How does degree heterogeneity affect an order-disorder transition?

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We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the majority rule, applied to dichotomous networks. The latter are composed of two kinds of nodes, each kind i being characterized by a degree k. Dichotomous networks are therefore a simple instance of heterogeneous networks, especially adapted in order to reveal the effect of degree heterogeneity. Our main result are that degree heterogeneity affects the location of the order-disorder transition and that the system exhibits non-equipartition of the average opinion between the two kinds of nodes. This effect is observed in the ordered phase and in the disordered phase.
Original languageEnglish
Issue number6
Publication statusPublished - 1 Jun 2007


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