Volume 78, Number 6, June 2007
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||25 May 2007|
How does degree heterogeneity affect an order-disorder transition?
GRAPES, Université de Liège - Sart-Tilman, B-4000 Liège, Belgium
Accepted: 7 May 2007
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 ki. 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.
PACS: 89.75.Fb – Structures and organization in complex systems / 87.23.Ge – Dynamics of social systems / 89.75.Hc – Networks and genealogical trees
© Europhysics Letters Association, 2007
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