Dynamic networks and directed percolation

¹  Minerva Center & Department of Physics, Bar-Ilan University - Ramat Gan, Israel
²  Center for Polymer Studies, Boston University - Boston, MA 02215, USA
³  Department of Mathematics, Bar-Ilan University - Ramat Gan, Israel

Corresponding author: parshani.roni@gmail.com

Received: 26 February 2010
Accepted: 26 April 2010

Abstract

We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the time evolution of the network. We show that the dynamic network undergoes a percolation phase transition at a critical concentration p_c, that decreases with the rate r at which the network links are changed. The behavior near criticality is universal and independent of r. We find that for dynamic random networks fundamental laws are changed. i) The size of the giant component at criticality scales with the network size N for all values of r, rather than as in static networks. ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as , compared to in a static network.