# Log-likelihood in fit_power_law{igraph}

The R package igraph has the fit_power_law function which, as you can imagine, can fit a power-law to a vector. As you can see in the reproducible example below, one of the outputs of this function is the Log-likelihood logLik of the fitted parameters.

question: is there a rule-of-thumb or a cut-off value that tells when the logLik indicates a good/bad fit? The documentation of the package is really poor in explaining how this parameter should be considered/interpreted

Reproducible example:

library(igraph)

# create a graph
set.seed(202)
g <- static.power.law.game(500, 1000, exponent.out= 2.2, exponent.in = -1, loops = FALSE, multiple = TRUE, finite.size.correction = TRUE)

# get the degree distribution like this:
d <- degree_distribution(g, mode ="all", cumulative = T)
d <- d[ d > 0] # remove unconnected nodes

# Fit power-law
fit <- fit_power_law(d, implementation = "R.mle")
fit

#> $continuous #> [1] TRUE #> #>$alpha
#> [1] 1.5419026
#>
#> $xmin #> [1] 0.028 #> #>$logLik
#> [1] 4.558483753
#>
#> $KS.stat #> [1] 0.1323368292 #> #>$KS.p
#> [1] 0.927129327

• Attention: in the call to fit_power_law(), the OP used a wrong impelementation argument with a misplaced e: fit_power_law(d, impelementation = "R.mle"). --- If written without typo, the output of fit_power_law(d, implementation = "R.mle") is different: Coefficients: alpha 0.7475 – knb Apr 8 '18 at 12:36

p-values should be used with care, but, for your question, you could look at the statistic that also also computed: