Percolation transition in a dynamically clustered network

Abstract

We consider a percolationlike phenomenon on a generalization of the Barabási-Albert model, where a modification of the growth dynamics directly allows formation of disconnected clusters. The transition is located with high precision by an original numerical technique based on the comparison of the largest and second largest clusters. A careful investigation focusing on finite size scaling allows us to highlight properties which would hardly be accessible by an analytical solution of cluster growth equations in the stationary limit. Our analysis shows that some critical features of the percolation transition are different from those observed in the case of dilution in fully grown networks. At variance with other models of percolation on growing networks we also find evidence that the order parameter approaches zero as a power of the field p- pc driving the transition, rather than as a stretched exponential. This behavior does not agree with the Berezinskii-Kosterlitz- Thouless scenario found in other similar models. For describing the phase in which a giant cluster develops, a key role is played by the crossover number of nodes Nx ∼ (p- pc) -ζ with ζ 4. This power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence. © 2007 The American Physical Society

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