# Modularity of the ABCD Random Graph Model with Community Structure

arXiv: https://arxiv.org/abs/2203.01480 · HTML: https://mlsanity.com/paper/2203.01480/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [Artificial Benchmark for Community Detection (ABCD): Fast Random Graph Model with Community Structure](https://mlsanity.com/paper/2002.00843/) (2020)
- [Ensemble Clustering for Graphs](https://mlsanity.com/paper/1809.05578/) (2018)
- [Modularity of ErdHos-R'enyi random graphs](https://mlsanity.com/paper/1808.02243/) (2018)
- [Modularity of regular and treelike graphs](https://mlsanity.com/paper/1606.09101/) (2016)

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

- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Properties and Performance of the ABCDe Random Graph Model with Community Structure](https://mlsanity.com/paper/2203.14899/) (2022)
- [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)
- [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 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 xi can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. In this paper, we investigate various theoretical asymptotic properties of the ABCD model. In particular, we analyze the modularity function, arguably, the most important graph property of networks in the context of community detection. Indeed, the modularity function is often used to measure the presence of community structure in networks. It is also used as a quality function in many community detection algorithms, including the widely used Louvain algorithm.