Exploiting the Block Structure of the Web for Computing PageRank

The web link graph has a nested block struc- ture: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this struc- ture to speed up the computation of PageRank by a 3-stage algorithm whereby (1) the local Page- Ranks of pages for each host are computed in- dependently using the link structure of that host, (2) these local PageRanks are then weighted by the "importance" of the corresponding host, and (3) the standard PageRank algorithm is then run using as its starting vector the weighted concate- nation of the local PageRanks. Empirically, this algorithm speeds up the computation of PageRank by a factor of 2 in realistic scenarios. Further, we develop a variant of this algorithm that effi- ciently computes many different "personalized" PageRanks, and a variant that efficiently recom- putes PageRank after node updates.