科研之友
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摘要
With the help of recursion relations derived from the self-similar structure, we obtain the solution of average path length, (d) over bar (t), for Apollonian networks. In contrast to the well-known numerical result (d) over bar (t)proportional to(ln N(t))(3/4) [J. S. Andrade, Jr. , Phys. Rev. Lett. 94, 018702 (2005)], our rigorous solution shows that the average path length grows logarithmically as (d) over bar (t)proportional to ln N(t) in the infinite limit of network size N(t). The extensive numerical calculations completely agree with our closed-form solution.
