PAFit (version 1.2.10)

generate_BA: Simulating networks from the generalized Barabasi-Albert model

Description

This function generates networks from the generalized Barabási-Albert model. In this model, the preferential attachment function is power-law, i.e. \(A_k = k^\alpha\), 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)

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 \(1\).

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 \(A_k = k^\alpha\).

Author

Thong Pham

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)