PageRank was first defined by S. Brinn and L. Page in 1998 in order to rank homepages on the Internet for use in search engines using a random walk on the web graph. While the original way to calculate PageRank is fast, due to the huge size and growth of the web there have been many attempts at improving upon the calculation speed of PageRank through various means. In this article we will look at a slightly dierent but equally important problem, namely how to improve the calculation speed of PageRank in a changing network where PageRank of an earlier stage of the network is available. In particular we consider two types of changes in the graph, the change in rank after changing the personalization vector used in calculating PageRank as well as added or removed edges between dierent strongly connected components in the network.