{"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/weighted-spectral-embedding-of-graphs","title":"Weighted Spectral Embedding of Graphs","arxiv_id":"1809.11115","date":"2018-09-28","proceeding":null,"authors":["Thomas Bonald","Alexandre Hollocou","Marc Lelarge"],"abstract":"We present a novel spectral embedding of graphs that incorporates weights\nassigned to the nodes, quantifying their relative importance. This spectral\nembedding is based on the first eigenvectors of some properly normalized\nversion of the Laplacian. We prove that these eigenvectors correspond to the\nconfigurations of lowest energy of an equivalent physical system, either\nmechanical or electrical, in which the weight of each node can be interpreted\nas its mass or its capacitance, respectively. Experiments on a real dataset\nillustrate the impact of weighting on the embedding.","url_abs":"http://arxiv.org/abs/1809.11115v2","url_pdf":"http://arxiv.org/pdf/1809.11115v2.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":"abstracts"},"code_links":[{"paper_slug":"weighted-spectral-embedding-of-graphs","repo_url":"https://github.com/tbonald/spectral_embedding","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}