Learning over Positive and Negative Edges with Contrastive Message Passing

Graph Contrastive Learning (GCL), which trains graph encoders by maximizing similarity between positive samples and minimizing it between negative ones, has emerged as a mainstream graph pre-training paradigm. It is widely recognized that positive samples are essential in GCLs. Ideally, maximizing the similarity of positive samples enables graph encoders to capture intrinsic semantic and patterns of graph data. However, we discover an interesting phenomenon: GCLs can achieve competitive performance even without positive samples. This motivates us to revisit the fundamental mechanism of positive samples in GCLs. From the perspective of Dirichlet energy, we theoretically finds that message passing, a key mechanism in graph encoders, trivializes the maximization of positive samples, preventing GCLs from effectively learning from positive samples. To address this, we propose SPGCL to mitigate the trivialization caused by message passing and restore the learning efficacy of positive samples. Specifically, we find that high Dirichlet energy features help positive samples provide effective learning signals while low Dirichlet energy features contribute little to positive learning signal but is useful for positive sampling. Based on this, SPGCL propagates only high Dirichlet energy features and uses low energy features to construct a probability matrix for reliable positive sampling. Extensive experiments demonstrate the effectiveness of SPGCL.

We introduce Contrastive FUSE, a fast and unified framework for scalable node representation learning in graphs with partially available pairwise node labels and no available node features. Unlike existing methods, we directly optimize a spectral contrastive objective that integrates community-aware structural signals with signed pairwise constraints. To support large-scale training, we replace the expensive modularity gradient with a lightweight approximation, which preserves the structure-seeking behavior of modularity while reducing the computational cost significantly. This yields an efficient optimization scheme with a natural gradient decomposition and adaptive learning-rate scaling, enabling fast iterative updates even on million-edge graphs. Extensive experiments on benchmark citation networks, large co-purchase graphs, and OGB datasets show that Contrastive FUSE achieves competitive or superior contrastive classification performance without relying on node features, while offering substantial runtime gains over existing baselines. These results highlight the effectiveness of coupling modularity-inspired structural learning with contrastive supervision for efficient and scalable contrastive node representation learning.

Many real-world graphs support multiple predictive tasks over the same underlying structure, creating an opportunity to reuse supervision across node classification (NC) and link prediction (LP). However, existing evaluations often rely on incompatible splits, observed-graph assumptions, and negative sampling rules, making conclusions about same-graph cross-task transfer unreliable. We formalize same-graph NC-LP transfer and propose a leakage-free protocol that fixes node and edge splits, uses a shared message-passing graph that excludes evaluated edges, and employs fixed negatives for LP. Across three backbones (GCN, GraphSAGE, GPS), we find that transfer is strongly directional and predictable: NC $\to$ LP is consistently beneficial on homophilic graphs, while LP $\to$ NC is fragile and can even degrade accuracy under naive representation reuse. LP $\to$ NC becomes reliably positive mainly in a structure-dominant regime where LP is easy but NC is unsaturated, suggesting that LP acts as structural pretraining. Finally, we introduce the CoTask Score (CTS) to summarize joint NC+LP utility when a shared encoder must serve both tasks, and show that simple dataset statistics, especially homophily, can guide mechanism choice and help avoid negative transfer.