  Continuous mixtures of distributions are widely employed in the statistical
literature as models for phenomena with highly divergent outcomes; in
particular, many familiar heavy-tailed distributions arise naturally as
mixtures of light-tailed distributions (e.g., Gaussians), and play an important
role in applications as diverse as modeling of extreme values and robust
inference. In the case of social networks, continuous mixtures of graph
distributions can likewise be employed to model social processes with
heterogeneous outcomes, or as robust priors for network inference. Here, we
introduce some simple families of network models based on continuous mixtures
of baseline distributions. While analytically and computationally tractable,
these models allow more flexible modeling of cross-graph heterogeneity than is
possible with conventional baseline (e.g., Bernoulli or $U|man$ distributions).
We illustrate the utility of these baseline mixture models with application to
problems of multiple-network ERGMs, network evolution, and efficient network
inference. Our results underscore the potential ubiquity of network processes
with nontrivial mixture behavior in natural settings, and raise some
potentially disturbing questions regarding the adequacy of current network data
collection practices.
