  We derive the sampling properties of random networks based on weights whose
pairwise products parameterize independent Bernoulli trials. This enables an
understanding of many degree-based network models, in which the structure of
realized networks is governed by properties of their degree sequences. We
provide exact results and large-sample approximations for power-law networks
and other more general forms. This enables us to quantify sampling variability
both within and across network populations, and to characterize the limiting
extremes of variation achievable through such models. Our results highlight
that variation explained through expected degree structure need not be
attributed to more complicated generative mechanisms.
