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PageRank in evolving tree graphs
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda. (MAM)
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania. (MAM)
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0002-1624-5147
Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
Vise andre og tillknytning
2018 (engelsk)Inngår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 375-390Kapittel i bok, del av antologi (Fagfellevurdert)
Abstract [en]

In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

sted, utgiver, år, opplag, sider
Springer, 2018. Vol. 271, s. 375-390
Serie
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
Emneord [en]
Breadth-first search, Forward edge, PageRank, Random walk, Tree, Forestry, Graph theory, Iterative methods, Random processes, Stochastic systems, Trees (mathematics)
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-41833DOI: 10.1007/978-3-030-02825-1_16Scopus ID: 2-s2.0-85058567338ISBN: 978-3-030-02824-4 (tryckt)OAI: oai:DiVA.org:mdh-41833DiVA, id: diva2:1274027
Konferanse
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Tilgjengelig fra: 2018-12-27 Laget: 2018-12-27 Sist oppdatert: 2018-12-31bibliografisk kontrollert

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