An algebraic method for calculating PageRank

Abstract

An algebraic method is proposed for finding PageRank estimates for pages of websites. The amount of calculation in the proposed method does not depend on the value of the damping coefficient, which allows obtaining more accurate estimates of the rankings of PageRank in comparison with analogues. A distinctive feature of the proposed method is a step-by-step performance of calculations simultaneously with the work of the graph traversal algorithm. The comparative analysis of algorithms for traversing graphs has shown that, in contrast to the depth search algorithm, the breadth search algorithm gives a more orderly arranged matrix of transitions, which has the blockwise Hessenberg form. The use of this circumstance makes it possible to reduce significantly the amount of calculations by the proposed method. The resulting equations describing the proposed method have a block structure that allows efficient distribution of the entire volume of operations to parallel computational threads . Proceeding from the fact that the bulk of the calculations can be performed while the graph traversal algorithm is running, the study has determined the conditions under which the proposed method makes it possible to obtain PageRank values faster than the known iterative algorithms. The applicability area of the developed method is, first of all, its use in direct verification of the reliability of posting advertising materials on a relevant web resource; therefore, it is limited to specific Internet sites or segments with no more than 10 4 or 10 5 pages.