On rank statistics of PageRank and MarkovRank

The well-known statistic PageRank was created in 1998 by co-founders of Google, Sergey Brin and Larry Page, to optimize the ranking of websites for their search engine outcomes. It is computed using an iterative algorithm, based on the idea that nodes with a larger number of incoming edges are more important. Google's PageRank involves some information from "aliens"; the 15% of information is regarded as the connections from the outside of the network system under consideration. Without involving the information from "aliens", Google's PageRank could not be well-defined. In this paper, seeking a stable statistic which is "close" to an "intrinsic" version of PageRank, we will introduce a new statistic called MarkovRank. A special attention will be paid to the comparison of rank statistics among standard-PageRank,"intrinsic-PageRank" and MarkovRank, and our conclusion is that the rank statistic of MarkovRank, which is always well-defined, is identical to that of "intrinsic-PageRank", as far as the latter is well-defined.