Confusion about updates in a graph algorithm

[ChaoGaoUCR]

Hi, I got confused about multi-version updates,
Let's say if we do a BFS with a static graph Graph_original,
and later it changed with a few additions and deletions to be Graph_updated,
in that case, in the aspen system, do we have to do two times BFS to Gaph_original and Graph_updated separately or we can do some modification based on an original graph?
Also, did the system supports algorithm like PageRank in a dynamic situation?