R Lambiotte and M Ausloos J. Stat. Mech. (2007) P08026 doi:10.1088/1742-5468/2007/08/P08026
R Lambiotte and M Ausloos
Show affiliationsThe majority rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; and an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.
E-print Number: physics/0703266
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89.65.Gh Economics; econophysics, financial markets, business and management
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics
Issue 08 (August 2007)
Received 29 March 2007, accepted for publication 20 July 2007
Published 21 August 2007
R Lambiotte and M Ausloos J. Stat. Mech. (2007) P08026
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