generate_BA: Simulating networks from the generalized Barabasi-Albert...

In PAFit: Generative Mechanism Estimation in Temporal Complex Networks

Description

This function generates networks from the generalized Barabási-Albert model. In this model, the preferential attachment function is power-law, i.e. A_k = k^α, and node fitnesses are all equal to 1. It is a wrapper of the more powerful function generate_net.

Usage

generate_BA(N              = 1000, 
            num_seed       = 2   , 
            multiple_node  = 1   , 
            m              = 1   ,
            alpha          = 1)

Arguments

N	Integer. Total number of nodes in the network (including the nodes in the seed graph). Default value is 1000.
num_seed	Integer. The number of nodes of the seed graph (the initial state of the network). The seed graph is a cycle. Default value is 2.
multiple_node	Positive integer. The number of new nodes at each time-step. Default value is 1.
m	Positive integer. The number of edges of each new node. Default value is 1.
alpha	Numeric. This is the attachment exponent in the attachment function A_k = k^α.

Value

The output is a PAFit_net object, which is a List contains the following four fields:

graph	a three-column matrix, where each row contains information of one edge, in the form of (from_id, to_id, time_stamp). from_id is the id of the source, to_id is the id of the destination.
type	a string indicates whether the network is "directed" or "undirected".
PA	a numeric vector contains the true PA function.
fitness	fitness values of nodes in the network. The fitnesses are all equal to 1.

Author(s)

Thong Pham [e-mail]

References

1. Albert, R. & Barabási, A. (1999). Emergence of scaling in random networks. Science, 286,509–512 (https://www.science.org/doi/10.1126/science.286.5439.509).

See Also

For subsequent estimation procedures, see get_statistics.

For other functions to generate networks, see generate_net, generate_ER, generate_BB and generate_fit_only.

Examples

  library("PAFit")
  # generate a network from the BA model with alpha = 1, N = 100, m = 1
  net <- generate_BA(N = 100)
  str(net)
  plot(net)

Example output

List of 4
 $ graph  : num [1:98, 1:3] 2 3 4 5 6 7 8 9 10 11 ...
 $ fitness: Named num [1:100] 1 1 1 1 1 1 1 1 1 1 ...
  ..- attr(*, "names")= chr [1:100] "1" "2" "3" "4" ...
 $ PA     : num [1:33] 1 1 2 3 4 5 6 7 8 9 ...
 $ type   : chr "directed"
 - attr(*, "class")= chr "PAFit_net"

PAFit documentation built on Jan. 18, 2022, 1:10 a.m.