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.
arXiv:2505. 03649v4 Announce Type: replace-cross Abstract: Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields.
arXiv:2510. 03690v4 Announce Type: replace Abstract: Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions.
arXiv:2607. 10074v1 Announce Type: new Abstract: Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations.
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
arXiv:2607. 05469v1 Announce Type: cross Abstract: Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks.
The paper introduces a data‑driven method for learning Random Geometric Graphs (RGGs) in probabilistic metric spaces. It defines a distance function based on the cumulative distribution of a disparity variable that captures differences in vertex connectivity and correlation of attached random variables, enabling edges to exist with a specified probability. The approach includes a rejection‑sampling technique for edge probability estimation and a closed‑form posterior for learning the inter‑observable correlation matrix, and it is demonstrated on highly multivariate real datasets.
arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.
arXiv:2608. 04381v1 Announce Type: cross Abstract: Self-supervised learning on graphs is largely shaped by contrastive methods that depend on carefully designed augmentations, and by generative methods that reconstruct node attributes in the input space.
arXiv:2606. 11562v1 Announce Type: new Abstract: Graph analysis underlies many applications whose answers cannot be looked up in a single record or retrieved along a path: laundering rings, drug repurposing, user preference, and scientific theme are all inferred from a node together with its neighbourhood.
arXiv:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem.
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs.