  The linear preferential attachment hypothesis has been shown to be quite
successful to explain the existence of networks with power-law degree
distributions. It is then quite important to determine if this mechanism is the
consequence of a general principle based on local rules. In this work it is
claimed that an effective linear preferential attachment is the natural outcome
of growing network models based on local rules. It is also shown that the local
models offer an explanation to other properties like the clustering hierarchy
and degree correlations recently observed in complex networks. These
conclusions are based on both analytical and numerical results of different
local rules, including some models already proposed in the literature.
