  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.
