Mean Weighted First-passage Time Of Random Walks On Three Classes Weighted Networks

In order to study the weighted networks structure characteristics,we need to learn an important performance indicator-the mean weighted first-passage time.In this paper,we mainly calculates the mean weighted first-passage time of random walks on three classes weighted deterministic networks.In details,the main contents of this paper are organized as follows:In Chapter 1,we introduce the development background and processes of weighted networks,and the basic concepts about calculating the mean weighted first-passage time of weighted networks.In Chapter 2,we use two methods to calculate the entire mean weighted first-passage time(EMWFPT)with random walks on a family of weighted treelike networks for the first time in the literatures.On the one hand,using the construction algorithm,we calculate the receiving and sending times for the central node to obtain the asymptotic behavior of the EMWFPT.On the other hand,applying the relationship equation between the EMWFPT and the average weighted shortest path,we also obtain the asymptotic behavior of the EMWFPT.And the dominating term of the EMWFPT scales linearly with network size in large network.In Chapter 3,we describe a technique that allows the exact analytical computation of the entire mean weighted first passage time(MWFPT)for infinite families of trees,This method bases on the relationship between characteristic polynomials at different generations of their Laplacian matrix and Laplacian eigenvalues to compute EMWFPT,whose key step here is to calculate the constant terms and the coefficients of first-order terms of characteristic polynomials.Finally,we obtain analytically the closed-form solutions to EMWFPT on the weighted tree networks,and show that the leading term of EMWFPT grows superlinearly with the network size.In Chapter 4,we introduce a family of weighted fractal networks.For the case of the weighted fractal networks the definition of modified box dimension is introduced,and a rigorous proof for its existence is given.Then,the modified box dimension depending on the weighted factor and the number of copies is deduced.Then we research the mean weighted receiving time.This result shows that the efficiency of the trapping process depends on the modified box dimension: the larger the value of modified box dimension,the more efficient the trapping process is.