Before 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, or scale well, but not both.We propose an extremely scalable measure, modularity-impact, that is directly derived from Newman's modularity. Unlike other measures, modularity-impact is signed, providing additional information about each node's role : hub within its community , or bridge between communities.
After revision: Group-centrality is an emerging area in Network Science which seeks to quantify 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 : hub within its community , or bridge between communities.