Multilayer Artificial Benchmark for Community Detection (mABCD)

TL;DR

The paper tackles the challenge of generating scalable multilayer networks with realistic community structure and inter-layer dependencies to support community-detection benchmarking and spreading analyses. It introduces mABCD, a multilayer extension of the ABCD family that uses a shared latent reference layer and a tunable edge-correlation framework to control within-layer structure and cross-layer dependencies, implemented efficiently in Julia with Python ports. The authors validate mABCD by analyzing inter-layer correlations, demonstrating controllable degree and partition correlations, examining edge cross-layer correlations, and benchmarking computational performance against multilayerGM, while showcasing spreading phenomena experiments under a multilayer MICM diffusion model. The work provides a flexible, fast, and interpretable generator for synthetic multilayer networks, enabling robust experimentation and methodological development in multilayer network science, albeit with limitations related to scale-free assumption and parameter estimation challenges.

Abstract

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.

Figures (17)

• Figure 1: Example of a multilayer network.
• Figure 2: Correlations between degrees, edges, and partitions presented as heatmaps for real-world networks: arxiv, aucs, cannes, ckmp, eutr-A, l2-course, lazega, and timik (layer names and explicit values have been removed for clarity). Note that there is no consistent trend across networks or within the given property.
• Figure 3: A schematic illustration of the mABCD model’s operating principle, exemplified by the generation of a three-layer network. The process consists of six steps. The first five are performed independently for each layer, yielding scale-free monoplex graphs with a known community structure drawn from a shared latent space. In the final step, the layers are glued through a sequence of rewirings to achieve the desired cross-layer edge correlations.
• Figure 4: Two partitions generated based on the same reference layer with $n=1{,}000$ nodes: (left) $q_1 = 1$ (all nodes active), $S_1 = 32$, $s_1 = 16$, $\beta_1=1.5$, (right): $q_2 = 0.5$ (50% nodes active), $S_2 = 50$, $s_2 = 25$, $\beta_2=1.5$ with inactive nodes shown in grey.
• Figure 5: Left: Kendall rank correlation coefficients between actors' labels and generated random variables $X_a = N(a/n,\sigma)$ for various values of $n$. Right: Difference between Kendall rank correlation coefficients for small values of $n$ and the ones for $n=1{,}000{,}000$.