  We consider that a network is an observation, and a collection of observed
networks forms a sample. In this setting, we provide methods to test whether
all observations in a network sample are drawn from a specified model. We
achieve this by deriving, under the null of the graphon model, the joint
asymptotic properties of average subgraph counts as the number of observed
networks increases but the number of nodes in each network remains finite. In
doing so, we do not require that each observed network contains the same number
of nodes, or is drawn from the same distribution. Our results yield joint
confidence regions for subgraph counts, and therefore methods for testing
whether the observations in a network sample are drawn from: a specified
distribution, a specified model, or from the same model as another network
sample. We present simulation experiments and an illustrative example on a
sample of brain networks where we find that highly creative individuals' brains
present significantly more short cycles.
