TL;DR
This paper constructs and analyzes the Google matrix of Twitter's 2009 network, revealing the influential users and the network's interconnectivity, which impacts information flow and opinion formation.
Contribution
It introduces the Google matrix analysis of Twitter's entire network, highlighting the dominant role of a small elite in controlling information flow.
Findings
Top PageRank nodes are more interconnected than in Wikipedia and British Universities.
A small elite of users controls the majority of information flow.
The network's structure influences opinion formation processes.
Abstract
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.
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