Graph fission in an evolving voter model.

ABSTRACT: We consider a simplified model of a social network in which individuals have one of two opinions (called 0 and 1) and their opinions and the network connections coevolve. Edges are picked at random. If the two connected individuals hold different opinions then, with probability 1 - ?, one imitates the opinion of the other; otherwise (i.e., with probability ?), the link between them is broken and one of them makes a new connection to an individual chosen at random (i) from those with the same opinion or (ii) from the network as a whole. The evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions. Letting ? be the fraction of voters holding the minority opinion after the evolution stops, we are interested in how ? depends on ? and the initial fraction u of voters with opinion 1. In case (i), there is a critical value ?(c) which does not depend on u, with ? ? u for ? > ?(c) and ? ? 0 for ? < ?(c). In case (ii), the transition point ?(c)(u) depends on the initial density u. For ? > ?(c)(u), ? ? u, but for ? < ?(c)(u), we have ?(?,u) = ?(?,1/2). Using simulations and approximate calculations, we explain why these two nearly identical models have such dramatically different phase transitions.

SUBMITTER: Durrett R 

PROVIDER: S-EPMC3309720 | biostudies-literature | 2012 Mar

REPOSITORIES: biostudies-literature