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 Barabási–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 β/ν, γ/ν and 1/ν 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.

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complex networks

majority rule

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