PAFit (version 0.8.7)

PAFit-package: A statistical sound method for joint estimation of the attachment function and node fitness in a temporal complex network by maximizing a suitable penalized log-likelihood function

Description

A method for estimating jointly the attachment function $A_k$ and node fitness $\eta_i$ of a temporal complex network is implemented in this package. The network's growth is assumed to follow a modified version of the fitness model, in which newly added edges, including newly edges between existed nodes, are connected to a degree $k$ node $v_i$ with probability proportional to the product of the attachment value $A_k$ and the fitness value $\eta_i$. The method makes no assumption on the functional form of either $A_k$ or $\eta_i$. By choosing suitable regularizations, good estimations of $A_k$ and $\eta_i$ can be obtained by maximizing the corresponding penalized log-likelihood function. We also implement a fast estimation of confidence intervals based on the Hessian of the penalized log likelihood. See the accompanying vignette for a tutorial.

For a list of references, please run the command: citation("PAFit").

Details

Package:

PAFit

Type:

Package

Version:

0.8.7

Date:

2016-10-18

License:

GPL-3

• PAFit: estimates the Preferential Attachment function and fitness function in a temporal complex network.
• GenerateNet: generates simulated networks based on the Barabasi-Albert model or the fitness model.
• GetStatistics: summarizes a matrix of edges into summary statistics ready for applying the PAFit function.

References

1. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Nonparametric Estimation of the Preferential Attachment Function in Complex Networks: Evidence of Deviations from Log Linearity, Proceedings of ECCS 2014, 141-153 (Springer International Publishing) (http://dx.doi.org/10.1007/978-3-319-29228-1_13).

2. 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 (http://dx.doi.org/10.1371/journal.pone.0137796).

3. Pham, T., Sheridan, P. & Shimodaira, H. (2016). Joint Estimation of Preferential Attachment and Node Fitness in Growing Complex Networks. Scientific Reports 6, Article number: 32558. doi:10.1038/srep32558 (www.nature.com/articles/srep32558).

Examples

library("PAFit")
data   <- GenerateNet(N = 100,m = 1,alpha = 1, mode = 1, shape = 0, rate = 0)
stats  <- GetStatistics(data$graph)
result <- PAFit(stats,only_PA = TRUE,stop_cond = 10^-3)
plot(x = result,data = stats,plot = "A")