  We give asymptotics for the cumulative distribution function (CDF) for
degrees of large dense random graphs sampled from a graphon. The proof is based
on precise asymptotics for binomial random variables. Replacing the indicator
function in the empirical CDF by a smoother function, we get general asymptotic
results for functionals of homomorphism densities for partially labeled graphs
with smoother functions. This general setting allows to recover recent results
on asymptotics for homomorphism densities of sampled graphon.
