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.

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.