  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 ptr and the consensus time tc depend upon the standard
deviation of the degree distribution.ptr increases while tc decreases with the
rise of it.Functions of ptr and tc are found.Theoretical analyses are in
accordance with simulation data.
