  In a random graph, counts for the number of vertices with given degrees will
typically be dependent. We show via a multivariate normal and a Poisson process
approximation that, for graphs which have independent edges, with a possibly
inhomogeneous distribution, only when the degrees are large can we reasonably
approximate the joint counts as independent. The proofs are based on Stein's
method and the Stein-Chen method with a new size-biased coupling for such
inhomogeneous random graphs, and hence bounds on distributional distance are
obtained. Finally we illustrate that apparent (pseudo-) power-law type
behaviour can arise in such inhomogeneous networks despite not actually
following a power-law degree distribution.
