Graph Transformers (GTs) are increasingly applied to social network analysis, yet their deployment is often constrained by fairness concerns. This issue is particularly critical in incomplete social networks, where sensitive attributes are frequently missing due to privacy and ethical restrictions. Existing solutions commonly generate these incomplete attributes, which may introduce additional biases and further compromise user privacy. To address this challenge, FairGE (Fair Graph Encoding) is introduced as a fairness-aware framework for GTs in incomplete social networks. Instead of generating sensitive attributes, FairGE encodes fairness directly through spectral graph theory. By leveraging the principal eigenvector to represent structural information and padding incomplete sensitive attributes with zeros to maintain independence, FairGE ensures fairness without data reconstruction. Theoretical analysis demonstrates that the method suppresses the influence of non-principal spectral components, thereby enhancing fairness. Extensive experiments on seven real-world social network datasets confirm that FairGE achieves at least a 16% improvement in both statistical parity and equality of opportunity compared with state-of-the-art baselines.

Fairness-aware federated graph neural networks (FedGNNs) necessitate consideration of both the server and the clients. However, fairness-aware methods struggle to enhance dual-perspective (i.e., server and clients) fairness without sacrificing utility due to the distributed learning framework. As a consequence, the utility sacrifices of fairness-aware graph learning methods are even exacerbated in federated frameworks. In this work we propose F3GL, a dual-perspective fairness federated graph learning method that enhances both global (for the server) and local fairness (for clients) while preserving utility. Through theoretical analysis, we delineate the similarity between original sensitive features and those after convolution under different spectra. Our findings reveal that only the principal eigenvalue contributes to enhancing this similarity. Moreover, our theoretical analysis applies universally to both clients and servers. Specifically, employing a specialized eigenvalue selection strategy allows for effective optimization of both local and global fairness. Drawing on these insights, we improve dual-perspective fairness through the lens of spectral graph theory without sacrificing utility. Experimental results on two real-world datasets show the superiority of F3GL over existing baselines.

Transformer-based semantic segmentation methods have demonstrated outstanding performance by leveraging global self-attention to effectively capture long-range dependence. However, there still exist two issues in existing works: (1) Most of them utilize the full-rank weight matrix to support the self-attention mechanism and feed-forward network in modelling long-range dependence between patches/pixels, resulting in a high computational cost during both training and inference. (2) Most of them ignore information interactions between high-level semantics and low-level structures during the image resolution recovery, which leads to the performance degradation in segmenting objects with complex boundaries. To tackle these challenges, a lightweight Kolmogorov-Arnold Transformer model (LKAFormer) is proposed for the image semantic segmentation, containing a two-stream lightweight Transformer encoder and a graph feature pyramid aggregation KAN-decoder. The former constructs a hierarchical feature cross-scale fusion pipeline to obtain sufficient semantics containing comprehensive multi-scale information via setting coarse-grained and fine-grained streams with different-size patches of images. In that pipeline, feature lightweight focusing modules model complex and long-range dependence across patches/pixels to refine image semantics with less computational costs by lightweight multi-head self-attention and lightweight feed-forward network designs. The latter leverages the learnable nonlinear transformation mechanism of the Kolmogorov-Arnold Transformer architecture to adaptively capture spatial structure dependence of distinct sub-regions of images. And then, it jointly performs the intra-scale graph fusion and cross-scale graph fusion during the image resolution recovery to enhance information interactions between high-level semantics and low-level structures, which achieves the robust boundary localization and texture refinement of segmentation objects. Finally, plentiful experiments are conducted on three challenging datasets, and the results show LKAFormer sets a new baseline in the image segmentation task in comparison with 11 methods.

Recent studies have highlighted significant fairness issues in Graph Transformer (GT) models, particularly against subgroups defined by sensitive features. Additionally, GTs are computationally intensive and memory-demanding, limiting their application to large-scale graphs. Our experiments demonstrate that graph partitioning can enhance the fairness of GT models while reducing computational complexity. To understand this improvement, we conducted a theoretical investigation into the root causes of fairness issues in GT models. We found that the sensitive features of higher-order nodes disproportionately influence lower-order nodes, resulting in sensitive feature bias. We propose Fairness-aware scalable GT based on Graph Partitioning (FairGP), which partitions the graph to minimize the negative impact of higher-order nodes. By optimizing attention mechanisms, FairGP mitigates the bias introduced by global attention, thereby enhancing fairness. Extensive empirical evaluations on six real-world datasets validate the superior performance of FairGP in achieving fairness compared to state-of-the-art methods.

Multimodal brain graph transformers have become one of the foundational architectures of graph foundation models for brain science, relying on multimodal brain network fusion. However, most current multimodal brain network fusion methods primarily focus on modality-specific information fusion. The interplays within structural-functional brain networks are often ignored. Therefore, they fail to acquire essential coupling information, which is crucial for obtaining robust joint brain network representations. This oversight inevitably limits the effectiveness and generalization of these representations in various downstream tasks. To this end, we propose a novel joint structural-functional brain graph transformer model (namely sfBGT). Technically, we design a cross-network assortativity quantification mechanism to enable structural-functional brain network coupling, thus capturing the interplays of brain structure and function. We then employ a multimodal graph transformer to effectively learn joint representations of structural-functional brain networks along with their coupling relation representations. Experimental results on three real-world datasets demonstrate the superiority of sfBGT over state-of-the-art baselines.

Graph-learning methods, especially graph neural networks (GNNs), have shown remarkable effectiveness in handling non-Euclidean data and have achieved great success in various scenarios. Existing GNNs are primarily based on message-passing schemes, that is, aggregating information from neighboring nodes. However, the diversity and complexity of complex systems from real-world circumstances are not sufficiently taken into account. In these cases, the individual should be treated as an agent, with the ability to perceive their surroundings and interact with other individuals, rather than just be viewed as nodes in existing graph approaches. Additionally, the pairwise interactions used in existing methods also lack the expressiveness for the higher-order complex relations among multiple agents, thus limiting the performance in various tasks. In this work, we propose a Multiagent Hypergraph Force-learning method dubbed MHGForce. First, we formalize the multiagent system (MAS) and illustrate its connection to graph learning. Then, we propose a generalized multiagent hypergraph-learning framework. In this framework, we integrate message-passing and force-based interactions to devise a pluggable method. The method empowers graph approaches to excel in downstream tasks while effectively maintaining structural information in the representations. Experimental results on the Cora, Citeseer, Cora-CA, Zoo, and NTU2012 datasets in node classification demonstrate the effectiveness and generality of our proposed method. We also discuss the characteristics of the MHGForce and explore its role through parametric analysis and visualization. Finally, we give a discussion, conclude our work, and propose future directions.

Fairness-aware Graph Neural Networks (GNNs) often face a challenging trade-off, where prioritizing fairness may require compromising utility. In this work, we re-examine fairness through the lens of spectral graph theory, aiming to reconcile fairness and utility within the framework of spectral graph learning. We explore the correlation between sensitive features and spectrum in GNNs, using theoretical analysis to delineate the similarity between original sensitive features and those after convolution under different spectra. Our analysis reveals a reduction in the impact of similarity when the eigenvectors associated with the largest magnitude eigenvalue exhibit directional similarity. Based on these theoretical insights, we propose FUGNN, a novel spectral graph learning approach that harmonizes the conflict between fairness and utility. FUGNN ensures algorithmic fairness and utility by truncating the spectrum and optimizing eigenvector distribution during the encoding process. The fairness-aware eigenvector selection reduces the impact of convolution on sensitive features while concurrently minimizing the sacrifice of utility. FUGNN further optimizes the distribution of eigenvectors through a transformer architecture. By incorporating the optimized spectrum into the graph convolution network, FUGNN effectively learns node representations. Experiments on six real-world datasets demonstrate the superiority of FUGNN over baseline methods. The codes are available at https://github.com/yushuowiki/FUGNN.

Anomaly detection (such as telecom fraud detection and medical image detection) has attracted the increasing attention of people. The complex interaction between multiple entities widely exists in the network, which can reflect specific human behavior patterns. Such patterns can be modeled by higher-order network structures, thus benefiting anomaly detection on attributed networks. However, due to the lack of an effective mechanism in most existing graph learning methods, these complex interaction patterns fail to be applied in detecting anomalies, hindering the progress of anomaly detection to some extent. In order to address the aforementioned issue, we present a higher-order structure based anomaly detection (GUIDE) method. We exploit attribute autoencoder and structure autoencoder to reconstruct node attributes and higher-order structures, respectively. Moreover, we design a graph attention layer to evaluate the significance of neighbors to nodes through their higher-order structure differences. Finally, we leverage node attribute and higher-order structure reconstruction errors to find anomalies. Extensive experiments on five real-world datasets (i.e., ACM, Citation, Cora, DBLP, and Pubmed) are implemented to verify the effectiveness of GUIDE. Experimental results in terms of ROC-AUC, PR-AUC, and Recall@K show that GUIDE significantly outperforms the state-of-art methods.