Before revision: The phenomena of community structure in real-world networks has been central to network science's success. While much attention has been paid to community detectionalgorithms and evaluation criteria, a related question has been overlooked: what would the change in modularity be if a node were to be deleted from a network ? In this work, we first show that the answer to this question can be calculated for all nodes in the network in O(m) time. Then ,  we show that this quantity has implications in three research areas within network science: community analysis, network robustness, and community deception.
After revision: Group-centrality is an emerging area in Network Science which seeks to quantify the importance of nodes within and between communities. Previous group-centrality measures either have strong theoretical underpinnings in community detection , we show that this quantity has implications in three research areas within network science: community analysis, network robustness, and community deception.