# Properties and Performance of the ABCDe Random Graph Model with Community Structure

arXiv: https://arxiv.org/abs/2203.14899 · HTML: https://mlsanity.com/paper/2203.14899/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 28 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)
- [Spectral Detection on Sparse Hypergraphs](https://mlsanity.com/paper/1507.04113/) (2015)
- [A Scalable Generative Graph Model with Community Structure](https://mlsanity.com/paper/1302.6636/) (2013)
- [Modularity of the ABCD Random Graph Model with Community Structure](https://mlsanity.com/paper/2203.01480/) (2022)

## Built on by (most cited first, 8 of 8)

- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (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)

In this paper, we investigate properties and performance of synthetic random graph models with a built-in community structure. Such models are important for evaluating and tuning community detection algorithms that are unsupervised by nature. We propose ABCDe, a multi-threaded implementation of the ABCD (Artificial Benchmark for Community Detection) graph generator. We discuss the implementation details of the algorithm and compare it with both the previously available sequential version of the ABCD model and with the parallel implementation of the standard and extensively used LFR (Lancichinetti--Fortunato--Radicchi) generator. We show that ABCDe is more than ten times faster and scales better than the parallel implementation of LFR provided in NetworKit. Moreover, the algorithm is not only faster but random graphs generated by ABCD have similar properties to the ones generated by the original LFR algorithm, while the parallelized NetworKit implementation of LFR produces graphs that have noticeably different characteristics.