# Hypergraph Artificial Benchmark for Community Detection (h-ABCD)

arXiv: https://arxiv.org/abs/2210.15009 · HTML: https://mlsanity.com/paper/2210.15009/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 63 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Structural Patterns and Generative Models of Real-world Hypergraphs](https://mlsanity.com/paper/2006.07060/) (2020)
- [Consistency of Spectral Hypergraph Partitioning under Planted Partition Model](https://mlsanity.com/paper/1505.01582/) (2015)
- [How Do Hyperedges Overlap in Real-World Hypergraphs? -- Patterns, Measures, and Generators](https://mlsanity.com/paper/2101.07480/) (2021)
- [Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach](https://mlsanity.com/paper/1807.02884/) (2018)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Artificial Benchmark for Community Detection (ABCD): Fast Random Graph Model with Community Structure](https://mlsanity.com/paper/2002.00843/) (2020)
- [Tensor Spectral Clustering for Partitioning Higher-order Network Structures](https://mlsanity.com/paper/1502.05058/) (2015)
- [Configuration Models of Random Hypergraphs](https://mlsanity.com/paper/1902.09302/) (2019)
- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data](https://mlsanity.com/paper/2103.05031/) (2021)
- [Modularity of the ABCD Random Graph Model with Community Structure](https://mlsanity.com/paper/2203.01480/) (2022)
- [Properties and Performance of the ABCDe Random Graph Model with Community Structure](https://mlsanity.com/paper/2203.14899/) (2022)
- [Efficiently inferring community structure in bipartite networks](https://mlsanity.com/paper/1403.2933/) (2014)
- [Higher-order clustering in networks](https://mlsanity.com/paper/1704.03913/) (2017)
- [Core-periphery detection in hypergraphs](https://mlsanity.com/paper/2202.12769/) (2022)
- [Model-based clustering in simple hypergraphs through a stochastic blockmodel](https://mlsanity.com/paper/2210.05983/) (2022)
- [Nonbacktracking spectral clustering of nonuniform hypergraphs](https://mlsanity.com/paper/2204.13586/) (2022)
- [Core-periphery Models for Hypergraphs](https://mlsanity.com/paper/2206.00783/) (2022)
- [Hypergraph patterns and collaboration structure](https://mlsanity.com/paper/2210.02163/) (2022)
- [Measuring and Modeling Bipartite Graphs with Community Structure](https://mlsanity.com/paper/1607.08673/) (2016)
- [Preferential attachment hypergraph with high modularity](https://mlsanity.com/paper/2103.01751/) (2021)
- [Adapting Stochastic Block Models to Power-Law Degree Distributions](https://mlsanity.com/paper/1904.05335/) (2019)
- [Entropy-based models to randomize real-world hypergraphs](https://mlsanity.com/paper/2207.12123/) (2022)

## Built on by (most cited first, 9 of 9)

- [Artificial Benchmark for Community Detection with Outliers (ABCD+o)](https://mlsanity.com/paper/2301.05749/) (2023)
- [Modularity Based Community Detection in Hypergraphs](https://mlsanity.com/paper/2406.17556/) (2024)
- [Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks](https://mlsanity.com/paper/2505.21748/) (2025)
- [Multilayer hypergraph clustering using the aggregate similarity matrix](https://mlsanity.com/paper/2301.11657/) (2023)
- [Self-similarity of Communities of the ABCD Model](https://mlsanity.com/paper/2312.00238/) (2023)
- [Predicting Properties of Nodes via Community-Aware Features](https://mlsanity.com/paper/2311.04730/) (2023)
- [Network Embedding Exploration Tool (NEExT)](https://mlsanity.com/paper/2503.15853/) (2025)
- [Multilayer Artificial Benchmark for Community Detection (mABCD)](https://mlsanity.com/paper/2507.10795/) (2025)
- [Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator](https://mlsanity.com/paper/2602.02044/) (2026)

## Abstract (arXiv)

The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter can be tuned to mimic its counterpart in the LFR model, the mixing parameter. In this paper, we introduce hypergraph counterpart of the ABCD model, h-ABCD, which produces random hypergraph with distributions of ground-truth community sizes and degrees following power-law. As in the original ABCD, the new model h-ABCD can produce hypergraphs with various levels of noise. More importantly, the model is flexible and can mimic any desired level of homogeneity of hyperedges that fall into one community. As a result, it can be used as a suitable, synthetic playground for analyzing and tuning hypergraph community detection algorithms.