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Abola, Benard
Publications (2 of 2) Show all publications
Abola, B., Biganda, P., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2018). PageRank in evolving tree graphs. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at 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 (pp. 375-390). Paper presented at 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. Springer, 271
Open this publication in new window or tab >>PageRank in evolving tree graphs
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2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 375-390Chapter in book (Refereed)
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.

Place, publisher, year, edition, pages
Springer, 2018
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
Keywords
Breadth-first search, Forward edge, PageRank, Random walk, Tree, Forestry, Graph theory, Iterative methods, Random processes, Stochastic systems, Trees (mathematics)
National Category
Computational Mathematics Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41833 (URN)10.1007/978-3-030-02825-1_16 (DOI)2-s2.0-85058567338 (Scopus ID)978-3-030-02824-4 (ISBN)
Conference
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
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Biganda, P., Abola, B., Engström, C., Mango, J. M., Kakuba, G. & Silvestrov, S. (2018). Traditional and lazy pageranks for a line of nodes connected with complete graphs. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at 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 (pp. 391-412). Paper presented at 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. Springer, 271
Open this publication in new window or tab >>Traditional and lazy pageranks for a line of nodes connected with complete graphs
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2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 391-412Chapter in book (Refereed)
Abstract [en]

PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Due to existence of diverse methods of random walk on the graph, variants of PageRank now exists. They include traditional (or normal) PageRank due to normal random walk and Lazy PageRank due to lazy random walk on a graph. In this article, we establish how the two variants of PageRank changes when complete graphs are connected to a line of nodes whose links between the nodes are in one direction. Explicit formulae for the two variants of PageRank are presented. We have noted that the ranks on a line graph are the same except their numerical values which differ. Further, we have observed that both normal random walk and lazy random walk on complete graphs spend almost the same time at each node.

Place, publisher, year, edition, pages
Springer, 2018
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009
Keywords
Graph, Lazy PageRank, PageRank, Random walk, Random processes, Stochastic systems, Websites, Complete graphs, Diverse methods, Explicit formula, Line graph, Numerical values, Graph theory
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41835 (URN)10.1007/978-3-030-02825-1_17 (DOI)2-s2.0-85058552957 (Scopus ID)978-3-030-02824-4 (ISBN)
Conference
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
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
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