Discrete surface growth process as a synchronization mechanism for scale-free complex networks.

We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A 19, L441 (1986)] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution P(k) approximately k;{-lambda} , where k is the degree of a node and lambda its broadness, and compare it with the usually applied Edward-Wilkinson process (EW) [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)]. In spite of both processes belonging to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents lambda<3 the scaling behavior of the roughness in the saturation cannot be explained by the EW process. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased. This nonphysical result is mainly due to finite size effects due to the underlying network. Contrarily, the discrete surface growth process does not present this flaw and is applicable for every lambda .