{"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/steady-and-ranging-sets-in-graph-persistence","title":"Steady and ranging sets in graph persistence","arxiv_id":"2009.06897","date":"2020-09-15","proceeding":null,"authors":["Mattia G. Bergomi","Massimo Ferri","Antonella Tavaglione"],"abstract":"Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \\textit{steady} and \\textit{ranging} sets: two standardized ways of producing persistence diagrams directly from graph-theoretical features. The two constructions are framed in the context of \\textit{indexing-aware persistence functions}. Furthermore, we introduce a sufficient condition for stability. Finally, we apply the steady- and ranging-based persistence constructions to toy examples and real-world applications.","url_abs":"https://arxiv.org/abs/2009.06897v3","url_pdf":"https://arxiv.org/pdf/2009.06897v3.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":"steady-and-ranging-sets-in-graph-persistence","repo_url":"https://github.com/mgbergomi/hubpersistence","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2009.06897","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}