Documentation & Interactive Demo

ABCD Family
of Benchmarks

Interactive documentation and live demo site for the ABCD family of random graph generators — from baseline community detection to hypergraphs and multilayer networks.

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New to synthetic networks? Read how the ABCD family works and why it exists.

Generators

012021

ABCD

The original

Baseline model with power-law degree and community-size distributions.

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022023

ABCD+o

With Outliers

Adds community-agnostic outlier nodes to the ABCD model.

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032025

ABCD+o²

Outliers + Overlap

Adds overlapping communities on top of the outlier-aware generator.

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042023

h-ABCD

Hypergraphs

Hypergraph counterpart of ABCD with controllable hyperedge homogeneity.

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052022

ABCDe

Parallel generator

Multi-threaded implementation focusing on speed and scalability.

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062025

mABCD

Multilayer

Generates multilayer networks with shared or independent structure.

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Bibliography

Artificial Benchmark for Community Detection (ABCD)2021

Authors: Kamiński, B.; Prałat, P.; Théberge, F.

APA: Kamiński, B., Prałat, P., & Théberge, F. (2021). Artificial Benchmark for Community Detection (ABCD)—Fast random graph model with community structure. Network Science, 9(2).

Open paper
ABCD+o (ABCD with Outliers)2023

Authors: Kamiński, B.; Prałat, P.; Théberge, F.

APA: Kamiński, B., Prałat, P., & Théberge, F. (2023). Artificial benchmark for community detection with outliers (ABCD+o). Applied Network Science.

Open paper
ABCD+o² (Outliers + Overlapping Communities)2025

Authors: Jordan Barrett, Ryan DeWolfe, Bogumił Kamiński, Paweł Prałat, Aaron Smith, François Théberge

APA: Barrett, J. et al. (2025). The Artificial Benchmark for Community Detection with Outliers and Overlapping Communities (ABCD+o²). arXiv preprint.

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Hypergraph Artificial Benchmark for Community Detection (h-ABCD)2023

Authors: Kamiński, B.; Prałat, P.; Théberge, F.

APA: Kamiński, B., Prałat, P., & Théberge, F. (2023). Hypergraph Artificial Benchmark for Community Detection (h-ABCD). arXiv preprint.

Open paper
ABCDe (Multi-threaded ABCD Generator)2022

Authors: Kamiński, B.; Olczak, T.; Pankratz, B.; Prałat, P.; Théberge, F.

APA: Kamiński, B., Olczak, T., Pankratz, B., Prałat, P., & Théberge, F. (2022). Properties and Performance of the ABCDe Random Graph Model with Community Structure. arXiv preprint.

Open paper
Multilayer ABCD (mABCD)2025

Authors: Łukasz Kraiński, Michał Czuba, Piotr Bródka, Paweł Prałat, Bogumił Kamiński, François Théberge

APA: Kraiński, Ł. et al. (2025). Multilayer Artificial Benchmark for Community Detection (mABCD). arXiv preprint.

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