Newman: Corrected Newman's method for estimating the preferential...
In thongphamthe/PAFit: Generative Mechanism Estimation in Temporal Complex Networks

Newman

R Documentation

Corrected Newman's method for estimating the preferential attachment function

Description

This function implements a correction proposed in [1] of the original Newman's method in [2] to estimate the preferential attachment function.

Usage

  Newman(net_object                              , 
         net_stat    = get_statistics(net_object), 
         start       = 1                         , 
         interpolate = FALSE)

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)`.
`start`	Positive integer. The starting time from which the method is applied. Default value is `1`.
`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`.

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 mean plus/minus two-standard-deviation interval.
loglinear_fit: this is the fitting result when we estimate \alpha.

Author(s)

Thong Pham thongphamthe@gmail.com

References

1. Pham, T., Sheridan, P. & Shimodaira, H. (2015). PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks. PLoS ONE 10(9): e0137796. (\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0137796")}).

2. Newman, M.. Clustering and preferential attachment in growing networks. Physical Review E. 2001;64(2):025102 (\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1103/PhysRevE.64.025102")}).

Examples

  library("PAFit")
  net        <- generate_net(N = 1000 , m = 1 , mode = 1 , alpha = 1 , s = 0)
  net_stats  <- get_statistics(net)
  result     <- Newman(net, net_stats)
  summary(result)
  # 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")

thongphamthe/PAFit documentation built on March 30, 2024, 4:14 p.m.