{"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/spectral-theory-of-unsigned-and-signed-graphs","title":"Spectral Theory of Unsigned and Signed Graphs. Applications to Graph Clustering: a Survey","arxiv_id":"1601.04692","date":"2016-01-18","proceeding":null,"authors":["Jean Gallier"],"abstract":"This is a survey of the method of graph cuts and its applications to graph\nclustering of weighted unsigned and signed graphs. I provide a fairly thorough\ntreatment of the method of normalized graph cuts, a deeply original method due\nto Shi and Malik, including complete proofs. The main thrust of this paper is\nthe method of normalized cuts. I give a detailed account for K = 2 clusters,\nand also for K > 2 clusters, based on the work of Yu and Shi. I also show how\nboth graph drawing and normalized cut K-clustering can be easily generalized to\nhandle signed graphs, which are weighted graphs in which the weight matrix W\nmay have negative coefficients. Intuitively, negative coefficients indicate\ndistance or dissimilarity. The solution is to replace the degree matrix by the\nmatrix in which absolute values of the weights are used, and to replace the\nLaplacian by the Laplacian with the new degree matrix of absolute values. As\nfar as I know, the generalization of K-way normalized clustering to signed\ngraphs is new. Finally, I show how the method of ratio cuts, in which a cut is\nnormalized by the size of the cluster rather than its volume, is just a special\ncase of normalized cuts.","url_abs":"http://arxiv.org/abs/1601.04692v1","url_pdf":"http://arxiv.org/pdf/1601.04692v1.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":"spectral-theory-of-unsigned-and-signed-graphs","repo_url":"https://github.com/jsedoc/SignedSpectralClustering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1601.04692","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}