Unusual percolation in simple small-world networks
Abstract
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of "telephone".
Cite
@article{arxiv.0802.1055,
title = {Unusual percolation in simple small-world networks},
author = {Reuven Cohen and Daryush Jonathan Dawid and Mehran Kardar and Yaneer Bar-Yam},
journal= {arXiv preprint arXiv:0802.1055},
year = {2009}
}
Comments
10 pages, 4 figures, revtex4