Scalable and Effective Conductance-based Graph Clustering

TL;DR

This paper introduces PCon, a scalable framework for conductance-based graph clustering that achieves high accuracy and efficiency on massive graphs, with theoretical guarantees and empirical success.

Contribution

It proposes a novel peeling-based framework and two algorithms with linear complexity, improving scalability and theoretical bounds for conductance-based clustering.

Findings

Achieves 5-42x speedup over baselines

Uses 1.4-7.8x less memory

Provides near-constant approximation ratio for clustering

Abstract

Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain satisfactory clustering qualities, or have high time and space complexity to achieve provable clustering qualities. To overcome these limitations, we devise a powerful \textit{peeling}-based graph clustering framework \textit{PCon}. We show that many existing solutions can be reduced to our framework. Namely, they first define a score function for each vertex, then iteratively remove the vertex with the smallest score. Finally, they output the result with the smallest conductance during the peeling process. Based on our framework, we propose two novel algorithms \textit{PCon\_core} and \emph{PCon\_de} with linear time and space complexity, which can efficiently and effectively identify clusters from massive graphs with more than a few billion edges. Surprisingly, we prove that \emph{PCon\_de} can identify clusters with near-constant approximation ratio, resulting in an important theoretical improvement over the well-known quadratic Cheeger bound. Empirical results on real-life and synthetic datasets show that our algorithms can achieve 5$\sim$42 times speedup with a high clustering accuracy, while using 1.4$\sim$7.8 times less memory than the baseline algorithms.