Description: 
In recent years there has been considerable interest in analyzing random graph models for the Web. We consider two such models - the Random Surfer model introduced by Blum et al. and the PageRank-based selection model proposed by Pandurangan et al.. It has been observed that search engines influence the growth of the Web. The PageRank-based selection model tries to capture the effect that these search engines have on the growth of the Web by adding new links according to Pagerank. The PageRank algorithm is used in the Google search engine for ranking search results. We show the equivalence of the two random graph models and carry out the analysis in the Random Surfer model, since it is easier to work with. We analyze the expected in-degree of vertices and show that it follows a powerlaw. We also analyze the expected PageRank of vertices and show that it also follows the same powerlaw as the expected degree. We show that in both models the expected degree and the PageRank of the first vertex, the root of the graph, follow the same powerlaw. However the power undergoes a phase-transition as we vary the parameter of the model. This peculiar behavior of the root has not been observed in previous analysis and simulations of the two models. This is joint work with Prasad Chebolu.

Runtime:32:34

Rating:TV-G