Newman: Corrected Newman's method for estimating the preferential...

In PAFit: Generative Mechanism Estimation in Temporal Complex Networks

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 α (when assume A_k = k^α), while ci is the mean plus/minus two-standard-deviation interval.

• loglinear_fit: this is the fitting result when we estimate α.

Author(s)

Thong Pham [e-mail]

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. (doi: 10.1371/journal.pone.0137796).

2. Newman, M.. Clustering and preferential attachment in growing networks. Physical Review E. 2001;64(2):025102 (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")

PAFit documentation built on Jan. 18, 2022, 1:10 a.m.