The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
The degree sequence of a scale-free random graph process
Random Structures & Algorithms
Using PageRank to Characterize Web Structure
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Random Structures & Algorithms
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The influence of search engines on preferential attachment
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The distribution of pageRank follows a power-law only for particular values of the damping factor
Proceedings of the 15th international conference on World Wide Web
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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. [7], and the PageRank-based selection model, proposed by Pandurangan et al. [18]. 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 [1] 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 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.