  We commented on Ref.[Andrade J S, Herrmann H J, Andrade R F S, et al. Phys.
Rev. Lett. 94, 018702 (2005)] and corrected the approach to estimate the degree
distribution of the Apollonian network. However, after reading our manuscript,
Herrmann indicated that it was due to a small typographic error and Herrmann et
al. published Ref. [Andrade J S, Herrmann H J, Andrade R F S, et al. Phys. Rev.
Lett. 102, 079901 (2009)]. In this paper, the relationship between an exponent
of power-law distributions and the exponent of cumulative distributions is
studied. For power-law distribution with geometrically growing domain, we prove
that its exponent is equal to the exponent of its cumulative distribution. We
carried out numerical simulations and obtain results that are in good agreement
with the theoretical analysis.
