Jeong: Jeong's method for estimating the preferential attachment...
In PAFit: Generative Mechanism Estimation in Temporal Complex Networks

Description Usage Arguments Value Author(s) References See Also Examples

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

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)

`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`.

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 α (when assume A_k = k^α), while ci is the confidence interval.
loglinear_fit: this is the fitting result when we estimate α.

Thong Pham thongphamthe@gmail.com

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

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.

  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")