{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/180804337","title":"The Gromov-Wasserstein distance between networks and stable network invariants","arxiv_id":"1808.04337","date":"2018-08-13","proceeding":null,"authors":["Samir Chowdhury","Facundo Mémoli"],"abstract":"We define a metric---the network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply network invariants based on optimal transport that approximate this distance by means of lower bounds. We test these methods on a range of simulated network datasets and on a dataset of real-world global bilateral migration. For our simulations, we define a network generative model based on the stochastic block model. This may be of independent interest for benchmarking purposes.","url_abs":"http://arxiv.org/abs/1808.04337v1","url_pdf":"http://arxiv.org/pdf/1808.04337v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"180804337","repo_url":"https://github.com/samirchowdhury/GWnets","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1808.04337","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}