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Most algorithms rely on prespecifiying the number of communities or use an arbitrary stopping rule. We provide a principled approach to selecting a nominal significance level for sequential community detection procedures by controlling the tolerance ratio, defined as the ratio of underfitting and overfitting probability of estimating the number of clusters in fitting a network. We introduce an algorithm for specifying this significance level from a user-specified tolerance ratio, and demonstrate its utility with a sequential modularity maximization approach in a stochastic block model framework. We evaluate the performance of the proposed algorithm through extensive simulations and demonstrate its utility in controlling the tolerance ratio in single-cell RNA sequencing clustering by cell type and by clustering a congressional voting network.<\/jats:p>","DOI":"10.1007\/s41109-023-00567-2","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T14:01:56Z","timestamp":1690898516000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Selecting a significance level in sequential testing procedures for community detection"],"prefix":"10.1007","volume":"8","author":[{"given":"Riddhi Pratim","family":"Ghosh","sequence":"first","affiliation":[]},{"given":"Ian","family":"Barnett","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"issue":"6749","key":"567_CR1","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1038\/43601","volume":"401","author":"R Albert","year":"1999","unstructured":"Albert R, Jeong H, Barab\u00e1si A-L (1999) Diameter of the world-wide web. 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