Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications
Abstract
Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted simple graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances visualize how mass is shifted to transform one network into another. Beyond reviewing existing transport-based approaches, we establish new spectral lower and upper bounds for the Bures-Wasserstein distance and characterize the tightness of the lower bound under eigenbasis perturbations. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world temporal network.
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BibTeX
@misc{hyun2026optimal,
title = {{Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications}},
author = {James Hyun and François G. Meyer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.27500},
eprint = {2608.27500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27500},
}
RIS
TY - UNPB
TI - Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications
AU - James Hyun
AU - François G. Meyer
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.27500
UR - https://arxiv.org/abs/2608.27500
AB - Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted simple graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances visualize how mass is shifted to transform one network into another. Beyond reviewing existing transport-based approaches, we establish new spectral lower and upper bounds for the Bures-Wasserstein distance and characterize the tightness of the lower bound under eigenbasis perturbations. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world temporal network.
ER -