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

doi:10.1088/1674-1056/19/6/060203

Abstract We have investigated the influence of the average degree $\langle k \rangle$ 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 $\langle k \rangle$ of the networks; a larger value of $\langle k \rangle$ 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 $\langle k \rangle$ is small. With the increase of $\langle k \rangle$, 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 $\langle k \rangle$. Our results may be helpful to understand structural effects on order--disorder phase transition in the context of the majority rule model.

Keywords: complex networks majority rule

Received: 19 September 2009
Accepted manuscript online:

PACS:	05.70.Fh	(Phase transitions: general studies)
	05.70.Jk	(Critical point phenomena)
	02.50.Ng	(Distribution theory and Monte Carlo studies)
	02.30.Oz	(Bifurcation theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10775060).

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Feng Cun-Fang(冯存芳), Guan Jian-Yue(关剑月), Wu Zhi-Xi(吴枝喜), and Wang Ying-Hai(汪映海) Effects of average degree of network on an order－disorder transition in opinion dynamics 2010 Chin. Phys. B 19 060203

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

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