# Artificial Benchmark for Community Detection with Outliers (ABCD+o)

arXiv: https://arxiv.org/abs/2301.05749 · HTML: https://mlsanity.com/paper/2301.05749/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 13 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Artificial Benchmark for Community Detection (ABCD): Fast Random Graph Model with Community Structure](https://mlsanity.com/paper/2002.00843/) (2020)
- [Modularity of the ABCD Random Graph Model with Community Structure](https://mlsanity.com/paper/2203.01480/) (2022)
- [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)
- [An Unsupervised Framework for Comparing Graph Embeddings](https://mlsanity.com/paper/1906.04562/) (2019)
- [A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphs](https://mlsanity.com/paper/2112.00075/) (2021)
- [Immunization of networks with non-overlapping community structure](https://mlsanity.com/paper/1806.05637/) (2018)
- [Ensemble Clustering for Graphs](https://mlsanity.com/paper/1809.05578/) (2018)
- [Integrating Network Embedding and Community Outlier Detection via Multiclass Graph Description](https://mlsanity.com/paper/2007.10231/) (2020)
- [Comparative evaluation of community-aware centrality measures](https://mlsanity.com/paper/2205.06995/) (2022)

## Built on by (most cited first, 7 of 7)

- [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)
- [Graph Data Augmentation via Contrastive Generator Inversion (textttDCBA)](https://mlsanity.com/paper/2610.05653/) (2026)

## Abstract (arXiv)

The Artificial Benchmark for Community Detection graph (ABCD) 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 extend the ABCD model to include potential outliers. We perform some exploratory experiments on both the new ABCD+o model as well as a real-world network to show that outliers possess some desired, distinguishable properties.