Before revision:  Then ,  we show that this quantity has implications in three research areas within network science: community analysis, network robustness, and community deception. Modularity-deltas are useful in community analysis as they are a semi-global measure , scalable like local measures but using global information through the network's partition.In robustness, modularity maximizing attack strategies are more efficient than betweenness-based ones, and are shown to damage the US Powergrid and European Road networks more effectively than degree based attacks .
After revision:  Then , we show that our measure gives the most effective attack strategy for a million-node infrastructure network, fragmenting it while removing less than 2\% of nodes. This is over 8 times more fragile than can be seen with previous group-centralities. We further find that the social media communication network demonstrates extreme robustness to group-centrality attacks, suggesting that user-based interventions to mitigate misinformation diffusion will be ineffective .