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

Shih-Chieh Wang () and Nobuyasu Ito
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Shih-Chieh Wang: RIKEN Center for Computational Science
Nobuyasu Ito: RIKEN Center for Computational Science

Journal of Computational Social Science, 2019, vol. 2, issue 1, No 8, 67-76

Abstract: 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.

Keywords: Agent model; Epidemic; Contact network (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s42001-019-00030-2

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