  Various important and useful quantities or measures that characterize the
topological network structure are usually investigated for a network, then they
are averaged over the samples. In this paper, we propose an explicit
representation by the beforehand averaged adjacency matrix over samples of
growing networks as a new general framework for investigating the
characteristic quantities. It is applied to some network models, and shows a
good approximation of degree distribution asymptotically. In particular, our
approach will be applicable through the numerical calculations instead of
intractable theoretical analysises, when the time-course of degree is a
monotone increasing function like power-law or logarithm.
