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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.
In this paper we consider so-called Google matrices and show that all eigenvalues ($lambda$) of them have a fundamental property $|lambda|leq 1$. The stochastic eigenvector corresponding to $lambda=1$ called the PageRank vector plays a central role i
In online social media systems users are not only posting, consuming, and resharing content, but also creating new and destroying existing connections in the underlying social network. While each of these two types of dynamics has individually been s
Hundreds of thousands of hashtags are generated every day on Twitter. Only a few become bursting topics. Among the few, only some can be predicted in real-time. In this paper, we take the initiative to conduct a systematic study of a series of challe
This article analyses public debate on Twitter via network representations of retweets and replies. We argue that tweets observable on Twitter have both a direct and mediated effect on the perception of public opinion. Through the interplay of the tw
The global public sphere has changed dramatically over the past decades: a significant part of public discourse now takes place on algorithmically driven platforms owned by a handful of private companies. Despite its growing importance, there is scan