Local, community and global centrality methods for analyzing networks

Abstract

We examine whether the prominence of individuals in different social networks is determined by their position in their community, the whole network or by the location of their community within the network. 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 central communities incorporate actors who are involved in mainstream activities for that network. We then conduct a detailed study of different social networks and determine how various global measures of prominence relate to structural centrality measures. We show that depending on the underlying measure of prominence, different combinations of local, global and community centrality play an important role in determining the prominence. Local and community centrality measures add new information on top of existing global measures. We show robustness of our results by studying different partitions of the data and different clustering methods. Our deconstruction of centrality allows us to study the underlying processes that contribute to prominence in more detail and develop more detailed and accurate models.