The BA-model 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", "psumtree-multiple", "bag"), start.graph = NULL)pa(...)
Number of vertices.
The power of the preferential attachment, the default is one, ie. linear preferential attachment.
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.
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.
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.
Logical, if true the total degree is used for calculating the citation probability, otherwise the in-degree is used.
The ‘attractiveness’ of the vertices with no adjacent edges. See details below.
Whether to create a directed graph.
The algorithm to use for the graph generation.
psumtree uses a partial prefix-sum tree to generate the graph, this
algorithm can handle any power and zero.appeal values and
never generates multiple edges. psumtree-multiple also uses a
partial prefix-sum tree, but the generation of multiple edges is allowed.
Before the 0.6 version igraph used this algorithm if power was not
one, or zero.appeal was not one. bag is the algorithm that
was previously (before version 0.6) used if power was one and
zero.appeal was one as well. It works by putting the ids of the
vertices into a bag (mutliset, really), exactly as many times as their
(in-)degree, plus once more. Then the required number of cited vertices are
drawn from the bag, with replacement. This method might generate multiple
edges. It only works if power and zero.appeal are equal one.
NULL or an igraph graph. If a graph, then the
supplied graph is used as a starting graph for the preferential attachment
algorithm. The graph should have at least one vertex. If a graph is supplied
here and the out.seq argument is not NULL, then it should
contain the out degrees of the new vertices only, not the ones in the
start.graph.
Passed to sample_pa.
A graph object.
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
$$P[i] \sim k_i^\alpha+a$$ 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.
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.
Barabasi, A.-L. and Albert R. 1999. Emergence of scaling in random networks Science, 286 509--512.
# NOT RUN {
g <- sample_pa(10000)
degree_distribution(g)
# }
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