need to sum up to one, it normalized
automatically.) out.dist
should contain non-negative numbers
and at east one element should be positive.
If both out.seq
and out.dist
are omitted or NULL then
m
will be used, it should be a positive integer constant and
m
edges will be added in each time step.
barabasi.game
generates a directed graph by default, set
directed
to FALSE
to generate an undirected graph. Note
that even if an undirected graph is generated k[i] denotes
the number of adjacent edges not initiated by the vertex itself and
not the total (in- + out-) degree of the vertex, unless the
out.pref
argument is set to TRUE
.
If the time.window
argument is not NULL then k[i] is
the number of adjacent edges of i added in the previous
time.window
time steps.
Note that barabasi.game
might generate graphs with multiple
edges.
A graph object.
Gabor Csardi csardi@rmki.kfki.hu
Barabasi, A.-L. and Albert R. 1999. Emergence of scaling in random networks Science, 286 509–512.
g <- barabasi.game(10000) degree.distribution(g)