Statistical inference for network samples using subgraph counts

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.

42 pages, 6 figures, 2 tables

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• Higher-order organization of complex networks
• The method of moments and degree distributions for network models
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• Optimal hypothesis testing for stochastic block models with growing degrees
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Cited by in corpus (3)

• Subgraphs in preferential attachment models
• Signatures of graphs for bicommutative Hopf algebras
• Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics