Google Matrix
A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages. The PageRank of each page can then be generated iteratively from the Google matrix using the power method. However, in order for the power method to converge, the matrix must be stochastic, Irreducible (mathematics), irreducible and aperiodic. Adjacency matrix ''A'' and Markov matrix ''S'' In order to generate the Google matrix ''G'', we must first generate an adjacency matrix ''A'' which represents the relations between pages or nodes. Assuming there are ''N'' pages, we can fill out ''A'' by doing the following: # A matrix element A_ is filled with 1 if node j has a link to node i, and 0 otherwise; this is the adjacency matrix of links. # A related matrix ''S'' corresponding to the transitions in a Markov chain#Properties of Markov chains, Markov chain of given network is constructed from ''A'' by dividing the ...
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