Abstract Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes trend to have different labels or dissimilar features, have recently attracted significant attention and found many real-world applications. Meanwhile, increasing efforts have been made to advance learning from graphs with heterophily. Various graph heterophily measures, benchmark datasets, and learning paradigms are emerging rapidly. In this survey, we comprehensively review existing works on learning from graphs with heterophily. First, we overview over 500 publications, of which more than 300 are directly related to heterophilic graphs. After that, we survey existing metrics of graph heterophily and list recent benchmark datasets. Further, we systematically categorize existing methods based on a hierarchical taxonomy including GNN models, learning paradigms and practical applications. In addition, broader topics related to graph heterophily are also included. Finally, we discuss the primary challenges of existing studies and highlight promising avenues for future research.

Fake news detection on social media is crucial to purifying the online environment and protecting public safety. Many existing methods explore the news propagation structures through graph neural networks (GNNs) to determine the truthfulness of news. End-to-end supervised GNNs notoriously depend on large amounts of labels. Recently, self-supervised graph pretraining has been a promising solution to alleviate the dependence on labels. However, the application of graph pretraining in fake news detection still suffers from two challenges: 1) the missing and unreliable interactions intrinsic in the news propagation structures seriously damage the pretraining performance. 2) There is an inherent gap between pretraining and downstream fake news detection tasks due to inconsistency in optimization objectives, which hinders the efficient transfer of pretrained prior knowledge and causes suboptimal detection results. To address the above two challenges, we propose RGCP, a structure redefined graph pretraining with contrastive prompting for fake news detection. Specifically, we design a propagation structure refinement module that adds potential implicit interactions and removes noisy interactions according to the connection probabilities between posts estimated under the guidance of self-supervised contrastive learning. Thereby, the redefined structures provide reliable news propagation patterns to generate robust pretrained news representations. Moreover, we propose a novel prompt tuning based on the contrastive learning module that reformulates the downstream fake news detection task in a similar form as the graph contrastive pretraining, bridging the optimization objective gap. The extensive experiments on benchmark datasets demonstrate the superiority of RGCP, achieving an average improvement of 10.15% in few-shot classification.

Denoising diffusion models have shown great potential in multiple research areas. Existing diffusion-based generative methods on de novo 3D molecule generation face two major challenges. Since majority heavy atoms in molecules allow connections to multiple atoms through single bonds, solely using pair-wise distance to model molecule geometries is insufficient. Therefore, the first one involves proposing an effective neural network as the denoising kernel that is capable to capture complex multi-body interatomic relationships and learn high-quality features. Due to the discrete nature of graphs, mainstream diffusion-based methods for molecules heavily rely on predefined rules and generate edges in an indirect manner. The second challenge involves accommodating molecule generation to diffusion and accurately predicting the existence of bonds. In our research, we view the iterative way of updating molecule conformations in diffusion process is consistent with molecular dynamics and introduce a novel molecule generation method named Geometric-Facilitated Molecular Diffusion (GFMDiff). For the first challenge, we introduce a Dual-track Transformer Network (DTN) to fully excevate global spatial relationships and learn high quality representations which contribute to accurate predictions of features and geometries. As for the second challenge, we design Geometric-facilitated Loss (GFLoss) which intervenes the formation of bonds during the training period, instead of directly embedding edges into the latent space. Comprehensive experiments on current benchmarks demonstrate the superiority of GFMDiff.

Searching for novel and diverse molecular candidates is a critical undertaking in drug and material discovery. Existing approaches have successfully adapted the diffusion model, the most effective generative model in image generation, to create 1D SMILES strings, 2D chemical graphs, or 3D molecular conformers. However, these methods are not efficient and flexible enough to generate 3D molecules with multiple desired properties, as they require additional training for the models for each new property or even a new combination of existing properties. Moreover, some properties may potentially conflict, making it impossible to find a molecule that satisfies all of them simultaneously. To address these challenges, we present a training-free conditional 3D molecular generation algorithm based on off-the-shelf unconditional diffusion models and property prediction models. The key techniques include modeling the loss of property prediction models as energy functions, considering the property relation between multiple conditions as a probabilistic graph, and developing a stable posterior estimation for computing the conditional score function. We conducted experiments on both single-objective and multi-objective 3D molecule generation, focusing on quantum properties, and compared our approach with the trained or fine-tuned diffusion models. Our proposed model achieves superior performance in generating molecules that meet the conditions, without any additional training cost.

Self-supervised learning (SSL) has become one of the most popular learning paradigms and has achieved remarkable success in the graph field. Recently, a series of pre-training studies on heterogeneous graphs (HGs) using SSL have been proposed considering the heterogeneity of real-world graph data. However, verification of the robustness of heterogeneous graph pre-training is still a research gap. Most existing researches focus on supervised attacks on graphs, which are limited to a specific scenario and will not work when labels are not available. In this paper, we propose a novel unsupervised heterogeneous graph rewriting attack via node clustering (HGAC) that can effectively attack HG pre-training models without using labels. Specifically, a heterogeneous edge rewriting strategy is designed to ensure the rationality and concealment of the attacks. Then, a tailored heterogeneous graph contrastive learning (HGCL) is used as a surrogate model. Moreover, we leverage node clustering results of the clean HGs as the pseudo-labels to guide the optimization of structural attacks. Extensive experiments exhibit powerful attack performances of our HGAC on various downstream tasks (i.e., node classification, node clustering, metapath prediction, and visualization) under poisoning attack and evasion attack.

Being the most cutting-edge generative methods, diffusion methods have shown great advances in wide generation tasks. Among them, graph generation attracts significant research attention for its broad application in real life. In our survey, we systematically and comprehensively review on diffusion-based graph generative methods. We first make a review on three mainstream paradigms of diffusion methods, which are denoising diffusion probabilistic models, score-based genrative models, and stochastic differential equations. Then we further categorize and introduce the latest applications of diffusion models on graphs. In the end, we point out some limitations of current studies and future directions of future explorations.