Generative Regularities in Multi-Layer Networks: A Shared-Latent Space Representation Approach

Understanding structural regularities across layers in multi-layer networks is essential for uncovering their underlying generative mechanisms. While link prediction has been widely explored in multi-layer networks, it is typically treated as an isolated technical problem, often missing its broader implications for network structure and the mechanisms driving edge formation. In this paper, we investigate the extent to which network layers exhibit shared generative regularities. By examining the alignment of latent representations across layers, we assess the similarity of their underlying mechanisms and leverage this alignment to improve predictive performance. To facilitate this, we introduce a new metric, C ross- L ayer G enerative C onsistency ( CLGC ), which quantitatively captures the degree of structural and generative alignment between network layers. CLGC is grounded in the shared-latent space framework, positing that layers generated by similar mechanisms will produce compatible latent representations. To realize this approach, we present SupportNet — Support prediction and consistency analysis in multi-layer Net works—a GCN-based model augmented with adversarial training to effectively learn robust shared-latent space representations. These representations support both accurate link prediction and interpretable evaluation of cross-layer generative consistency. Experiments on real-world multi-layer networks demonstrate that SupportNet delivers strong link prediction results improving AUC by 17.47%, AP by 40.41% and AUPR by 39.59% on the Kapferer dataset, while CLGC reveals significant patterns of structural and generative alignment among layers.