  The exact formula for the average path length of Apollonian networks is
found. With the help of recursion relations derived from the self-similar
structure, we obtain the exact solution of average path length, $\bar{d}_t$,
for Apollonian networks. In contrast to the well-known numerical result
$\bar{d}_t \propto (\ln N_t)^{3/4}$ [Phys. Rev. Lett. \textbf{94}, 018702
(2005)], our rigorous solution shows that the average path length grows
logarithmically as $\bar{d}_t \propto \ln N_t$ in the infinite limit of network
size $N_t$. The extensive numerical calculations completely agree with our
closed-form solution.
