Community Detection Using Slow Mixing Markov Models

TL;DR

This paper introduces a community detection method based on analyzing slow mixing Markov random walks on graphs, leveraging coupling from the past to identify tightly-knit vertex groups.

Contribution

It presents a novel approach that uses Markov chain mixing times and coupling techniques to detect communities, with theoretical analysis on specific graph models.

Findings

Effective in stochastic block models and LFR graphs

Theoretical guarantees on community detection performance

Demonstrates the utility of slow mixing properties for clustering

Abstract

The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches community detection in graphs by constructing Markov random walks on the graphs. The mixing properties of the random walk are then used to identify communities. We use coupling from the past as an algorithmic primitive to translate the mixing properties of the walk into revealing the community structure of the graph. We analyze the performance of our algorithms on specific graph structures, including the stochastic block models (SBM) and LFR random graphs.