PAFit (version 1.2.10)

generate_BB: Simulating networks from the Bianconi-Barabasi model

Description

This function generates networks from the Bianconi-Barabási model. It is a ‘preferential attachment with fitness’ model. In this model, the preferential attachment function is linear, i.e. \(A_k = k\), and node fitnesses are sampled from some probability distribution.

Usage

generate_BB(N              = 1000   , 
            num_seed       = 2      , 
            multiple_node  = 1      , 
            m              = 1      ,
            mode_f         = "gamma", 
            s              = 10     )

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 name of each value is the ID of the node.

Arguments

The parameters can be divided into two groups.

The first group specifies basic properties of the network:

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.

The final group of parameters specifies the distribution from which node fitnesses are generated:

mode_f

String. Possible values:"gamma", "log_normal" or "power_law". This parameter indicates the true distribution for node fitness. "gamma" = gamma distribution, "log_normal" = log-normal distribution. "power_law" = power-law (pareto) distribution. Default value is "gamma".

s

Non-negative numeric. The inverse variance parameter. The mean of the distribution is kept at \(1\) and the variance is \(1/s\) (since node fitnesses are only meaningful up to scale). This is achieved by setting shape and rate parameters of the Gamma distribution to \(s\); setting mean and standard deviation in log-scale of the log-normal distribution to \(-1/2*log (1/s + 1)\) and \((log (1/s + 1))^{0.5}\); and setting shape and scale parameters of the pareto distribution to \((s+1)^{0.5} + 1\) and \((s+1)^{0.5}/((s+1)^{0.5} + 1)\). If s is 0, all node fitnesses \(\eta\) are fixed at 1 (i.e., Barabási-Albert model). The default value is 10.

Author

Thong Pham

References

1. Bianconni, G. & Barabási, A. (2001). Competition and multiscaling in evolving networks. Europhys. Lett., 54, 436 (tools:::Rd_expr_doi("10.1209/epl/i2001-00260-6")).

See Also

For subsequent estimation procedures, see get_statistics.

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

Examples

  library("PAFit")
  # generate a network from the BB model with alpha = 1, N = 100, m = 1
  # The inverse variance of the Gamma distribution of node fitnesses is s = 10
  net <- generate_BB(N = 100,m = 1,mode = 1, s = 10)
  str(net)
  plot(net)