Triadic Closure-Heterogeneity-Harmony GCN for Link Prediction

2025-04-29

AI Summary

To address the poor generalizability of traditional heuristic methods and the neglect of node attributes and structural relationships in existing GNNs for link prediction in complex networks, this paper proposes a physics-informed graph neural network framework. It explicitly incorporates two statistical-physics-inspired topological metrics—triadic closure and degree heterogeneity—into a GCN architecture, forming a three-module collaborative design: anchor-feature construction, topology-enhanced representation learning, and deep probabilistic prediction. The method jointly leverages shortest-path-based anchor features and node attributes. Evaluated on nine real-world datasets—including both attribute-free and large-scale attributed networks—it achieves state-of-the-art performance and significantly improves cross-network generalizability. This work effectively bridges statistical physics modeling and graph deep learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Link prediction aims to estimate the likelihood of connections between pairs of nodes in complex networks, which is beneficial to many applications from friend recommendation to metabolic network reconstruction. Traditional heuristic-based methodologies in the field of complex networks typically depend on predefined assumptions about node connectivity, limiting their generalizability across diverse networks. While recent graph neural network (GNN) approaches capture global structural features effectively, they often neglect node attributes and intrinsic structural relationships between node pairs. To address this, we propose TriHetGCN, an extension of traditional Graph Convolutional Networks (GCNs) that incorporates explicit topological indicators -- triadic closure and degree heterogeneity. TriHetGCN consists of three modules: topology feature construction, graph structural representation, and connection probability prediction. The topology feature module constructs node features using shortest path distances to anchor nodes, enhancing global structure perception. The graph structural module integrates topological indicators into the GCN framework to model triadic closure and heterogeneity. The connection probability module uses deep learning to predict links. Evaluated on nine real-world datasets, from traditional networks without node attributes to large-scale networks with rich features, TriHetGCN achieves state-of-the-art performance, outperforming mainstream methods. This highlights its strong generalization across diverse network types, offering a promising framework that bridges statistical physics and graph deep learning.

Problem

• Predicts node connections in complex networks accurately
• Overcomes limitations of heuristic and GNN methods
• Integrates topological features for better generalization

Innovation

• Extends GCN with triadic closure and heterogeneity
• Uses shortest path distances for topology features
• Integrates topological indicators into deep learning