{"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/scalable-detection-of-statistically","title":"Scalable detection of statistically significant communities and hierarchies, using message-passing for modularity","arxiv_id":"1403.5787","date":"2014-03-23","proceeding":null,"authors":["Pan Zhang","Cristopher Moore"],"abstract":"Modularity is a popular measure of community structure. However, maximizing\nthe modularity can lead to many competing partitions, with almost the same\nmodularity, that are poorly correlated with each other. It can also produce\nillusory \"communities\" in random graphs where none exist. We address this\nproblem by using the modularity as a Hamiltonian at finite temperature, and\nusing an efficient Belief Propagation algorithm to obtain the consensus of many\npartitions with high modularity, rather than looking for a single partition\nthat maximizes it. We show analytically and numerically that the proposed\nalgorithm works all the way down to the detectability transition in networks\ngenerated by the stochastic block model. It also performs well on real-world\nnetworks, revealing large communities in some networks where previous work has\nclaimed no communities exist. Finally we show that by applying our algorithm\nrecursively, subdividing communities until no statistically-significant\nsubcommunities can be found, we can detect hierarchical structure in real-world\nnetworks more efficiently than previous methods.","url_abs":"http://arxiv.org/abs/1403.5787v3","url_pdf":"http://arxiv.org/pdf/1403.5787v3.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":"scalable-detection-of-statistically","repo_url":"https://github.com/bwalker1/ModularityBP_Cpp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"stochastic-block-model","task_name":"Stochastic Block Model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}