# Statistical inference for network samples using subgraph counts

arXiv: https://arxiv.org/abs/1701.00505 · HTML: https://mlsanity.com/paper/1701.00505/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2017.

## Built on by (most cited first, 4 of 4)

- [Network two-sample test for block models](https://mlsanity.com/paper/2406.06014/) (2024)
- [Differentially Describing Groups of Graphs](https://mlsanity.com/paper/2201.04064/) (2021)
- [Higher-order accurate two-sample network inference and network hashing](https://mlsanity.com/paper/2208.07573/) (2022)
- [Interpretable Network Representation Learning with Principal Component Analysis](https://mlsanity.com/paper/2106.14238/) (2021)

## Abstract (arXiv)

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.