PageRank vs. Katz Status Index, a Theoretical Approach

In World Wide Web search engines, it is important to have a good ranking system. One of the most famous ranking components is the PageRank system by Google. However, PageRank is protected by patents and it is impossible for other companies to use it in their search engines. There is an old model, called Katz status index, that is reported to work very similar to PageRank. If the quality of Katz status index turns out to be similar to or better than that of PageRank, it could become a patent-free alternative to PageRank. We consider the problem of comparing Katz status index to PageRank in this paper with some preliminary results on the theoretical comparison and give a proposal for practical comparison of the two models.