Robustness modularity in complex networks

TL;DR

This paper introduces a new robustness-based measure for assessing network modularity, addressing limitations of traditional methods like Girvan-Newman modularity, and demonstrates its effectiveness on artificial and real networks.

Contribution

The paper proposes a novel robustness-based modularity measure and two related quality functions, improving the assessment of community structure strength in networks.

Findings

Robustness modularity effectively assesses community strength.

New measures correlate strongly with robustness modularity.

Applicable to various clustering algorithms.

Abstract

A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to make this assessment, but it has a number of drawbacks. Most importantly, it is not clearly interpretable, given that the measure can take relatively large values on partitions of random networks without communities. Here we propose a new measure based on the concept of robustness: modularity is the probability to find trivial partitions when the structure of the network is randomly perturbed. This concept can be implemented for any clustering algorithm capable of telling when a group structure is absent. Tests on artificial and real graphs reveal that robustness modularity can be used to assess and compare the strength of the community structure of different networks. We also introduce two other quality functions: modularity difference, a suitably normalized version of the GN modularity; information modularity, a measure of distance based on information compression. Both measures are strongly correlated with robustness modularity, and are promising options as well.