An implementation of a framework for modelling and inferencing the attachment mechanisms of temporal complex networks. For estimating the attachment function in isolation, we implement Jeong's method, the corrected Newman's method and the PAFit method. For estimating node fitnesses in isolation, we implement the PAFit method. For jointly estimating the attachment function and node fitnesses, we implement the PAFit method. The package also provides flexible methods to generate a wide range of temporal networks based on PA and fitness. See the accompanying vignette for a tutorial. For a list of references, please run the command: citation("PAFit")
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Package:  PAFit 
Type:  Package 
Version:  0.9.7.5 
Date:  20170301 
License:  GPL3 
The main functions are as follows.
Basic utilities:
GenerateNet
: generates a wide range of networks based on the preferential attachment and fitness mechanisms. See the manual for wrappers of this function to generate wellknown network models.
GetStatistics
: summarizes a matrix of edges into summary statistics ready for estimating the preferential attachment function or node fitness
Functions to estimate the attachment function in isolation:
Jeong
: by Jeong's method (Ref. 1)
Newman
: by the corrected Newman's method (Refs. 2, 3)
OnlyA_Estimate
: by PAFit method (Ref. 3)
Function to estimate node fitnesses in isolation:
OnlyF_Estimate
: by PAFit method (Ref. 3)
Function to estimate the attachment function and node fitnesses jointly:
JointEstimate
: by PAFit method (Ref. 4)
Thong Pham, Paul Sheridan, Hidetoshi Shimodaira. Maintainer: Thong Pham thongpham@thongpham.net
1. Jeong, H., Néda, Z. & Barabási, A. . Measuring preferential attachment in evolving networks. Europhysics Letters. 2003;61(61):567–572. doi: 10.1209/epl/i2003001669 (http://iopscience.iop.org/article/10.1209/epl/i2003001669/fulltext/).
2. Newman, M.. Clustering and preferential attachment in growing networks. Physical Review E. 2001;64(2):025102 (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.025102).
3. 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).
4. 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).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  ## Not run:
### Jointly estimate the attachment function and node fitnesses
library("PAFit")
# size of initial network = 100
# number of new nodes at each timestep = 100
# Ak = k; prior of node fitnesses = 5
net < GenerateNet(N = 1000 , m = 50 ,
num_seed = 100 , multiple_node = 100,
mode = 1 , alpha = 1 ,
shape = 5 , rate = 5)
net_stats < GetStatistics(net$graph)
#Joint estimation of attachment function Ak and node fitness
result < JointEstimate(net$graph, net_stats)
summary(result$estimate_result)
# true function
true_A < pmax(result$estimate_result$center_k,1)
#plot the estimated PA function
plot(result$estimate_result , net_stats)
lines(result$estimate_result$center_k, true_A, col = "red") # true line
legend("topleft" , legend = "True function" , col = "red" , lty = 1 , bty = "n")
#plot distribution of estimated node fitnesses
plot(result$estimate_result , net_stats, plot = "f")
#plot the estimated node fitnesses and true node fitnesses
plot(result$estimate_result , net_stats, true = net$fitness, plot = "true_f")
## End(Not run)

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