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Recently, it has been argued that using\ninstead a more complicated, non-symmetric and higher dimensional operator,\nrelated to the non-backtracking walk on the graph, leads to improved\nperformance in detecting clusters, and even to optimal performance for the\nstochastic block model. Here, we propose to use instead a simpler object, a\nsymmetric real matrix known as the Bethe Hessian operator, or deformed\nLaplacian. We show that this approach combines the performances of the\nnon-backtracking operator, thus detecting clusters all the way down to the\ntheoretical limit in the stochastic block model, with the computational,\ntheoretical and memory advantages of real symmetric matrices.","url_abs":"http://arxiv.org/abs/1406.1880v2","url_pdf":"http://arxiv.org/pdf/1406.1880v2.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-clustering-of-graphs-with-the-bethe","repo_url":"https://github.com/Jonas1312/CommunityDetection","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"spectral-clustering-of-graphs-with-the-bethe","repo_url":"https://github.com/jonas1312/community-detection-in-graphs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"spectral-clustering-of-graphs-with-the-bethe","repo_url":"https://github.com/zhanghuijun-hello/Stochastic-block-model-Bethe-Hessian-Spectral-clustering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"stochastic-block-model","task_name":"Stochastic Block Model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1406.1880","atlas_url":"https://app.syntology.ai/?focus=1406.1880","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1406.1880"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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