Random Walks On Two Classes Of Self-similar Weighted Networks

This paper mainly investigates two aspects,which involve the average trapping time on weighted scale-free m-triangulation networks and some exact results of first-passage properties on weighted pesudofractal scale-free networks.On the one hand,the model of weighted scale-free m-tri angulation networks can be built by introducing the weight factor,and the average trapping time for weight-dependent is deduced basing on the topological properties of networks.In terms of its good self-similarity,we achieve the analytic expression of the average trapping time via iterative calculations.Results show that the corresponding analytic expression referring to the weight factor r and the growth factor m is obtained,which obeys a power-law function with exponent (?).Or rather the smaller r and m are,the higher efficiency of the trapping process is.On the other hand,we establish the model of weighted pesudofractal scale-free networks and propose a new edge weighting which allocates rt to the value of new edge on Gt,the first passage properties can be researched in the mode of weight-dependent at the same time.Furthermore,a few of precise results and the fluctuation of the index are available by means of the probability generating function.Results indicates that the first return time fluctuates greatly while the global first passage time fluctuates slightly,which draws a conclusion that the global first passage time is more reliable than the first return time.