PAFit (version 1.2.10)

Jeong: Jeong's method for estimating the preferential attachment function

Description

This function estimates the preferential attachment function by Jeong's method.

Usage

Jeong(net_object                               , 
      net_stat  = get_statistics(net_object)   , 
      T_0_start = 0                            ,
      T_0_end   = round(net_stat$T * 0.75)     ,
      T_1_start = T_0_end + 1                  ,
      T_1_end   = net_stat$T                   ,
      interpolate = FALSE)

Value

Outputs an PA_result object which contains the estimated attachment function. In particular, it contains the following field:

• k and A: a degree vector and the estimated PA function.

• center_k and theta: when we perform binning, these are the centers of the bins and the estimated PA values for those bins.

• g: the number of bins used.

• alpha and ci: alpha is the estimated attachment exponenet \(\alpha\) (when assume \(A_k = k^\alpha\)), while ci is the confidence interval.

• loglinear_fit: this is the fitting result when we estimate \(\alpha\).

Arguments

net_object

an object of class PAFit_net that contains the network.

net_stat

An object of class PAFit_data which contains summerized statistics needed in estimation. This object is created by the function get_statistics. Default value is get_statistics(net_object).

T_0_start

Positive integer. The starting time-step of the T_0_interval. Default value is 0.

T_0_end

Positive integer. The ending time-step of T_0_interval. Default value is round(net_stat$T * 0.75).

T_1_start

Positive integer. The starting time-step of the T_1_interval. Default value is T_0_end + 1.

T_1_end

Positive integer. The ending time-step of T_1_interval. Default value is net_stat$T.

interpolate

Logical. If TRUE then all the gaps in the estimated PA function are interpolated by linear interpolating in logarithm scale. Default value is FALSE.

Author

Thong Pham

References

1. Jeong, H., Néda, Z. & Barabási, A. . Measuring preferential attachment in evolving networks. Europhysics Letters. 2003;61(61):567–572. (tools:::Rd_expr_doi("10.1209/epl/i2003-00166-9")).

See Also

See get_statistics for how to create summerized statistics needed in this function.

See Newman and only_A_estimate for other methods to estimate the attachment function in isolation.

Examples

  library("PAFit")
  net        <- generate_net(N = 1000 , m = 1 , mode = 1 , alpha = 1 , s = 0)
  net_stats  <- get_statistics(net)
  result     <- Jeong(net, net_stats)
  # true function
  true_A     <- result$center_k
  #plot the estimated attachment function
  plot(result , net_stats)
  lines(result$center_k, true_A, col = "red") # true line
  legend("topleft" , legend = "True function" , col = "red" , lty = 1 , bty = "n")