Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (2): 32-48.doi: 10.3969/j.issn.1000-5641.2019.02.004

• Mathematics • Previous Articles     Next Articles

Average homogeneous and non-homogeneous weighted receiving time in recursive weighted Koch networks

ALHADDAD Mansour A. A., MOHAMMAD Gareeb   

  1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
  • Received:2017-07-17 Online:2019-03-25 Published:2019-03-27

Abstract: In this paper, we introduce the recursive homogeneous weighted Koch network model for real systems with a scaling factor t ∈ (0, 1) and the non-homogeneous model with scaling factors t, s∈ (0, 1) or t, r, s ∈ (0, 1). These models were constructed using the recursive division method and motivated by experimental study of aviation networks and metabolic networks. As a process of fundamental dynamics, we study the recursive homogeneous and non-homogeneous weighted Koch networks with a random walk; for all steps, the walker who is starting from an existing node moves uniformly to one of its nearest neighbors Γ(j) lying on the layers Le, e=0, 1, …, m. In order to study homogeneous and non-homogeneous models, the recursive division method and singular value decomposition were used to calculate the sum of the mean weighted longest paths (MWLP) for all nodes absorbed at the target node placed in one of the merging nodes {pi:i=1, 2, 3}. Finally, in a large network, the average weighted receiving time (AWRT) for homogeneous and nonhomogeneous models grows sub-linearly with the network's order.

Key words: homogeneous weighted Koch network, non-homogeneous weighted Koch network, recursive division method, average weighted receiving time

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