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A Perron–Frobenius theory for block matrices associated to a multiplex network

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  • Romance, Miguel
  • Solá, Luis
  • Flores, Julio
  • García, Esther
  • García del Amo, Alejandro
  • Criado, Regino

Abstract

The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.

Suggested Citation

  • Romance, Miguel & Solá, Luis & Flores, Julio & García, Esther & García del Amo, Alejandro & Criado, Regino, 2015. "A Perron–Frobenius theory for block matrices associated to a multiplex network," Chaos, Solitons & Fractals, Elsevier, vol. 72(C), pages 77-89.
    • Handle: RePEc:eee:chsofr:v:72:y:2015:i:c:p:77-89
    DOI: 10.1016/j.chaos.2014.12.020
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    Cited by:

    1. 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.
    2. Deng, Zheng-Hong & Huang, Yi-Jie & Gu, Zhi-Yang & Liu, Dan & Gao, Li, 2018. "Multigames with voluntary participation on interdependent networks and the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 151-157.
    3. Pérez, Sergio Iglesias & Moral-Rubio, Santiago & Criado, Regino, 2023. "Combining multiplex networks and time series: A new way to optimize real estate forecasting in New York using cab rides," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Iglesias Pérez, Sergio & Moral-Rubio, Santiago & Criado, Regino, 2021. "A new approach to combine multiplex networks and time series attributes: Building intrusion detection systems (IDS) in cybersecurity," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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