Exact analytical solution of average path length for Apollonian networks

Details Exact analytical solution of average path length for Apollonian networks Exact analytical solution of average path length for Apollonian networks

2007-06-24

arxiv.org/abs/0706.3491v2

Phys. Rev. E 77, 017102 (2008)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures

Scientific paper

10.1103/PhysRevE.77.017102

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.

Affiliated with

Also associated with

No associations

Rating

Exact analytical solution of average path length for Apollonian networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exact analytical solution of average path length for Apollonian networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact analytical solution of average path length for Apollonian networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-704113