# Multilayer Artificial Benchmark for Community Detection (mABCD)

arXiv: https://arxiv.org/abs/2507.10795 · HTML: https://mlsanity.com/paper/2507.10795/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 74 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 24 of 24)

- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Community Detection in Multiplex Networks](https://mlsanity.com/paper/1910.07646/) (2019)
- [Artificial Benchmark for Community Detection (ABCD): Fast Random Graph Model with Community Structure](https://mlsanity.com/paper/2002.00843/) (2020)
- [GC-Bench: An Open and Unified Benchmark for Graph Condensation](https://mlsanity.com/paper/2407.00615/) (2024)
- [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)
- [Artificial Benchmark for Community Detection with Outliers (ABCD+o)](https://mlsanity.com/paper/2301.05749/) (2023)
- [Towards effective visual analytics on multiplex and multilayer networks](https://mlsanity.com/paper/1501.01666/) (2015)
- [Characterizing interactions in online social networks during exceptional events](https://mlsanity.com/paper/1506.09115/) (2015)
- [Quantifying layer similarity in multiplex networks: a systematic study](https://mlsanity.com/paper/1711.11335/) (2017)
- [Bayan Algorithm: Detecting Communities in Networks Through Exact and Approximate Optimization of Modularity](https://mlsanity.com/paper/2209.04562/) (2022)
- [A multilayer network dataset of interaction and influence spreading in a virtual world](https://mlsanity.com/paper/1702.06373/) (2017)
- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Rank-Refining Seed Selection Methods for Budget Constrained Influence Maximisation in Multilayer Networks under Linear Threshold Model](https://mlsanity.com/paper/2405.18059/) (2024)
- [A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks](https://mlsanity.com/paper/1608.06196/) (2016)
- [Relating modularity maximization and stochastic block models in multilayer networks](https://mlsanity.com/paper/1804.01964/) (2018)
- [Network Diffusion -- Framework to Simulate Spreading Processes in Complex Networks](https://mlsanity.com/paper/2405.18085/) (2024)
- [The Artificial Benchmark for Community Detection with Outliers and Overlapping Communities (ABCD+o2)](https://mlsanity.com/paper/2506.05486/) (2025)
- [A Method for Group Extraction and Analysis in Multilayer Social Networks](https://mlsanity.com/paper/1612.02377/) (2016)
- [Influence Spread in the Heterogeneous Multiplex Linear Threshold Model](https://mlsanity.com/paper/2008.04383/) (2020)
- [Community Detection and Improved Detectability in Multiplex Networks](https://mlsanity.com/paper/1909.10477/) (2019)
- [A Synthetic Network Generator for Covert Network Analytics](https://mlsanity.com/paper/2008.04445/) (2020)
- [Influence of Information Blocking on the Spread of Virus in Multilayer Networks](https://mlsanity.com/paper/2301.11611/) (2023)

## Built on by (most cited first, 1 of 1)

- [Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator](https://mlsanity.com/paper/2602.02044/) (2026)

## Abstract (arXiv)

One of the most persistent challenges in network science is the development of various synthetic graph models to support subsequent analyses. Among the most notable frameworks addressing this issue is the Artificial Benchmark for Community Detection (ABCD) model, a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model but it is faster, more interpretable, and can be investigated analytically. In this paper, we use the underlying ingredients of ABCD and introduce its variant, mABCD, thereby addressing the gap in models capable of generating multilayer networks. The uniqueness of the proposed approach lies in its flexibility at both levels of modelling: the internal structure of individual layers and the inter-layer dependencies, which together make the network a coherent structure rather than a collection of loosely coupled graphs. In addition to the conceptual description of the framework, we provide a comprehensive analysis of its efficient Julia implementation. Finally, we illustrate the applicability of mABCD to one of the most prominent problems in the area of complex systems: spreading phenomena analysis.