WEIGHT-DEPENDENT WALKS AND AVERAGE SHORTEST WEIGHTED PATH ON THE WEIGHTED ITERATED FRIENDSHIP GRAPHS

Abstract

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 [Formula: see text] and [Formula: see text], 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 [Formula: see text], the ASWP is bounded, and when [Formula: see text], the ASWP is linearly related to the order of the networks.