arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
By Dai Hai Nguyen, Koji Tsuda
arXiv:2608.27500v3 Announce Type: replace-cross
Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...
By James Hyun, Fran\c{c}ois G. Meyer
arXiv:2609.15437v1 Announce Type: cross
Abstract: End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderin...
By Federico M\'endez, Paul Krzakala, Gabriel Melo, Charlotte Laclau, R\'emi Flamary, Florence d'Alch\'e-Buc
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
By James Hyun, Fran\c{c}ois G. Meyer
arXiv:2608.29635v1 Announce Type: new
Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
By Lutz Oettershagen, Honglian Wang, Aristides Gionis
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
By Ao Xu, Tieru Wu