  We propose a rate equation approach to compute two vertex correlations in
scale-free growing network models based in the preferential attachment
mechanism. The formalism, based on previous work of Szab\'o \textit{et al.}
[Phys. Rev. E \textbf{67} 056102 (2002)] for the clustering spectrum, measuring
three vertex correlations, is based on a rate equation in the continuous degree
and time approximation for the average degree of the nearest neighbors of
vertices of degree $k$, with an appropriate boundary condition. We study the
properties of both two and three vertex correlations for linear preferential
attachment models, and also for a model yielding a large clustering
coefficient. The expressions obtained are checked by means of extensive
numerical simulations. The rate equation proposed can be generalized to more
sophisticated growing network models, and also extended to deal with related
correlation measures. As an example, we consider the case of a recently
proposed model of weighted networks, for which we are able to compute a
weighted two vertex correlation function, taking into account the strength of
the interactions between connected vertices.
