Effects of average degree of network on an order-disorder transition in opinion dynamics

We have investigated the influence of the average degree < k > of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule (VMR) model is applied to Watts-Strogatz (WS) small-world networks and Barabasi-Albert (BA) scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order-disorder transition point of the VMR model is greatly affected by the average degree < k > of the networks; a larger value of < k > results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree < k > is small. With the increase of < k >, BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents beta/nu, gamma/nu and 1/nu for several values of average degree < k >. Our results may be helpful to understand structural effects on order-disorder phase transition in the context of the majority rule model.