Null-adjusted persistence function for high-resolution community detection

TL;DR

This paper introduces null-adjusted persistence, a new community detection objective combining modularity and persistence probability, which overcomes their individual limitations and improves detection resolution in complex networks.

Contribution

The paper proposes null-adjusted persistence, a novel objective function for community detection that integrates features of modularity and persistence probability, with proven properties and an efficient maximization method.

Findings

Null-adjusted persistence overcomes modularity's resolution limit.

It detects higher resolution communities in dense, large networks.

The method outperforms modularity maximization on benchmark and real networks.

Abstract

Modularity and persistence probability are two widely used quality functions for detecting communities in complex networks. In this paper, we introduce a new objective function called null-adjusted persistence, which incorporates features from both modularity and persistence probability, as it implies a comparison of persistence probability with the same null model of modularity. We prove key analytic properties of this new function. We show that the null-adjusted persistence overcomes the limitations of modularity, such as scaling behavior and resolution limits, and the limitation of the persistence probability, which is an increasing function with respect to the cluster size. We propose to find the partition that maximizes the null-adjusted persistence with a variation of the Louvain method and we tested its effectiveness on benchmark and real networks. We found out that maximizing null-adjusted persistence outperforms modularity maximization, as it detects higher resolution partitions in dense and large networks.