Use this if you are using igraph from R
The BAmodel is a very simple stochastic algorithm for building a graph.
sample_pa( n, power = 1, m = NULL, out.dist = NULL, out.seq = NULL, out.pref = FALSE, zero.appeal = 1, directed = TRUE, algorithm = c("psumtree", "psumtreemultiple", "bag"), start.graph = NULL ) pa(...)
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 
Numeric vector, the distribution of the number of edges to
add in each time step. This argument is only used if the 
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 indegree is used. 
zero.appeal 
The ‘attractiveness’ of the vertices with no adjacent edges. See details below. 
directed 
Whether to create a directed graph. 
algorithm 
The algorithm to use for the graph generation.

start.graph 

... 
Passed to 
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 indegree 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
nonnegative 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.
sample_pa
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
.
A graph object.
Gabor Csardi csardi.gabor@gmail.com
Barabasi, A.L. and Albert R. 1999. Emergence of scaling in random networks Science, 286 509–512.
g < sample_pa(10000) degree_distribution(g)