  Community-aware centrality is an emerging research area in network science
concerned with the importance of nodes in relation to community structure.
Measures are a function of a network's structure and a given partition.
Previous approaches extend classical centrality measures to account for
community structure with little connection to community detection theory. In
contrast, we propose cluster-quality vitality measures, i.e., modularity
vitality, a community-aware measure which is well-grounded in both centrality
and community detection theory. Modularity vitality quantifies positive and
negative contributions to community structure, which indicate a node's role as
a community bridge or hub. We derive a computationally efficient method of
calculating modularity vitality for all nodes in O(M + NC) time, where C is the
number of communities. We systematically fragment networks by removing central
nodes, and find that modularity vitality consistently outperforms existing
community-aware centrality measures. Modularity vitality is over 8 times more
effective than the next-best method on a million-node infrastructure network.
This result does not generalize to social media communication networks, which
exhibit extreme robustness to all community-aware centrality attacks. This
robustness suggests that user-based interventions to mitigate misinformation
diffusion will be ineffective. Finally, we demonstrate that modularity vitality
provides a new approach to community-deception.
