A Unified Framework for Community Detection and Model Selection in Blockmodels

TL;DR

This paper introduces a unified framework that simultaneously performs community detection and model selection in blockmodels, leveraging spectral geometry and loss functions to improve accuracy and consistency across a hierarchy of models.

Contribution

It proposes a novel unified approach combining community detection and model selection using spectral geometry insights and loss functions, with theoretical guarantees and practical validation.

Findings

High accuracy in community detection and model selection demonstrated in simulations

Outperforms or matches state-of-the-art methods in experiments

Effective application to real-world networks shows practical utility

Abstract

Blockmodels are a foundational tool for modeling community structure in networks, with the stochastic blockmodel (SBM), degree-corrected blockmodel (DCBM), and popularity-adjusted blockmodel (PABM) forming a natural hierarchy of increasing generality. While community detection under these models has been extensively studied, much less attention has been paid to the model selection problem, i.e., determining which model best fits a given network. Building on recent theoretical insights about the spectral geometry of these models, we propose a unified framework for simultaneous community detection and model selection across the full blockmodel hierarchy. A key innovation is the use of loss functions that serve a dual role: they act as objective functions for community detection and as test statistics for hypothesis testing. We develop a greedy algorithm to minimize these loss functions and establish theoretical guarantees for exact label recovery and model selection consistency under each model. Extensive simulation studies demonstrate that our method achieves high accuracy in both tasks, outperforming or matching state-of-the-art alternatives. Applications to five real-world networks further illustrate the interpretability and practical utility of our approach. R code for implementing the method is available at https://github.com/subhankarbhadra/model-selection.