Constant Approximation for Normalized Modularity and Associations Clustering

TL;DR

This paper introduces a linear-time algorithm that provides a constant-factor approximation for graph clustering objectives like normalized modularity and associations, which are important for understanding community structure.

Contribution

It presents the first constant-factor approximation algorithms for normalized modularity and normalized associations in graph clustering.

Findings

Linear-time constant-approximate algorithm developed

First constant-factor approximation for normalized modularity

First constant-factor approximation for normalized associations

Abstract

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show that our definition is closely related to popular clustering measures, namely normalized associations, which is a dual of the normalized cut objective, and normalized modularity. We give a linear time constant-approximate algorithm for our objective, which implies the first constant-factor approximation algorithms for normalized modularity and normalized associations.