Statistical inference for network samples using subgraph counts

TL;DR

This paper develops statistical methods to test if a collection of observed networks are drawn from a specified model, using subgraph counts and asymptotic properties, applicable even with varying network sizes.

Contribution

It introduces a novel approach to infer network models from samples of networks with different sizes using joint asymptotic analysis of subgraph counts.

Findings

Methods for testing network sample distributions against models

Joint confidence regions for subgraph counts

Application to brain networks showing differences in short cycles

Abstract

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.