  It is of paramount importance to uncover influential nodes to control
diffusion phenomena in a network. In recent works, there is a growing trend to
investigate the role of the community structure to solve this issue. Up to now,
the vast majority of the so-called community-aware centrality measures rely on
non-overlapping community structure. However, in many real-world networks, such
as social networks, the communities overlap. In other words, a node can belong
to multiple communities. To overcome this drawback, we propose and investigate
the "Overlapping Modularity Vitality" centrality measure. This extension of
"Modularity Vitality" quantifies the community structure strength variation
when removing a node. It allows identifying a node as a hub or a bridge based
on its contribution to the overlapping modularity of a network. A comparative
analysis with its non-overlapping version using the
Susceptible-Infected-Recovered (SIR) epidemic diffusion model has been
performed on a set of six real-world networks. Overall, Overlapping Modularity
Vitality outperforms its alternative. These results illustrate the importance
of incorporating knowledge about the overlapping community structure to
identify influential nodes effectively. Moreover, one can use multiple ranking
strategies as the two measures are signed. Results show that selecting the
nodes with the top positive or the top absolute centrality values is more
effective than choosing the ones with the maximum negative values to spread the
epidemic.
