Graph Neural Networks (GNNs) have received increasing attention due to their ability to handle graph-structured data, yet their explainability remains a significant challenge. An effective solution is to provide the GNN models with counterfactual explanations, which aim to answer “How should the input instance be perturbed to change the model's prediction?". However, existing works mainly focus on generating explanations that can effectively alter model predictions, while neglecting whether the explanations remain aligned with the original data distribution, leading to the distribution shift problem. To address this problem, we propose a novel method called ICExplainer for generating explanations within the original distribution. Specifically, we introduce graph diffusion-based generative model into the counterfactual reasoning, treating it as an optimization objective for graph distribution learning. Taking insights from variational inference, we use it to estimate the true distribution of the input graphs to retain essential structural and semantic information. The inferred distribution is then utilized as prior knowledge to guide the reverse process, ensuring that generated explanations are both counterfactual and distributionally coherent. Extensive experiments conducted on both synthetic and real-world datasets demonstrate the superior performance of ICExplainer over existing methods.

Variational autoencoders (VAEs) have been widely used for node clustering, with existing methods mainly focusing on enhancing the expressiveness of their latent space. Recently, the integration of diffusion models with VAEs has provided new opportunities to achieve this objective. However, the mechanism by which the diffusion model improves performance remains unclear. To bridge this gap, we conduct an empirical analysis from the perspective of graph spectral theory, revealing that the signal modulation induced by diffusion models closely aligns with the low-frequency spectral characteristics of VAEs, which in turn explains their effectiveness. Nevertheless, further experiments highlight that diffusion models exhibit limitations in modulating high-frequency signals, which diverge from the spectral characteristics of VAEs. Moreover, existing diffusion methods fail to enable the latent space to adequately capture and reflect cluster-specific characteristics. To address these challenges, we propose a novel plug-and-play method, FVD, to improve the performance of VAE-based methods in node clustering tasks. Specifically, we incorporate the graph wavelet transform as a secondary signal modulator, enabling independent adjustments of specific frequency bands to better align with the spectral characteristics of VAEs. Additionally, we introduce the Student's t-distribution as a conditional constraint in the reverse process of FVD, deriving a more compact variational lower bound. This enhancement preserves fine-grained node information while focusing on clustering details, effectively mitigating the cluster collapse phenomenon. Comprehensive experimental results demonstrate that integrating FVD with existing methods achieves competitive performance improvements in most cases.

Variational autoencoder performs well in community detection on static networks, but it is difficult to directly extend to continuous dynamic networks. The main reason is that traditional methods mainly rely on adjacency structures to complete the inference and generation processes. However, continuous dynamic networks cannot be described by this structure because the inherent timeliness and causality information of the network would be lost. To address this issue, we propose a novel variational autoencoder, CT-VAE, for community detection in continuous dynamic networks, along with its scalable variant, CT-CAVAE. By conceptualizing node interactions as event streams and adopting the Hawkes process to capture temporal dynamics and causality, and incorporating them into the inference process, CT-VAE can effectively extend the traditional inference approach to continuous dynamic networks. Additionally, in the generation phase, CT-VAE combines pseudo-labeling and compact constraint strategies to facilitate the reconstruction process of non-adjacent structures. For the scalable variant, CT-CAVAE, end-to-end community detection is achieved by cleverly combining Gaussian mixture distribution. Extensive experimental results demonstrate that the proposed CT-VAE and CT-CAVAE achieve more favorable performance compared with the state-of-the-art baselines.

Signed networks are commonly used to represent positive and negative relationships in the real world. Link sign prediction in signed networks is a significant research topic. In the past decades, various link sign prediction methods have been proposed. However, most of them following the message-passing paradigm encounter two challenges: i) capture the relationship between nodes and their high-order neighborhoods, and ii) alleviate the over-smoothing problem. To address these challenges, we propose a method called Signed Graph Transformer (SGTrans), which uses a node sequence encoding approach based on Transformer. For the first challenge, we introduce three types of positional encoding, guided by path-level balance theory, while adding more network layers to capture the relationships between nodes and their high-order neighborhoods effectively. For the second challenge, SGTrans utilizes self-attention to handle a sampled relevant node sequence rather than message passing. This approach not only minimizes the introduction of excessive irrelevant node information but also alleviates the over-smoothing problem. Extensive experiments are conducted on four real-world datasets, and the results illustrate the effectiveness of SGTrans.

Dynamic link prediction (DLP) is a crucial task in graph learning, aiming to predict future links between nodes at subsequent time in dynamic graphs. Recently, graph masked autoencoders (GMAEs) have shown promising performance in self-supervised learning. However, their application to DLP is under-explored. Existing GMAEs struggle to capture temporal dependencies, and their random masking causes crucial information loss for DLP. Moreover, most existing DLP methods rely on local information, ignoring global information and failing to capture complex features in real-world dynamic graphs. To address these issues, we propose DyGMAE, a novel dynamic GMAE method specifically designed for DLP. DyGMAE introduces a Multi-Scale Masking Strategy (MSMS), which generates multiple graph views by masking parts of the edges and tries to reconstruct them. Additionally, a multi-scale masking representation alignment module with a contrastive learning objective is employed to align representations which are encoded by unmasked edges across these views. Through this design, different masked views can provide diverse information to alleviate the drawbacks of random masking, and contrastive learning can align different views to mitigate the problem of exploiting local and global information simultaneously. Experiments on benchmark datasets show DyGMAE achieves superior performance in the DLP task.

Methods based on variational bayes theorytare widely used to detect community structures in networks. In recent years, many related methods have emerged that provide valuable insights into variational bayes theory. Remarkably, a fundamental assumption remains incomprehensible. Variational bayes-based methods typically employ a posterior distribution that follows a gaussian distribution to approximate the unknown prior distribution. However, the complexity and irregularity of node distributions in real-world networks prompt us to consider what characteristics of network information are suitable for the posterior distribution. Mathematically, inappropriate low- and high-frequency signals in expectation inference and variance inference can intensify the adverse effects of community distortion and ambiguity. To analysis these two phenomena and propose reasonable countermeasures, we conduct an empirical study. It is found that appropriately compressing low-frequency signals during expectation inference and amplifying high-frequency signals during variance inference are effective strategies. Based on these two strategies, this paper proposes a novel variational bayes plug-in, namely VBPG, to boost the performance of existing variational bayes-based community detection methods. Specifically, we modulate the frequency signals during expectation and variance inference to generate a new gaussian distribution. This strategy improves the fitting accuracy between the posterior distribution and the unknown true distribution without altering the modules of existing methods. The comprehensive experimental results validate that methods using VBPG achieve competitive performance improvements in most cases.

Community detection in multiplex networks has received considerable attention in recent years. However, existing methods that combine graph embedding and downstream tasks still face two challenges. The first is how to fully explore the correlation among the layers in the multiplex networks, and the second is how to make the learned node representation more applicable to the community detection tasks. Aiming at these challenges, we propose a novel self-supervised multiplex community detection model called MGCAE which is based on graph neural networks. To solve the first challenge, we compute the mutual information maximization loss in the self-supervision module. The mutual information includes global representation and common representation of nodes in different layers, and node representation in each layer. For the second challenge, we combine a Bernoulli-Poisson loss and a modularity maximization loss to jointly optimize the reconstruction of the original adjacency matrix, which is in line with the rigorous theory of modularity. We treat graph convolutional autoencoder (GCAE) as the backbone framework and train it by using the unified loss mentioned above. In addition, the model obtains the community detection results in an end-to-end manner, which makes the model independent of downstream tasks and more stable. Experiments on real-world attributed multiplex network datasets demonstrate the effectiveness of our model.

Existing community detection methods for attributed multiplex networks focus on exploiting the complementary information from different topologies, while they are paying little attention to the role of attributes. However, we observe that real attributed multiplex networks exhibit two unique features, namely, consistency and homogeneity of node attributes. Therefore, in this paper, we propose a novel method, called ACDM, which is based on these two characteristics of attributes, to detect communities on attributed multiplex networks. Specifically, we extract commonality representation of nodes through the consistency of attributes. The collaboration between the homogeneity of attributes and topology information reveals the particularity representation of nodes. The comprehensive experimental results on real attributed multiplex networks well validate that our method outperforms state-of-the-art methods in most networks.

Since existing methods are often not effective to detect communities with multiple topics in attributed networks, we propose a method named SSAGCN via Autoencoder-style self-supervised learning. SSAGCN firstly designs an adaptive graph convolutional network (AGCN), which is treated as the encoder for fusing topology information and attribute information automatically, and then utilizes a dual decoder to simultaneously reconstruct network topology and attributes. By further introducing the modularity maximization and the joint optimization strategies, SSAGCN can detect communities with multiple topics in an end-to-end manner. Experimental results show that SSAGCN outperforms state-of-the-art approaches, and also can be used to conduct topic analysis well.

Community detection is one of the hottest research topics in attributed networks analysis. Nonnegative matrix factorization (NMF) is widely used in community detection of attributed networks because of its high interpretability and extensibility. However, the existing NMF based methods still encounter some obstacles which affect the performance of community detection. Firstly, it is impossible to solve the problem of sparse semantic description. Besides, these methods cannot integrate the heterogeneity of topology structure and nodes attributes. Obviously, these methods cannot accurately identify community structure and assign specific semantic descriptions to each community. To overcome the aforementioned problems, we propose a novel method which combines graph neural networks with weighted-traction regularization. Moreover, we use graph neural networks to discover the semantic characteristics between adjacent nodes which can alleviate the problem of sparse semantic description. Furthermore, the regularizer we proposed can improve the performance of community detection in attributed networks. Experiments on some real attributed networks show that the method we proposed not only is better than some representative related methods but also can assign specific semantic descriptions to each community at the same time.