ARGO: Ricci curvature-guided Graph Convolutional Network framework for community detection in biological networks

Understanding the modular architecture of gene co-expression networks is critical for deciphering the regulatory mechanisms underlying tissue-specific functions and disease etiology. Recently, network curvature measures, particularly Ollivier–Ricci curvature, have emerged as effective geometric descriptors that capture local topological heterogeneity and global structural robustness within complex biological systems. In this study, we present ARGO, a Ricci curvature-guided Graph Convolutional Network framework designed for enhanced community detection in gene co-expression networks. ARGO explicitly integrates edge-wise Ollivier–Ricci curvature as a geometric prior to modulate message-passing dynamics within a Graph Convolutional Network, facilitating curvature-weighted aggregation of node features and subsequently improving latent space representations. The learned embeddings serve as the basis for the analysis of the networks, enabling the identification of biologically relevant and topologically stable modules. We applied the framework to the well-known community detection scenario and analyzed twelve curated tissue-specific networks derived from the iNetModels 2.0 resource, observing superior modularity and interpretability relative to standard and curvature-weighted Louvain methods. This paper represents an extended and enhanced version of our previously published conference contribution — “Biological Community Detection with Graph Neural Network and Network Curvature Analysis on Gene Co-expression Networks” (Milano et al., 2025).