A Survey on Theoretical Advances of Community Detection in Networks

TL;DR

This survey reviews recent theoretical advances in community detection methods within networks, focusing on their properties, consistency, and potential future research directions.

Contribution

It systematically summarizes and compares various community detection approaches and their theoretical guarantees, highlighting recent progress and open problems.

Findings

Spectral clustering and semidefinite relaxations show promising consistency results.

Belief propagation and pseudo-likelihood methods have strong theoretical foundations.

Future research directions include robust detection and incorporation of nodal covariates.

Abstract

Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted attention in many different fields, including computer science, statistics, social sciences, among others. Numerous approaches for community detection have been proposed in literature, from ad-hoc algorithms to systematic model-based approaches. The large number of available methods leads to a fundamental question: whether a certain method can provide consistent estimates of community labels. The stochastic blockmodel (SBM) and its variants provide a convenient framework for the study of such problems. This article is a survey on the recent theoretical advances of community detection. The authors review a number of community detection methods and their theoretical properties, including graph cut methods, profile likelihoods, the pseudo-likelihood method, the variational method, belief propagation, spectral clustering, and semidefinite relaxations of the SBM. The authors also briefly discuss other research topics in community detection such as robust community detection, community detection with nodal covariates and model selection, as well as suggest a few possible directions for future research.