PAFit (version 1.2.10)

Newman: 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)

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 \(\alpha\).

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.

Author

Thong Pham

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. (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 (tools:::Rd_expr_doi("10.1103/PhysRevE.64.025102")).

See Also

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

See Jeong, 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     <- 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")