Modularity measure of networks with overlapping communities

TL;DR

This paper introduces a new non-fuzzy measure to evaluate and rank overlapping community partitions in networks, aiding in both assessment and detection of community structures.

Contribution

It presents a novel measure specifically designed for overlapping communities, addressing the challenge of ranking and optimizing such partitions.

Findings

The measure effectively ranks overlapping community partitions.

It can be used to evaluate clustering quality.

The measure supports community detection optimization.

Abstract

In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and during finding the overlapping community-structure by optimization methods. The theoretical problem referring to the separation of overlapping modules is discussed, and an example for possible applications is given as well.