Counting communities in weighted Stochastic Block Models via semidefinite programming
Statistics Theory
2025-02-25 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.2502.15891,
title = {Counting communities in weighted Stochastic Block Models via semidefinite programming},
author = {Deborah Oliveira and Andressa Cerqueira and Roberto Oliveira},
journal= {arXiv preprint arXiv:2502.15891},
year = {2025}
}
Comments
This is a first draft. Comments are welcome