{"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/hierarchical-block-structures-and-high","title":"Hierarchical Block Structures and High-resolution Model Selection in Large Networks","arxiv_id":"1310.4377","date":"2013-10-16","proceeding":null,"authors":["Tiago P. Peixoto"],"abstract":"Discovering and characterizing the large-scale topological features in\nempirical networks are crucial steps in understanding how complex systems\nfunction. However, most existing methods used to obtain the modular structure\nof networks suffer from serious problems, such as being oblivious to the\nstatistical evidence supporting the discovered patterns, which results in the\ninability to separate actual structure from noise. In addition to this, one\nalso observes a resolution limit on the size of communities, where smaller but\nwell-defined clusters are not detectable when the network becomes large. This\nphenomenon occurs not only for the very popular approach of modularity\noptimization, which lacks built-in statistical validation, but also for more\nprincipled methods based on statistical inference and model selection, which do\nincorporate statistical validation in a formally correct way. Here we construct\na nested generative model that, through a complete description of the entire\nnetwork hierarchy at multiple scales, is capable of avoiding this limitation,\nand enables the detection of modular structure at levels far beyond those\npossible with current approaches. Even with this increased resolution, the\nmethod is based on the principle of parsimony, and is capable of separating\nsignal from noise, and thus will not lead to the identification of spurious\nmodules even on sparse networks. Furthermore, it fully generalizes other\napproaches in that it is not restricted to purely assortative mixing patterns,\ndirected or undirected graphs, and ad hoc hierarchical structures such as\nbinary trees. Despite its general character, the approach is tractable, and can\nbe combined with advanced techniques of community detection to yield an\nefficient algorithm that scales well for very large networks.","url_abs":"http://arxiv.org/abs/1310.4377v6","url_pdf":"http://arxiv.org/pdf/1310.4377v6.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":"hierarchical-block-structures-and-high","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":[{"task_slug":"community-detection","task_name":"Community Detection"},{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1310.4377","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}