{"title":"Detectability of hierarchical communities in networks","authors":"Leto Peel, Michael T. Schaub","doi":"10.1103/physreve.110.034306","DOIUrl":null,"url":null,"abstract":"We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analyzed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for nonhierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"83 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.034306","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analyzed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for nonhierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.