Scalable and Effective Conductance-based Graph Clustering

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 textitpeeling-based graph clustering framework textitPCon. 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 textitPConcore and PConde 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 PConde 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 5~42 times speedup with a high clustering accuracy, while using 1.4~7.8 times less memory than the baseline algorithms.