Layered Division and Global Allocation for Community Detection in Multilayer Network

TL;DR

LDGA addresses the challenge of community detection in multilayer networks by separating layer-wise division from global allocation. It introduces a layer-aligned Transformer backbone, a community-latent encoder with learnable prototypes, and a differentiable multilayer modularity loss to train end-to-end. The approach yields state-of-the-art results on synthetic and real-world multilayer networks, showing strong robustness to the number of communities and scalable performance due to sparse attention. This work provides a practical, modularity-driven framework for accurate, scalable CDMN in Web-scale multilayer systems.

Abstract

Community detection in multilayer networks (CDMN) is to divide a set of entities with multiple relation types into a few disjoint subsets, which has many applications in the Web, transportation, and sociology systems. Recent neural network-based solutions to the CDMN task adopt a kind of representation fusion and global division paradigm: Each node is first learned a kind of layer-wise representations which are then fused for global community division. However, even with contrastive or attentive fusion mechanisms, the fused global representations often lack the discriminative power to capture structural nuances unique to each layer. In this paper, we propose a novel paradigm for the CDMN task: Layered Division and Global Allocation (LDGA). The core idea is to first perform layer-wise group division, based on which global community allocation is next performed. Concretely, LDGA employs a multi-head Transformer as the backbone representation encoder, where each head is for encoding node structural characteristics in each network layer. We integrate the Transformer with a community-latent encoder to capture community prototypes in each layer. A shared scorer performs layered division by generating layer-wise soft assignments, while global allocation assigns each node the community label with highest confidence across all layers to form the final consensus partition. We design a loss function that couples differentiable multilayer modularity with a cluster balance regularizer to train our model in an unsupervised manner. Extensive experiments on synthetic and real-world multilayer networks demonstrate that our LDGA outperforms the state-of-the-art competitors in terms of higher detected community modularities. Our code with parameter settings and datasets are available at https://anonymous.4open.science/r/LDGA-552B/.

Figures (5)

• Figure 1: Illustration of the two paradigms for community detection in multiplex networks. (a) and (b): representation fusion and global division (existing approaches); (c): layered division and global allocations (ours in this paper).
• Figure 2: The overview of LDGA framework (FFN denotes feed-forward networks). LDGA first generates layer-wise soft assignments via Layered Division. In Global Allocation, it assigns each node its highest-confidence community across layers (e.g., node 1 to community 1). The model is trained end-to-end by maximizing a differentiable multilayer modularity objective.
• Figure 3: Experiments with different $N$ on mLFR datasets, $N$ denotes the number of nodes in the network.
• Figure 4: Modularity with different pre-specified maximum numbers of communities $\kappa$ on ten real-world datasets.
• Figure 5: Real community amount on different datasets

Theorems & Definitions (2)

• Definition 1: Multi-layer Network
• Definition 2: Multi-layer Network Community Detection