Abstract
Some dynamical processes in a small-world network shows a critical transition at a finite disorder phi(c) of the network, in contrast with the geometrical properties that exhibit the critical behavior at phi(c)=0. Although it has been pointed out in previous works that the transition is related to the structural properties of the network, it is still not very clear why the transition occurs at phi(c) not equal 0. In this paper we present a simple social model of efficiency dynamics in small-world networks, which also shows a transition at phi(c)>0. We obtain the critical point with phi(c) approximately equal 0.098 from the finite-size analysis. It is found that both the geometrical properties of the network and the specific dynamical characters of the model contribute to the critical transition. This work is useful for understanding this kind of transition occurring in many dynamical processes in small-world networks.
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