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New highlights and a new centrality measure based on the Adapted PageRank Algorithm for urban networks

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  • Agryzkov, Taras
  • Tortosa, Leandro
  • Vicent, Jose F.

Abstract

The Adapted PageRank Algorithm (APA) proposed by Agryzkov et al. provides us a method to establish a ranking of nodes in an urban network. We can say that it constitutes a centrality measure in urban networks, with the main characteristic that is able to consider the importance of data obtained from the urban networks in the process of computing the centrality of every node. Starting from the basic idea of this model, we modify the construction of the matrix used for the classification of the nodes in order of importance. In the APA model, the data matrix is constructed from the original idea of PageRank vector, given an equal chance to jump from one node to another, regardless of the topological distance between nodes. In the new model this idea is questioned. A new matrix with the data network is constructed so that now the data from neighboring nodes are considered more likely than data from the nodes that are farther away. In addition, this new algorithm has the characteristic that depends on a parameter α, which allows us to decide the importance attached, in the computation of the centrality, to the topology of the network and the amount of data associated with the node. Various numerical experiments with a network of very small size are performed to test the influence of the data associated with the nodes, depending always on the choice of the parameter α. Also we check the differences between the values produced by the original APA model and the new one. Finally, these measures are applied to a real urban network, in which we perform a visual comparison of the results produced by the various measures calculated from the algorithms studied.

Suggested Citation

  • Agryzkov, Taras & Tortosa, Leandro & Vicent, Jose F., 2016. "New highlights and a new centrality measure based on the Adapted PageRank Algorithm for urban networks," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 14-29.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:14-29
    DOI: 10.1016/j.amc.2016.06.036
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    References listed on IDEAS

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    1. Porta, Sergio & Crucitti, Paolo & Latora, Vito, 2006. "The network analysis of urban streets: A dual approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 853-866.
    2. Chen, Zengqiang & Dehmer, Matthias & Shi, Yongtang, 2015. "Bounds for degree-based network entropies," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 983-993.
    3. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
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    Cited by:

    1. Bowater, David & Stefanakis, Emmanuel, 2023. "Extending the Adapted PageRank Algorithm centrality model for urban street networks using non-local random walks," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    2. Aleja, David & Criado, Regino & García del Amo, Alejandro J. & Pérez, Ángel & Romance, Miguel, 2019. "Non-backtracking PageRank: From the classic model to hashimoto matrices," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 283-291.
    3. Li, Zhitao & Tang, Jinjun & Zhao, Chuyun & Gao, Fan, 2023. "Improved centrality measure based on the adapted PageRank algorithm for urban transportation multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Mirco Nanni & Leandro Tortosa & José F Vicent & Gevorg Yeghikyan, 2020. "Ranking places in attributed temporal urban mobility networks," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-25, October.
    5. Tortosa, Leandro & Vicent, Jose F. & Yeghikyan, Gevorg, 2021. "An algorithm for ranking the nodes of multiplex networks with data based on the PageRank concept," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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