The phase transition of the voter model on evolving scale-free networks

Abstract

The voter model on a social network can explain consensus formation, where real networks feature a heterogeneous degree distribution and also change in time. We study the voter model in an environment with both features: a rank one scale-free network evolving in time by each vertex updating its edge neighbourhood at rate $\kappa$.

When $\kappa \gg 1$ the dynamic giant has no effect up to a polylogarithmic correction, but for more slowly changing graphs consensus takes $\frac{1}{\kappa }$ longer without a dynamic giant. This continues until $\kappa \ll \frac{1}{N}$, where this factor $\frac{1}{\kappa }$ becomes $\frac{N}{logN}$.