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On principal eigenpair of temporal-joined adjacency matrix for spreading phenomenon

Author

Listed:
  • Shih-Chieh Wang

    (RIKEN Center for Computational Science)

  • Nobuyasu Ito

    (RIKEN Center for Computational Science
    The University of Tokyo)

Abstract

This paper reports a framework of analysis of spreading herbivore of individual-based system with time evolution network $$\widetilde{A}(t)$$ A ~ ( t ) . By employing a sign function $$\theta _1 \left( x \right)$$ θ 1 x , $$\theta _1 \left( 0 \right) =0$$ θ 1 0 = 0 , $$\theta _1 \left( x \right) =1$$ θ 1 x = 1 $$x \in {\mathbb {N}}$$ x ∈ N , the dynamic equation of spreading is in a matrix multiplication expression. Based on that, a method of combining temporal network is reported. The risk of been-spread and the ability to spread can be illustrated by the principal eigenpair of temporal-joined matrix in a system. The principal eigenpair of post-joined matrix can estimate the step number to the farthest agent $$S_i$$ S i in a non-time evolution network system $${\widetilde{A}}\left( t\right) ={\widetilde{A}}$$ A ~ t = A ~ as well.

Suggested Citation

  • Shih-Chieh Wang & Nobuyasu Ito, 2019. "On principal eigenpair of temporal-joined adjacency matrix for spreading phenomenon," Journal of Computational Social Science, Springer, vol. 2(1), pages 67-76, January.
    • Handle: RePEc:spr:jcsosc:v:2:y:2019:i:1:d:10.1007_s42001-019-00030-2
    DOI: 10.1007/s42001-019-00030-2
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    References listed on IDEAS

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    1. Eugenio Valdano & Chiara Poletto & Armando Giovannini & Diana Palma & Lara Savini & Vittoria Colizza, 2015. "Predicting Epidemic Risk from Past Temporal Contact Data," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-19, March.
    2. Wang, Shih-Chieh & Ito, Nobuyasu, 2018. "Pathogenic–dynamic epidemic agent model with an epidemic threshold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1038-1045.
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