  Global degree/strength based preferential attachment is widely used as an
evolution mechanism of networks. But it is hard to believe that any individual
can get global information and shape the network architecture based on it. In
this paper, it is found that the global preferential attachment emerges from
the local interaction models, including distance-dependent preferential
attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal
of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys.
Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A.
Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the
attachment rate depends linearly on the degree or strength, while for
acquaintance network model, the dependence follows a sublinear power law. It
implies that for the evolution of social networks, local contact could be more
fundamental than the presumed global preferential attachment. This is onsistent
with the result observed in the evolution of empirical email networks.
