We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain feature...

Based on the study about the basic idea of PageRank algorithm, combining with the MapReduce distributed programming concepts, the paper first proposed a parallel PageRank algorithm based on adjacency list which is suitable for massive data processing. Then, after examining the essential characteristics of iteration hidden behind the PageRank, it provided an iteration acceleration model based on...

Background. Although the World Taekwondo federation currently applies the APIS ranking method to calculate the Olympic rankings, some limitations exist. Objectives. This study applies the PageRank model to Olympics Taekwondo rankings. Methods. The 2015-2018 World Taekwondo Grand Prix competition results for women’s four weight classes (-49kg, -57kg, -67kg, +67kg) were used as research data, t...

We give an improved algorithm for computing personalized PageRank vectors with tight error bounds which can be as small as O(n−k) for any fixed positive integer k. The improved PageRank algorithm is crucial for computing a quantitative ranking for edges in a given graph. We will use the edge ranking to examine two interrelated problems — graph sparsification and graph partitioning. We can combi...

The importance of a Web page is an inherently subjective matter, which depends on the readers interests, knowledge and attitudes. But there is still much that can be said objectively about the relative importance of Web pages. This paper describes PageRank, a method for rating Web pages objectively and mechanically, e ectively measuring the human interest and attention devoted to them. We compa...

The importance of a Web page is an inherently subjective matter, which depends on the readers interests, knowledge and attitudes. But there is still much that can be said objectively about the relative importance of Web pages. This paper describes PageRank, a method for rating Web pages objectively and mechanically, e ectively measuring the human interest and attention devoted to them. We compa...

We are going to consider a variation of the PageRank vector called the personal PageRank vector. Where PageRank measures the importance of nodes overall, the personal PageRank vector measures the importance of nodes with respect to a give node u. It does this by modifying the walk so that with probability α it jumps back to u, rather than to a random node. We denote the vector that satisfies th...

The concept of pagerank was first started as a way for determining the ranking of Webpages by Web search engines. Based on relations in interconnected networks, pagerank has become a major tool for addressing fundamental problems arising in general graphs, especially for large information networks with hundreds of thousands of nodes. A notable notion of pagerank, introduced by Brin and Page and...

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as the frequency that a random surfer visits a Web page, and thus it reflects the popularity of a Web page. We study the effect of newly created links on Google PageRank. We discuss to what extent a page can control its PageRank. Using asymptotic analysis we provide simple conditions...

This paper shows for the first time that there are multiple PageRank definitions, and that more is required to justify PageRank than is offered in the literature ([1], [2] and [5]). Adopting a formal approach, this paper provides a justification of PageRank. It also shows that the irreducibility restriction on the PageRank transition matrix [5] is unnecessary. This is important because it gives...