Limited Attention and Centrality in Social Networks

How does one find important or influential people in an online social network? Researchers have proposed a variety of centrality measures to identify individuals that are, for example, often visited by a random walk, infected in an epidemic, or receive many messages from friends. Recent research suggests that a social media users' capacity to respond to an incoming message is constrained by their finite attention, which they divide over all incoming information, i.e., information sent by users they follow. We propose a new measure of centrality --- limited-attention version of Bonacich's Alpha-centrality --- that models the effect of limited attention on epidemic diffusion. The new measure describes a process in which nodes broadcast messages to their out-neighbors, but the neighbors' ability to receive the message depends on the number of in-neighbors they have. We evaluate the proposed measure on real-world online social networks and show that it can better reproduce an empirical influence ranking of users than other popular centrality measures.