Phase transitions in dynamical random graphs
Research output: Contribution to journal › Article
Abstract
We study a largetime limit of a Markov process whose states are finite graphs. The number of the vertices is described by a supercritical branching process, and the dynamics of edges is determined by the rates of appending and deleting. We find a phase transition in our model similar to the one in the random graph model G (n,p). We derive a formula for the line of critical parameters which separates two different phases: one is where the size of the largest component is proportional to the size of the entire graph, and another one, where the size of the largest component is at most logarithmic with respect to the size of the entire graph. In the supercritical phase we find the asymptotics for the size of the largest component.
Details
Authors  

Organisations  
Research areas and keywords  Subject classification (UKÄ) – MANDATORY
Keywords

Original language  English 

Pages (fromto)  10071032 
Journal  Journal of Statistical Physics 
Volume  123 
Issue number  5 
Publication status  Published  2006 
Publication category  Research 
Peerreviewed  Yes 