PageRank 1998

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An algorithm, the basis of Google, that ranks relative importance of web pages based on traffic and connectivity on the graph. One major consideration of this study is that web pages are free from quality control and are influenced by profit seeking ventures.

Simplified PageRank: Rank R(u) = c • ∑ R(v)/Nv, v in Bu where

Recall Matrix multiplication of A•x, x in Rn and A is m x n is defined as the dot product of x with each m rows of A.

Another formalization in Linear Algebra: let A be a square matrix of dimensionality = to number of pages

Cycles within the graph will result in a feedback loop affecting pagerank, but it is shown that the estimated pagerank determined at each iteration of the algorithm converges in log n iterations.