Statistical inference for network samples using subgraph counts

Understand

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.