A community-aware centrality framework based on overlapping modularity.

Key nodes play a vital role in propagation phenomena. Recent works exploit the networks’ community structure to identify these nodes. Most of the so-called “community-aware” centrality measures consider non-overlapping community structures. However, nodes may belong to more than one community. This work proposes “Overlapping Modularity Vitality” that identifies critical nodes based on their contribution to the network’s overlapping modularity. It allows to target top hubs or bridges or simultaneously both types of nodes. We use three alternative definitions of overlapping modularity to investigate this framework (reciprocity membership, degree membership, and node similarity). We perform extensive simulations based on the Susceptible-Infected-Recovered (SIR) model in an epidemic spreading process scenario. Results show that the proposed measures outperform their non-overlapping counterpart and prominent overlapping centrality measures reported in the literature. Reciprocity membership performs well with limited resources when targeting hubs first. With more resources, degree membership and node similarity outperform their alternatives when targeting bridges first.