Local modularity measure for network clusterizations

TL;DR

This paper introduces a new local modularity measure, LQ, for network clusterizations that better captures local cluster structures and cohesion, complementing the traditional global modularity Q.

Contribution

The paper proposes a localized modularity measure LQ that emphasizes local cluster connectivity, providing a more detailed view of network modularity.

Findings

LQ identifies more cohesive clusters in biological networks.

LQ offers a higher granularity view of network structure.

Optimization of LQ complements global modularity measures.

Abstract

Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity $Q$ has been introduced as a measure to assess the quality of clusterizations. $Q$ has a global view, while in many real-world networks clusters are linked mainly \emph{locally} among each other (\emph{local cluster-connectivity}). Here, we introduce a new measure, localized modularity $LQ$, which reflects local cluster structure. Optimization of $Q$ and $LQ$ on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.