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Toward General Digraph Contrastive Learning: A Dual Spatial Perspective

Daohan Su, Yang Zhang, Xunkai Li, Rong-Hua Li, Guoren Wang

TL;DR

This work tackles the challenge of graph contrastive learning on directed graphs by introducing S2-DiGCL, a dual-spatial framework that combines real-domain path augmentation with complex-domain personalized magnetic perturbations. By constructing two complementary views and optimizing a dual InfoNCE objective, the method captures both local directional flows and global directional semantics, supported by a theoretical analysis based on Magnetic Von Neumann Entropy. The approach achieves state-of-the-art performance across seven real-world digraph datasets for node classification and link prediction, while demonstrating robustness and efficiency through ablations and scalability experiments. Overall, S2-DiGCL offers a principled, scalable, and direction-aware paradigm for unsupervised learning on directed graphs, with potential extensions to other structured data domains.

Abstract

Graph Contrastive Learning (GCL) has emerged as a powerful tool for extracting consistent representations from graphs, independent of labeled information. However, existing methods predominantly focus on undirected graphs, disregarding the pivotal directional information that is fundamental and indispensable in real-world networks (e.g., social networks and recommendations).In this paper, we introduce S2-DiGCL, a novel framework that emphasizes spatial insights from complex and real domain perspectives for directed graph (digraph) contrastive learning. From the complex-domain perspective, S2-DiGCL introduces personalized perturbations into the magnetic Laplacian to adaptively modulate edge phases and directional semantics. From the real-domain perspective, it employs a path-based subgraph augmentation strategy to capture fine-grained local asymmetries and topological dependencies. By jointly leveraging these two complementary spatial views, S2-DiGCL constructs high-quality positive and negative samples, leading to more general and robust digraph contrastive learning. Extensive experiments on 7 real-world digraph datasets demonstrate the superiority of our approach, achieving SOTA performance with 4.41% improvement in node classification and 4.34% in link prediction under both supervised and unsupervised settings.

Toward General Digraph Contrastive Learning: A Dual Spatial Perspective

TL;DR

This work tackles the challenge of graph contrastive learning on directed graphs by introducing S2-DiGCL, a dual-spatial framework that combines real-domain path augmentation with complex-domain personalized magnetic perturbations. By constructing two complementary views and optimizing a dual InfoNCE objective, the method captures both local directional flows and global directional semantics, supported by a theoretical analysis based on Magnetic Von Neumann Entropy. The approach achieves state-of-the-art performance across seven real-world digraph datasets for node classification and link prediction, while demonstrating robustness and efficiency through ablations and scalability experiments. Overall, S2-DiGCL offers a principled, scalable, and direction-aware paradigm for unsupervised learning on directed graphs, with potential extensions to other structured data domains.

Abstract

Graph Contrastive Learning (GCL) has emerged as a powerful tool for extracting consistent representations from graphs, independent of labeled information. However, existing methods predominantly focus on undirected graphs, disregarding the pivotal directional information that is fundamental and indispensable in real-world networks (e.g., social networks and recommendations).In this paper, we introduce S2-DiGCL, a novel framework that emphasizes spatial insights from complex and real domain perspectives for directed graph (digraph) contrastive learning. From the complex-domain perspective, S2-DiGCL introduces personalized perturbations into the magnetic Laplacian to adaptively modulate edge phases and directional semantics. From the real-domain perspective, it employs a path-based subgraph augmentation strategy to capture fine-grained local asymmetries and topological dependencies. By jointly leveraging these two complementary spatial views, S2-DiGCL constructs high-quality positive and negative samples, leading to more general and robust digraph contrastive learning. Extensive experiments on 7 real-world digraph datasets demonstrate the superiority of our approach, achieving SOTA performance with 4.41% improvement in node classification and 4.34% in link prediction under both supervised and unsupervised settings.
Paper Structure (37 sections, 2 theorems, 27 equations, 5 figures, 4 tables)

This paper contains 37 sections, 2 theorems, 27 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Graph Contrastive Learning
  5. Directed Graph Neural Network
  6. Proposed Method
  7. Complex Domain Personalized Magnetic Perturbation
  8. Real Domain Path Augmentation
  9. Contrastive Objective
  10. Theoretical Analysis
  11. Magnetic Von Neumann Entropy
  12. Spectral Properties of Magnetic Perturbation
  13. Interpretation and Implications
  14. Controlled Structural Diversity
  15. Stability of Magnetic Perturbation
  16. ...and 22 more sections

Key Result

Theorem 1

Assume that $\mathbf{L}^{(q)}$ depends smoothly on $q$ and that eigenvalues are simple almost everywhere (so that $\lambda_k^{(q)}$ are differentiable a.e.). Then Consequently, the sign of $\partial H_{VN}/\partial q$ is governed by the correlation between eigenvalues and their $q$-sensitivities: if higher-frequency modes (i.e., larger $\lambda_k^{(q)}$) grow faster in $q$ than lower ones, then $

Figures (5)

  • Figure 1: Illustration of naive (Upper) vs. personalized (Lower) augmentations from real and complex spatial perspectives. Uniform perturbations fail to distinguish heterophilous nodes or asymmetric directional flows, while personalized perturbations adapt augmentation strength and phase shifts to each node’s topology, enabling direction-aware contrastive learning in S2-DiGCL.
  • Figure 2: Overview of S2-DiGCL, including a complex-domain global personalized magnetic Laplacian augmentation (Left), a real-domain local path augmentation (Right) and a novel contrastive strategy that combines both perspectives (Upper).
  • Figure 3: Visualization results on CoraML.
  • Figure 4: Performance with different parameters.
  • Figure 5: Time efficiency on Citeseer.

Theorems & Definitions (4)

  • Definition 1: Magnetic Von Neumann Entropy
  • Definition 2: Perturbation Entropy Variation
  • Theorem 1: Monotonic Entropy Response
  • Theorem 2: Bounded Entropy Variation