{"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/parsimonious-module-inference-in-large","title":"Parsimonious module inference in large networks","arxiv_id":"1212.4794","date":"2012-12-19","proceeding":null,"authors":["Tiago P. Peixoto"],"abstract":"We investigate the detectability of modules in large networks when the number\nof modules is not known in advance. We employ the minimum description length\n(MDL) principle which seeks to minimize the total amount of information\nrequired to describe the network, and avoid overfitting. According to this\ncriterion, we obtain general bounds on the detectability of any prescribed\nblock structure, given the number of nodes and edges in the sampled network. We\nalso obtain that the maximum number of detectable blocks scales as $\\sqrt{N}$,\nwhere $N$ is the number of nodes in the network, for a fixed average degree\n$<k>$. We also show that the simplicity of the MDL approach yields an efficient\nmultilevel Monte Carlo inference algorithm with a complexity of $O(\\tau N\\log\nN)$, if the number of blocks is unknown, and $O(\\tau N)$ if it is known, where\n$\\tau$ is the mixing time of the Markov chain. We illustrate the application of\nthe method on a large network of actors and films with over $10^6$ edges, and a\ndissortative, bipartite block structure.","url_abs":"http://arxiv.org/abs/1212.4794v4","url_pdf":"http://arxiv.org/pdf/1212.4794v4.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":"parsimonious-module-inference-in-large","repo_url":"https://git.skewed.de/count0/graph-tool","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"mdl","method_name":"MDL"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1212.4794","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}