# Network Global Testing by Counting Graphlets

arXiv: https://arxiv.org/abs/1807.08440 · HTML: https://mlsanity.com/paper/1807.08440/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2018.

## Built on by (most cited first, 5 of 5)

- [On the Power of the Weisfeiler-Leman Test for Graph Motif Parameters](https://mlsanity.com/paper/2309.17053/) (2023)
- [Higher-order accurate two-sample network inference and network hashing](https://mlsanity.com/paper/2208.07573/) (2022)
- [Testing High-dimensional Multinomials with Applications to Text Analysis](https://mlsanity.com/paper/2301.01381/) (2023)
- [A generative neural network model for random dot product graphs](https://mlsanity.com/paper/2204.07634/) (2022)
- [Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Models](https://mlsanity.com/paper/2406.05340/) (2024)

## Abstract (arXiv)

Consider a large social network with possibly severe degree heterogeneity and mixed-memberships. We are interested in testing whether the network has only one community or there are more than one communities. The problem is known to be non-trivial, partially due to the presence of severe degree heterogeneity. We construct a class of test statistics using the numbers of short paths and short cycles, and the key to our approach is a general framework for canceling the effects of degree heterogeneity. The tests compare favorably with existing methods. We support our methods with careful analysis and numerical study with simulated data and a real data example.