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:2606. 00934v1 Announce Type: cross Abstract: Network data are ubiquitous across the social sciences, biology, and information systems.
By Feifan Jiang, Yinan Bu, Shihao Wu, Gongjun Xu, Ji Zhu
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.
By Ali Azizpour, Reza Ramezanpour, Santiago Segarra
arXiv:2608. 10845v1 Announce Type: cross Abstract: Spectral clustering methods for network data are commonly based on a few matrix representations, such as the adjacency matrix and the symmetric Laplacian.
By John Park, Ning Hao
arXiv:2512. 02694v3 Announce Type: replace-cross Abstract: We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding.
By Vedanta Thapar, Renaud Lambiotte, George T. Cantwell
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
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.
By Dalia Chakrabarty, Kangrui Wang, Chuqiao Zhang, Ye Liu
SynCo is a synthetic graph generator that lets users control node degree distributions and sub‑community structures, addressing limitations of existing generators that rely on power‑law distributions and lack flexibility. It is evaluated on graph mimicking, hyperparameter tuning, and node clustering, outperforming state‑of‑the‑art methods while preserving original data distributions. SynCo can generate large graphs with up to 2.1 million nodes.
By Guilherme Henrique Messias, Mariana Caravanti de Souza, Sylvia Iasulaitis, Alan Dem\'etrius Baria Valejo
arXiv:2506.02825v3 Announce Type: replace-cross
Abstract: We present the OmniMatch algorithm for seeded multiple graph matching. In the setting of $d$-dimensional Random Dot Product Graphs (RDPG), we...
By Tong Qi, Vera Andersson, Peter Viechnicki, Vince Lyzinski
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.
By Sergio Rozada, Yiming Qin, Manuel Madeira, Pascal Frossard, Alejandro Ribeiro
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.
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