In this paper, we present the weighted iterated friendship graphs and study the trapping problem on the weighted iterated friendship graphs. It can be found that for $0<r<1$ and $r=1$, the relationship between the average trapping time (ATT) and network size is sublinear and linear, respectively. By controlling the parameters of the weighted iterated friendship graphs, the models are changed to the self-similar weighted networks. The average shortest weighted path (ASWP) in the self-similar weighted friendship graphs is studied. The results show that when $0<r<1$, the ASWP is bounded, and when $r=1$, the ASWP is linearly related to the order of the networks.

中文翻译：

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加权迭代友谊图上的加权平均步行和平均最短加权路径

在本文中，我们提出了加权迭代友谊图并研究了加权迭代友谊图上的陷阱问题。可以发现，对于$0<r<1$和$r=1$，平均捕获时间（ATT）和网络大小之间的关系分别是亚线性和线性的。通过控制加权迭代友谊图的参数，将模型变为自相似加权网络。研究了自相似加权友谊图中的平均最短加权路径（ASWP）。结果表明，当$0<r<1$, ASWP 是有界的, 当$r=1$, ASWP 与网络的阶数线性相关。