  This short communication uses a simple experiment to show that fitting to a
power law distribution by using graphical methods based on linear fit on the
log-log scale is biased and inaccurate. It shows that using maximum likelihood
estimation (MLE) is far more robust. Finally, it presents a new table for
performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to
power-law distributions in which the power-law exponent is estimated using MLE.
The techniques presented here will advance the application of complex network
theory by allowing reliable estimation of power-law models from data and
further allowing quantitative assessment of goodness-of-fit of proposed
power-law models to empirical data.
