  The personalized PageRank algorithm is one of the most versatile tools for
the analysis of networks. In spite of its ubiquity, maintaining personalized
PageRank vectors when the underlying network constantly evolves is still a
challenging task. To address this limitation, this work proposes a novel
distributed algorithm to locally update personalized PageRank vectors when the
graph topology changes. The proposed algorithm is based on the use of Chebyshev
polynomials and a novel update equation that encompasses a large family of
PageRank-based methods. In particular, the algorithm has the following
advantages: (i) it has faster convergence speed than state-of-the-art
alternatives for local PageRank updating; and (ii) it can update the solution
of recent generalizations of PageRank for which no updating algorithms have
been developed. Experiments in a real-world temporal network of an autonomous
system validate the effectiveness of the proposed algorithm.
