A PageRank update refers to the process of computing new PageRank valuesafter a change(s) (addition or removal of links/vertices) has occurred in real-lifenetworks. The purpose of updating is to avoid re-calculating the values from scratch.To efficiently carry out the update, we consider PageRank to be the expected numberof visits to a target vertex if multiple random walks are performed, starting at eachvertex once and weighing each of these walks by a weight value. Hence, it mightbe looked at as updating a non-normalized PageRank. We focus on networks of treegraphs and propose an approach to sequentially update a scaled adjacency matrix afterevery change, as well as the levels of the vertices. In this way, we can update thePageRank of affected vertices by their corresponding levels.