Social bots are increasingly polluting online platforms by spreading misinformation and engaging in coordinated manipulation, posing severe threats to cybersecurity. Graph Neural Networks (GNNs) have become mainstream for social bot detection due to their ability to integrate structural and attribute features, with spectral-based approaches demonstrating particular efficacy due to discriminative patterns in the spectral domain. However, current spectral GNN methods face two limitations: (1) their broad-spectrum fitting mechanisms degrade the focus on bot-specific spectral features, and (2) certain domain knowledge valuable for bot detection, e.g., low homophily correlates with high-frequency features, has not been fully incorporated into existing methods. To address these challenges, we propose HW-GNN, a novel homophily-aware graph spectral network with Gaussian window constraints. Our framework introduces two key innovations: (i) a Gaussian-window constrained spectral network that employs learnable Gaussian windows to highlight bot-related spectral features, and (ii) a homophily-aware adaptation mechanism that injects domain knowledge between homophily ratios and frequency features into the Gaussian window optimization process. Through extensive experimentation on multiple benchmark datasets, we demonstrate that HW-GNN achieves state-of-the-art bot detection performance, outperforming existing methods with an average improvement of 4.3% in F1-score, while exhibiting strong plug-in compatibility with existing spectral GNNs.

Heterogeneous graphs (HGs) are common in real-world scenarios and often exhibit heterophily. However, most existing studies focus on either heterogeneity or heterophily in isolation, overlooking the prevalence of heterophilic HGs in practical applications. Such ignorance leads to their performance degradation. In this work, we first identify two main challenges in modeling heterophily HGs: (1) varying heterophily distributions across hops and meta-paths; (2) the intricate and often heterophily-driven diversity of semantic information across different meta-paths. Then, we propose the Adaptive Heterogeneous Graph Neural Network (AHGNN) to tackle these challenges. AHGNN employs a heterophily-aware convolution that accounts for heterophily distributions specific to both hops and meta-paths. It then integrates messages from diverse semantic spaces using a coarse-to-fine attention mechanism, which filters out noise and emphasizes informative signals. Experiments on seven real-world graphs and twenty baselines demonstrate the superior performance of AHGNN, particularly in high-heterophily situations.

Spectral Graph Neural Networks (SGNNs) have achieved remarkable performance in tasks such as node classification due to their ability to learn flexible filters. Typically, these filters are learned under the supervision of downstream tasks, enabling SGNNs to adapt to diverse structural patterns. However, in scenarios with limited labeled data, SGNNs often struggle to capture the optimal filter shapes, resulting in degraded performance, especially on graphs with heterophily. Meanwhile, the rapid progress of Large Language Models (LLMs) has opened new possibilities for enhancing graph learning without modifying graph structure or requiring task-specific training. In this work, we propose a novel framework that leverages LLMs to estimate the homophily level of a graph and uses this global structural prior to guide the construction of spectral filters. Specifically, we design a lightweight and plug-and-play pipeline where a small set of labeled node pairs is formatted as natural language prompts for the LLM, which then predicts the graph's homophily ratio. This estimated value informs the spectral filter basis, enabling SGNNs to adapt more effectively to both homophilic and heterophilic structures. Extensive experiments on multiple benchmark datasets demonstrate that our LLM-assisted spectral framework consistently improves performance over strong SGNN baselines.

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. In this paper, we highlight the significance of graph homophily, a pivotal factor for graph domain alignment, which, however, has long been overlooked in existing approaches. Specifically, our analysis first reveals that homophily discrepancies exist in benchmarks. Moreover, we also show that homophily discrepancies degrade GDA performance from both empirical and theoretical aspects, which further underscores the importance of homophily alignment in GDA. Inspired by this finding, we propose a novel homophily alignment algorithm that employs mixed filters to smooth graph signals, thereby effectively capturing and mitigating homophily discrepancies between graphs. Experimental results on a variety of benchmarks verify the effectiveness of our method.

Federated Graph Learning (FGL) empowers clients to collaboratively train Graph neural networks (GNNs) in a distributed manner while preserving data privacy. However, FGL methods usually require that the graph data owned by all clients is homophilic to ensure similar neighbor distribution patterns of nodes. Such an assumption ensures that the learned knowledge is consistent across the local models from all clients. Therefore, these local models can be properly aggregated as a global model without undermining the overall performance. Nevertheless, when the neighbor distribution patterns of nodes vary across different clients (e.g., when clients hold graphs with different levels of heterophily), their local models may gain different and even conflict knowledge from their node-level predictive tasks. Consequently, aggregating these local models usually leads to catastrophic performance deterioration on the global model. To address this challenge, we propose FedHERO, an FGL framework designed to harness and share insights from heterophilic graphs effectively. At the heart of FedHERO is a dual-channel GNN equipped with a structure learner, engineered to discern the structural knowledge encoded in the local graphs. With this specialized component, FedHERO enables the local model for each client to identify and learn patterns that are universally applicable across graphs with different patterns of node neighbor distributions. FedHERO not only enhances the performance of individual client models by leveraging both local and shared structural insights but also sets a new precedent in this field to effectively handle graph data with various node neighbor distribution patterns. We conduct extensive experiments to validate the superior performance of FedHERO against existing alternatives.

As compliance with privacy regulations becomes increasingly critical, the growing demand for data privacy has highlighted the significance of machine unlearning in many real world applications, such as social network and recommender systems, many of which can be represented as graph-structured data. However, existing graph unlearning algorithms indiscriminately modify edges or nodes from well-trained models without considering the potential impact of such structural modifications on fairness. For example, forgetting links between nodes with different genders in a social network may exacerbate group disparities, leading to significant fairness concerns. To address these challenges, we propose a novel approach that jointly optimizes the graph structure and the corresponding model for fair unlearning tasks. Specifically,our approach rewires the graph to enhance unlearning efficiency by removing redundant edges that hinder forgetting while preserving fairness through targeted edge augmentation. Additionally, we introduce a worst-case evaluation mechanism to assess the reliability of fair unlearning performance. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed approach in achieving superior unlearning outcomes.

Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous graphs, many real-world graphs exhibit heterogeneous patterns where nodes and edges have multiple types. This paper fills this gap by introducing the first approach for heterogeneous graph structure learning (HGSL). To this end, we first propose a novel statistical model for the data-generating process (DGP) of heterogeneous graph data, namely hidden Markov networks for heterogeneous graphs (H2MN). Then we formalize HGSL as a maximum a-posterior estimation problem parameterized by such DGP and derive an alternating optimization method to obtain a solution together with a theoretical justification of the optimization conditions. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate that our proposed method excels in learning structure on heterogeneous graphs in terms of edge type identification and edge weight recovery.

The detection of malicious social bots has become a crucial task, as bots can be easily deployed and manipulated to spread disinformation, promote conspiracy messages, and more. Most existing approaches utilize graph neural networks (GNNs)to capture both user profle and structural features,achieving promising progress. However, they still face limitations including the expensive training on large underlying graph, the performance degration when similar neighborhood patterns' assumption preferred by GNNs is not satisfied, and the dynamic features of bots in a highly adversarial context. Motivated by these limitations, this paper proposes a method named BSG4Bot with an intuition that GNNs training on Biased SubGraphs can improve both performance and time/space efficiency in bot detection. Specifically, BSG4Bot first pre-trains a classifier on node features efficiently to define the node similarities, and constructs biased subgraphs by combining the similarities computed by the pre-trained classifier and the node importances computed by Personalized PageRank (PPR scores). BSG4Bot then introduces a heterogeneous GNN over the constructed subgraphs to detect bots effectively and efficiently. The relatively stable features, including the content category and temporal activity features, are explored and incorporated into BSG4Bot after preliminary verification on sample data. The extensive experimental studies show that BSG4Bot outperforms the state-of-the-art bot detection methods, while only needing nearly 1/5 training time.