# Generalized Hypergeometric Ensembles: Statistical Hypothesis Testing in Complex Networks

arXiv: https://arxiv.org/abs/1607.02441 · HTML: https://mlsanity.com/paper/1607.02441/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2016.

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

- [Learning Group Importance using the Differentiable Hypergeometric Distribution](https://mlsanity.com/paper/2203.01629/) (2022)

## Abstract (arXiv)

Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the foundation for the inference of topological patterns, the definition of network-analytic measures, as well as for model selection and statistical hypothesis testing. Contributing to the foundation of these data analysis techniques, in this Letter we introduce generalized hypergeometric ensembles, a broad class of analytically tractable statistical ensembles of finite, directed and weighted networks. This framework can be interpreted as a generalization of the classical configuration model, which is commonly used to randomly generate networks with a given degree sequence or distribution. Our generalization rests on the introduction of dyadic link propensities, which capture the degree-corrected tendencies of pairs of nodes to form edges between each other. Studying empirical and synthetic data, we show that our approach provides broad perspectives for model selection and statistical hypothesis testing in data on complex networks.