Counting communities in weighted Stochastic Block Models via semidefinite programming

TL;DR

This paper introduces a semidefinite programming approach to accurately estimate the number of communities in weighted stochastic block models, supported by universality results and sequential testing methods.

Contribution

It develops a novel semidefinite programming-based hypothesis testing framework for community detection in weighted SBMs, including universality results and community estimators.

Findings

Effective hypothesis tests for community number estimation

Universality results for SDP-based functions

Sequential testing procedure for community count

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.