Selecting a significance level in sequential testing procedures for community detection

TL;DR

This paper introduces a principled method for selecting the significance level in sequential community detection algorithms, improving the reliability of estimating the number of communities in networks.

Contribution

It proposes a new algorithm to choose the significance level based on a user-defined tolerance ratio, enhancing existing sequential community detection methods.

Findings

Effective control of the tolerance ratio demonstrated in simulations

Improved accuracy in community number estimation in real data

Versatile application across different network types

Abstract

While there have been numerous sequential algorithms developed to estimate community structure in networks, there is little available guidance and study of what significance level or stopping parameter to use in these sequential testing procedures. 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.