Learning multilayer network representation via rotational graph convolutional networks

Multilayer networks provide a natural representation for complex systems in which entities are coupled through heterogeneous relations within and across layers. The key challenge is to learn representations that preserve intra-layer topology while capturing relation-specific transformations across heterogeneous layers, so that the learned embeddings can support structural inference and downstream analysis. However, existing methods often rely on layer-wise modeling, graph flattening, or simple cross-layer aggregation, making it difficult to characterize many-to-many inter-layer dependencies. To address this problem, we propose the Rotational Graph Convolutional Network (RT-GCN), a relation-aware framework that models inter-layer dependencies as rotations in a complex vector space and selectively fuses cross-layer signals through relation-aware attention and consistency gating. Experiments on four real-world multilayer datasets show that RT-GCN learns expressive and interpretable representations. It achieves superior performance in link prediction, remains robust under inter-layer link sparsity, and further supports centrality measurement and visualization analysis, indicating its effectiveness for multilayer network representation learning.