# Central limit theorems for local network statistics

arXiv: https://arxiv.org/abs/2006.15738 · HTML: https://mlsanity.com/paper/2006.15738/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Higher-order accurate two-sample network inference and network hashing](https://mlsanity.com/paper/2208.07573/) (2022)

## Abstract (arXiv)

Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically counted globally, and existing approaches fail to describe vertex-specific characteristics. On the other hand, rooted subgraph counts - counts focusing on any given vertex's neighborhood - are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model which generalizes many popular statistical network models. This result enables a shift in the statistical analysis of large graphs, from estimating network summaries, to estimating models linking local network structure and vertex-specific covariates. As an example, we consider a school friendship network and show that local friendship patterns are significant predictors of gender and race.