Recent advances in generic large models, such as GPT and DeepSeek, have motivated the introduction of universality to graph pre-training, aiming to learn rich and generalizable knowledge across diverse domains using graph representations to improve performance in various downstream applications. However, most existing methods face challenges in learning effective knowledge from generic graphs, primarily due to simplistic data alignment and limited training guidance. The issue of simplistic data alignment arises from the use of a straightforward unification for highly diverse graph data, which fails to align semantics and misleads pre-training models. The problem with limited training guidance lies in the arbitrary application of in-domain pre-training paradigms to cross-domain scenarios. While it is effective in enhancing discriminative representation in one data space, it struggles to capture effective knowledge from many graphs. To address these challenges, we propose a novel Latent sEmantic Distribution Alignment (LEDA) model for universal graph pre-training. Specifically, we first introduce a dimension projection unit to adaptively align diverse domain features into a shared semantic space with minimal information loss. Furthermore, we design a variational semantic inference module to obtain the shared latent distribution. The distribution is then adopted to guide the domain projection, aligning it with shared semantics across domains and ensuring cross-domain semantic learning. LEDA exhibits strong performance across a broad range of graphs and downstream tasks. Remarkably, in few-shot cross-domain settings, it significantly outperforms in-domain baselines and advanced universal pre-training models.

Graph Neural Networks (GNNs) have recently achieved significant success in several graph-related tasks. However, traditional GNNs and their variants are constantly limited by the implicit homophily, assuming neighboring nodes belong to the same class. This results in weak performance on heterophilic graphs where most nodes are linked to neighbors of different classes. Despite the numerous attempts to adequately deal with heterophily, most methods still use the uniform propagation aggregation mechanism. In this paper, we argue that identifying neighbors with different class labels and exploiting them individually is crucial for heterophilic GNNs. We then propose a simple and efficient novel co-training approach, EG-GCN, which uses group aggregation to handle homophilic and heterophilic neighbors separately. In EG-GCN, we first use an edge discriminator to classify edges and split the neighborhood of every node into two parts. We then apply group graph convolution to the divided neighborhoods to obtain node representations. During training, we continuously optimize the edge discriminator to improve neighborhood partition and use the node classification results to identify highly confident unlabeled nodes to expand the edge training set. This co-training strategy enables both components to enhance each other mutually. Extensive experiments demonstrate that EG-GCN significantly outperforms the state-of-the-art approaches.