PageRank for networks, graphs, and Markov chains

In this work it is described how a partitioning of a graph into components can be used to calculate PageRank in a large network and how such a partitioning can be used to re-calculate PageRank as the network changes. Although calculating PageRank is considered a problem, it is worth noing that the s...

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Bibliographic Details
Published in:Theory of probability and mathematical statistics 2018, Vol.96, p.59-82
Main Authors: Engström, C., Silvestrov, S.
Format: Article
Language:English
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Summary:In this work it is described how a partitioning of a graph into components can be used to calculate PageRank in a large network and how such a partitioning can be used to re-calculate PageRank as the network changes. Although calculating PageRank is considered a problem, it is worth noing that the same partitioning method could be used when working with Markov chains in general or solving linear systems as long as the method used for solving a single component is chosen appropriately. An algorithm for calculating PageRank using a modified partitioning of the graph into strongly connected components is described. Moreover, the paper also focuses on the calculation of PageRank in a changing graph from two different perspectives, by considering specific types of changes in the graph and calculating the difference in rank before and after certain types of edge additions or removals between components. Moreover, some common specific types of graphs for which it is possible to find analytic expressions for PageRank are considered, and in particular the complete bipartite graph and how PageRank can be calculated for such a graph. Finally, several open directions and problems are described.
ISSN:0094-9000
1547-7363
DOI:10.1090/tpms/1034