Abstract
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.
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Acknowledgements
This research was supported by the Swedish International Development Cooperation Agency (Sida), International Science Programme (ISP) in Mathematical Sciences (IPMS), Sida Bilateral Research Program (Makerere University and University of Dar-es-Salaam). We are also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardålen University for providing an excellent and inspiring environment for research education and research. The authors are grateful to Dmitrii Silvestrov for useful comments and discussions.
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Abola, B., Biganda, P.S., Engström, C., Mango, J.M., Kakuba, G., Silvestrov, S. (2018). PageRank in Evolving Tree Graphs. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Stochastic Processes and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 271. Springer, Cham. https://doi.org/10.1007/978-3-030-02825-1_16
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