A fast multilevel algorithm for graph clustering and community detection

TL;DR

This paper introduces a fast multilevel algorithm for graph clustering that maximizes modularity by reducing the problem to a minimum cut problem, enabling efficient and high-quality community detection.

Contribution

The paper presents a novel reduction of modularity maximization to a minimum cut problem, improving speed and clustering quality over existing methods.

Findings

Algorithm finds higher quality clusterings.

Significantly faster than previous algorithms.

Effective use of existing graph partitioning software.

Abstract

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random (unstructured) graph. In this paper we show that the problem of finding a partition maximizing the modularity of a given graph G can be reduced to a minimum weighted cut problem on a complete graph with the same vertices as G. We then show that the resulted minimum cut problem can be efficiently solved with existing software for graph partitioning and that our algorithm finds clusterings of a better quality and much faster than the existing clustering algorithms.