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Triadic Closure-Heterogeneity-Harmony GCN for Link Prediction

Ke-ke Shang, Junfan Yi, Michael Small, Yijie Zhou

TL;DR

TriHetGCN tackles link prediction by fusing physics-inspired topology cues with graph neural networks. It builds topology-aware node features via shortest-path distances to a small set of anchor nodes and integrates triadic closure (Common Neighbors) and network heterogeneity (degree differences) into the GCN propagation with learnable weights. The model delivers state-of-the-art performance across nine real-world datasets, including those with and without node attributes, and ablation experiments reveal complementary benefits of CN and HI signals. This approach bridges statistical physics and deep learning, offering robust generalization for diverse networks and enabling effective link prediction even when node attributes are absent. The work also discusses computational considerations and future extensions to dynamic graphs.

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.

Triadic Closure-Heterogeneity-Harmony GCN for Link Prediction

TL;DR

TriHetGCN tackles link prediction by fusing physics-inspired topology cues with graph neural networks. It builds topology-aware node features via shortest-path distances to a small set of anchor nodes and integrates triadic closure (Common Neighbors) and network heterogeneity (degree differences) into the GCN propagation with learnable weights. The model delivers state-of-the-art performance across nine real-world datasets, including those with and without node attributes, and ablation experiments reveal complementary benefits of CN and HI signals. This approach bridges statistical physics and deep learning, offering robust generalization for diverse networks and enabling effective link prediction even when node attributes are absent. The work also discusses computational considerations and future extensions to dynamic graphs.

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.
Paper Structure (17 sections, 9 equations, 3 figures, 7 tables, 1 algorithm)

This paper contains 17 sections, 9 equations, 3 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Heuristics-based link prediction
  4. Learning-based link prediction
  5. Methodology
  6. Problem Statement
  7. Evaluation Metric
  8. Model overview
  9. Topology feature construction
  10. Graph structural representation
  11. Connection probability prediction
  12. Experiment
  13. Datasets
  14. Experimental settings
  15. Performance Comparison
  16. ...and 2 more sections

Figures (3)

  • Figure 1: In (a), it is observed that two red nodes share a significant number of blue nodes as their common neighbors. This indicates a high level of overlap in their immediate connections within the network. When a dashed line is introduced to directly link the two red nodes, multiple closed triangular structures are formed. This phenomenon aligns with the sociological principle of triadic closure, which posits that individuals in a social network tend to form connections with each other if they share mutual acquaintances or common neighbors. Triadic closure is a fundamental mechanism underlying the clustering behavior observed in many real-world networks. (b) highlights an issue related to structural heterogeneity within the network. Specifically, the connectivity pattern demonstrates a hierarchical decrease in the degree distribution as we move from the red nodes to the yellow nodes, and subsequently to the blue nodes. The degree of a node, defined as the number of edges connected to it, decreases progressively across these layers. Furthermore, there is a pronounced disparity between the node with the highest degree (often referred to as a hub node) and the nodes with minimal connectivity, such as leaf nodes. This structural heterogeneity reflects the uneven distribution of connections within the network, where hub nodes serve as central points of interaction, while peripheral nodes exhibit significantly lower levels of connectivity.
  • Figure 2: An overview of the proposed TriHetGCN framework, which integrates physical statistic rules and GCN for link prediction, is presented as follows: (a) Topology Feature Construction: This module constructs node attributes based on the shortest paths from each node to $M$ selected anchor points, leveraging the underlying network structure. (b) Heuristics Indicators: This component utilizes physical rules, specifically the Common Neighbors (CN) and Heterogeneity Index (HI) within the network's topological structure, to capture explicit local relationships between nodes. (c) Topology-Aware Graph Representation: This module enhances the GCN framework by incorporating local pairwise node relationships into the convolutional operator, refining its ability to capture fine-grained structural details through interactions between neighboring nodes. It then employs the node aggregation mechanism of GCN to extract global graph structural features. (d) Connection Probability Prediction: This component uses the complete spatial features as input variables and predicts the likelihood of link connections via a fully connected neural network.
  • Figure 3: Network Heterogeneity and Triangle Structure: The distribution of these two structural properties across selected datasets is illustrated. Degree heterogeneity is measured by the coefficient of degree variation (x-axis). The common neighbor property is measured by the average clustering coefficient, which is proportional to the number of closed triangles in the network (y-axis). Each point represents a dataset, labeled by its name.