Deconstructing centrality: Thinking locally and ranking globally in networks

We examine whether the prominence of individuals in different social networks is determined by their position in their local network or by how the community to which they belong relates to other communities. To this end, we introduce two new measures of centrality, both based on communities in the network: local and community centrality. Community centrality is a novel concept that we introduce to describe how central one's community is within the whole network. We introduce an algorithm to estimate the distance between communities and use it to find the centrality of communities. Using data from several social networks, we show that community centrality is able to capture the importance of communities in the whole network. We then conduct a detailed study of different social networks and determine how various global measures of prominence relate to structural centrality measures.Our measures deconstruct global centrality along local and community dimensions. In some cases, prominence is determined almost exclusively by local information, while in others a mix of local and community centrality matters. Our methodology is a step toward understanding of the processes that contribute to an actor's prominence in a network.