  We construct the Google matrix of the entire Twitter network, dated by July
2009, and analyze its spectrum and eigenstate properties including the PageRank
and CheiRank vectors and 2DRanking of all nodes. Our studies show much stronger
inter-connectivity between top PageRank nodes for the Twitter network compared
to the networks of Wikipedia and British Universities studied previously. Our
analysis allows to locate the top Twitter users which control the information
flow on the network. We argue that this small fraction of the whole number of
users, which can be viewed as the social network elite, plays the dominant role
in the process of opinion formation on the network.
