# Effects of attachment preferences on coevolution of opinions and networks

L.-X. Zhong, F. Ren, T. Qiu, J.-R. Xu, B.-H. Chen, and C.-F. Liu

Physica A, **389**(13), 2557-2565, 2010.

In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a heterogeneous network structure is easier to be reached with more high-degree-preferential (HDP) nodes. There exists high correlation between the convergence time and the network heterogeneity. The heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network: with preferential attachment and long-time evolvement, most of the nodes would become separated and only a few leaders would have immediate neighbors. Analytical calculations based on mean field theory reveal that both the transition point $p_{tr}$and the consensus time $\tau$ depend upon the standard deviation of the degree distribution $\sigma_{d}$. $p_{tr}$ increases while $\tau$ decreases with the rise of $\sigma_{d}$. Functions of $p_{tr} = \langle k \rangle / \left( \langle k \rangle + 1\right)$ and $\tau = a\left(N\right)K / \left( \sigma_{D}^2 - K\right)$ are found. Theoretical analyses are in accordance with simulation data.