The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.
By Krzysztof Choromanski, Isaac Reid, Arijit Sehanobish, Avinava Dubey
arXiv:2607. 10074v1 Announce Type: new Abstract: Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations.
By My Le, Luana Ruiz, Souvik Dhara
arXiv:2604. 12211v2 Announce Type: replace Abstract: Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications.
By Xiang Gu, Huichun Zhang, Jian Sun
The paper investigates methods for estimating average distances in large static graphs, comparing a graph sampling approach (Random Walk) with landmark-based techniques such as the Size Estimation Framework (SEF) and the Eppstein‑Wang (EW) algorithm. Random Walk proved unreliable for small samples and costly for larger ones, while landmark methods using HyperLogLog were more efficient. Experiments on undirected, unweighted graphs showed that the EW algorithm achieves very low error (≈0.02%) and can use a subset of only 100 nodes for accurate estimation, outperforming SEF in accuracy and speed.
By Kartikey Ahlawat
arXiv:2503. 06396v2 Announce Type: replace Abstract: The minimum vertex cover (MVC) problem seeks to identify the smallest set of vertices that cover all edges in an undirected graph.
By Chanjuan Liu, Qiqi Bao, Yu Zhang, Enqiang Zhu
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