How does degree heterogeneity affect an order-disorder transition?R. Lambiotte
GRAPES, Université de Liège - Sart-Tilman, B-4000 Liège, Belgium
received 9 February 2007; accepted in final form 7 May 2007; published June 2007
published online 25 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.
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