### Information

- March 29, 2007
- 11:50 am - 12:15 pm

# Optimizing PageRank by choosing outlinks

##### Paul Van Dooren (Université Catholique de Louvain)

Google has established its well-known PageRank that classifies the pages of the World Wide Web by scoring each of them. The PageRank of a page represents the probability of presence of a random surfer on that page. This surfer goes with probability $c$ from one page to another page following the hyperlinks, and with probability $1-c$ from one page to any page on the web with a prescribed probability. The PageRank vector can be seen as the normalized Perron vector of a positive matrix: the Google matrix, taking into account the random surfer motion described above.

If one wishes now to maximize one's own PageRank, one can only control one's own outlinks to other pages. The goal is to increase one element of the Perron vector by changing some elements of the Google matrix. We decribe an optimal strategy for selecting one's outlinks when they can all be chosen arbitrarily, as well as when some of the outinks are imposed in advance. We also address the same problem for a group of people who want to optimise their PageRank sum.