Unusual percolation in simple small-world networks Export

@article{citeulike:4971588, abstract = {We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a one-dimensional underlying lattice. We find a nonclassical 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.\”}, author = {Cohen, Reuven and Dawid, Daryush J. and Kardar, Mehran and Yam, Yaneer B.}, citeulike-article-id = {4971588}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000079000006066112000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v79/e066112}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/PhysRevE.79.066112}, doi = {10.1103/PhysRevE.79.066112}, issn = {1539-3755}, journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, keywords = {critical\_phenomena, critical\_points, explosive\_percolation, networks, percolation, small-world}, month = {June}, number = {6}, pages = {066112+}, posted-at = {2009-10-21 14:45:19}, priority = {2}, publisher = {APS}, title = {Unusual percolation in simple small-world networks}, url = {http://dx.doi.org/10.1103/PhysRevE.79.066112}, volume = {79}, year = {2009} }

TY - JOUR ID - citeulike:4971588 L3 - citeulike-article-id:4971588 N2 - We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a one-dimensional underlying lattice. We find a nonclassical 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.” IS - 6 JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) SN - 1539-3755 TI - Unusual percolation in simple small-world networks PB - APS VL - 79 SP - 066112 KW - critical_phenomena KW - critical_points KW - explosive_percolation KW - networks KW - percolation KW - small-world AU - Cohen, Reuven AU - Dawid, Daryush AU - Kardar, Mehran AU - Yam, Yaneer PY - 2009/06// UR - http://dx.doi.org/10.1103/PhysRevE.79.066112 ER -