Is the 25 billion dollar eigenvector robust enough?

Ranking algorithms play a crucial role in information technologies and numerical analysis due to their efficiency in high dimensions and wide range of possible applications, including Internet ranking, scientometrics and systemic risk in finance (SinkRank, DebtRank).

The traditional approach to Internet ranking goes back to the famous work of Sergey Brin and Larry Page, who developed the initial method PageRank (PR) in order to rank websites for search engine results based on linear algebra rules. But how robust is this method in times of rapid Internet growth? Recent works studied robust reformulations of the PageRank model for the case when links in the network structure may vary, i.e., some links may appear or disappear influencing the transportation matrix defined by the network structure. In the article, the authors make a further step forward, allowing the network to vary not only in links, but also in the number of nodes. They focus on growing network structures and develop methods for ranking of networks uncertain both in size and in structure.