{"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/nonlinear-modified-pagerank-problem-for-local","title":"Nonlinear Modified PageRank Problem for Local Graph Partitioning","arxiv_id":"2409.01834","date":"2024-09-03","proceeding":null,"authors":["Costy Kodsi","Dimosthenis Pasadakis"],"abstract":"A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a strategy for obtaining a numerical solution to the generalised problem. Sets of vertices are formed according to the ranking supplied by the solution, and a conductance criterion decides upon the set that best represents the cluster around a starting vertex. Experiments on both synthetic and real-world inspired graphs demonstrate the capability of the approach to not only produce low conductance sets, but to also recover local clusters with an accuracy that consistently surpasses state-of-the-art algorithms.","url_abs":"https://arxiv.org/abs/2409.01834v1","url_pdf":"https://arxiv.org/pdf/2409.01834v1.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":"nonlinear-modified-pagerank-problem-for-local","repo_url":"https://github.com/dmspas/nonlinear_modified_pagerank","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}