The paper introduces Bayesian matrix-valued graphs (BMVG), where each edge is represented by a symmetric positive-definite matrix instead of a scalar weight, allowing the capture of direction-dependent interactions in scientific graphs. Using the affine-invariant Riemannian metric, BMVG quantifies deformation magnitude and signed directions of edge changes across contexts, and demonstrates competitive performance against existing methods in precision recovery and structural change detection. Experiments on weather data and TCGA-BRCA gene networks show that BMVG can reveal context-dependent reconfigurations in spatial coupling and gene-module interactions.
By Papri Dey
The paper introduces a moment-guided edge sampling framework that quantifies how local edge edits affect global graph structure using spectral moments of the random-walk transition matrix. Two complementary methods— a combinatorial closed‑form update for low‑order moments and a low‑rank approach exploiting locality and cyclic trace invariance— enable efficient computation of moment changes for single or batched edits. These moment changes serve as interpretable structural signatures, and preserving them is shown to retain key graph properties such as triangle‑weighted clustering, while also improving performance in supervised node classification and graph contrastive learning.
By Weibin Cai, Reza Zafarani
arXiv:2604.02535v2 Announce Type: replace
Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
By Zeyang Huang, Angelos Chatzimparmpas, Thomas H\"ollt, Takanori Fujiwara
arXiv:2507.23559v2 Announce Type: replace-cross
Abstract: Certain data are naturally modeled by networks or weighted graphs, be they biological networks or mobility networks. When there is no canonic...
By Elodie Maignant, Xavier Pennec, Alain Trouv\'e, Anna Calissano
arXiv:2607. 20896v1 Announce Type: new Abstract: Spatial transcriptomics assays remain costly and technically demanding, restricting transcriptome-wide profiling to specialist settings and preventing routine clinical deployment.
By Kritanu Chattopadhyay, Soumya Chatterjee, Ondrej Krejcar, Debotosh Bhattacharjee
arXiv:2608. 04460v1 Announce Type: cross Abstract: The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry.
By Yuyang Zhang, Weihan Xu, Xuehai Zhou, Shucheng Cao, Qihuang Zhang
The paper introduces Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
By Moritz Piening, Christian Wald
arXiv:2606. 08258v1 Announce Type: cross Abstract: Understanding and comparing structures in scalar fields is a central challenge in scientific visualization, with applications ranging from feature analysis to temporal and structural comparison.
By Guangyu Meng, Mingzhe Li, Erin Wolf Chambers
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
By Rachid Caich, Yassine Abbahaddou
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
By Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu
arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
By Qi Shao, Hao Guo, Jiawen Chen, Duxin Chen, Wenwu Yu
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
By Harvey Chen, Nicolas Zilberstein, Santiago Segarra