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I have a set of graphs (each with the same nodes but with edges' weights defined by different research subjects) for which I would like to report statistics. One of these statistics is the betweenness centrality of each node, which, for each graph, has a heavy-tailed distribution (reported to usually be a power law). Nevertheless, I have calculated the betweenness centrality for each node in each research subject's graph, and, again for each node, this empirical data fits well a heavy-tailed distribution, although it seems more lognormal than a power law, according to Gillespie's implementation in R (poweRlaw) of Clauset et al. method. I would like to report these results, but I do not know if the first parameter in this packages' estimation is the $median=\exp(\mu)=\theta$ or $\mu$. From the example with the moby corpus, it seems that the parameter is $\mu$, as its value is negative (-17.9), but the documentation is frankly lacking in this sense, as it focuses on power laws.

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Colin Gillespie answered this question on GitHub. It follows the parameterization of rlnorm, hence the first parameter estimated is $\mu$.

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