# Network two-sample test for block models

arXiv: https://arxiv.org/abs/2406.06014 · HTML: https://mlsanity.com/paper/2406.06014/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [Graph Matching: Relax at Your Own Risk](https://mlsanity.com/paper/1405.3133/) (2014)
- [Network histograms and universality of blockmodel approximation](https://mlsanity.com/paper/1312.5306/) (2013)
- [Hypothesis Testing For Network Data in Functional Neuroimaging](https://mlsanity.com/paper/1407.5525/) (2014)
- [Two-sample Hypothesis Testing for Inhomogeneous Random Graphs](https://mlsanity.com/paper/1707.00833/) (2017)
- [Spectral Alignment of Graphs](https://mlsanity.com/paper/1602.04181/) (2016)
- [On clustering network-valued data](https://mlsanity.com/paper/1606.02401/) (2016)
- [Simultaneous whole-animal 3D-imaging of neuronal activity using light field microscopy](https://mlsanity.com/paper/1401.5333/) (2014)
- [Change point localization in dependent dynamic nonparametric random dot product graphs](https://mlsanity.com/paper/1911.07494/) (2019)
- [Optimal network online change point localisation](https://mlsanity.com/paper/2101.05477/) (2021)
- [Statistical inference for network samples using subgraph counts](https://mlsanity.com/paper/1701.00505/) (2017)
- [Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks](https://mlsanity.com/paper/1904.05330/) (2019)
- [Hypothesis testing for populations of networks](https://mlsanity.com/paper/1911.03783/) (2019)
- [Bayesian community detection for networks with covariates](https://mlsanity.com/paper/2203.02090/) (2022)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)

## Built on by (most cited first, 2 of 2)

- [Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)](https://mlsanity.com/paper/2506.02825/) (2025)
- [Query-Limited Community Recovery in Stochastic Block Models](https://mlsanity.com/paper/2606.02055/) (2026)

## Abstract (arXiv)

We consider the two-sample testing problem for networks, where the goal is to determine whether two sets of networks originated from the same stochastic model. Assuming no vertex correspondence and allowing for different numbers of nodes, we address a fundamental network testing problem that goes beyond simple adjacency matrix comparisons. We adopt the stochastic block model (SBM) for network distributions, due to their interpretability and the potential to approximate more general models. The lack of meaningful node labels and vertex correspondence translate to a graph matching challenge when developing a test for SBMs. We introduce an efficient algorithm to match estimated network parameters, allowing us to properly combine and contrast information within and across samples, leading to a powerful test. We show that the matching algorithm, and the overall test are consistent, under mild conditions on the sparsity of the networks and the sample sizes, and derive a chi-squared asymptotic null distribution for the test. Through a mixture of theoretical insights and empirical validations, including experiments with both synthetic and real-world data, this study advances robust statistical inference for complex network data.