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arXiv · 2502.15891

Counting communities in weighted Stochastic Block Models via semidefinite programming

Deborah Oliveira·Andressa Cerqueira·Roberto Oliveira
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Abstract

We consider the problem of estimating the number of communities in a weighted balanced Stochastic Block Model. We construct hypothesis tests based on semidefinite programming and with a statistic coming from a GOE matrix to distinguish between any two candidate numbers of communities. This is possible due to a universality result for a semidefinite programming-based function that we also prove. The tests are then used to form a sequential test to estimate the number of communities. Furthermore, we also construct estimators of the communities themselves.

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Deborah Oliveira, Andressa Cerqueira, Roberto Oliveira. 2025-02-21. Counting communities in weighted Stochastic Block Models via semidefinite programming. https://arxiv.org/abs/2502.15891

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