The paper studies the stability of graph-aware continuous‑time generative models that use a graph filter combined with a learned graph neural network. It derives explicit Wasserstein bounds showing how relative graph perturbations affect the generated distributions, and proposes a principled framework for designing stable graph filters that preserve heat‑diffusion smoothing while improving structural stability. Experiments on synthetic and fMRI data demonstrate that these stable filters enhance robustness and match or surpass the generative quality of a heat‑equation baseline.
By Martin Schmidt, Gonzalo Mateos
arXiv:2607. 07510v1 Announce Type: cross Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations.
By Martin Schmidt, Gonzalo Mateos
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation.
arXiv:2609.39739v1 Announce Type: new
Abstract: Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures...
By Luca Miglior, Alessio Gravina, Davide Bacciu
arXiv:2608. 19914v1 Announce Type: new Abstract: Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks.
By Chuansen Peng, Yifan Xia, Jinshan Zhong, Xiaojing Shen
The paper investigates how signed graph filters respond to structural changes such as edge additions, deletions, and sign flips. It shows that both the nature of the edge perturbation and the correlation among node features jointly influence the stability of learned representations. Leveraging this insight, the authors propose a perturbation strategy that targets structurally influential signed edges, and experiments demonstrate that this approach causes greater embedding drift, polarity change, and link‑prediction degradation than baseline methods.
By Ning Zhang, Li Zhang
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations.
The article reviews the problem of learning graph structures from data, noting that research has traditionally split into two paths: inferring the topology of a single graph from observations on it, and learning a generative distribution from multiple observed graphs to sample new ones. It proposes a unified framework that treats both as inverse problems of a common graph generation process, reviews key methods, and discusses their interrelations, strengths, and limitations. The review highlights opportunities for cross‑paradigm integration and outlines future research directions.
By Xiaowen Dong, Hoi-To Wai, Siheng Chen, Laura Toni, Dorina Thanou
arXiv:2402. 17500v2 Announce Type: replace-cross Abstract: A central question of network science is how functional properties of systems emerge from their structure.
By Christian Nauck, Michael Lindner, Nora Molkenthin, J\"urgen Kurths, Eckehard Sch\"oll, J\"org Raisch, Frank Hellmann
The paper identifies a limitation of discrete graph diffusion models: independent edge updates combined with exchangeability force the terminal prior to be an Erdős–Rényi graph, which hampers denoising and leads to loss of node heterogeneity. To overcome this, the authors propose a Latent Sociability Prior (LSP) and a joint diffusion process that co‑evolves latent sociability variables with graph structure, eliminating edge independence while maintaining exchangeability. Experiments on several graph generation datasets show that this approach better captures graph distributions than baseline methods that lack node features.
By Adarsh Jamadandi, Nicolas Keriven, Aline Roumy
arXiv:2606. 17684v1 Announce Type: cross Abstract: Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications.
By Arturo P\'erez-Peralta, Sandra Ben\'itez-Pe\~na, Blas Kolic, Rosa E. Lillo
arXiv:2607. 21263v1 Announce Type: new Abstract: Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice.
By Purui Zhang, Feng Ji, Yanan Zhao, Bihan Wen, Wee Peng Tay