Local modularity measure for network clusterizations

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 locally among each other (local cluster connectivity). Here we introduce a measure of 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.