title: The entire mean weighted first-passage time on a family of weighted treelike networks.
abstract: In this paper, we consider the entire mean weighted first-passage time (EMWFPT) with random walks on a family of weighted treelike networks. The EMWFPT on weighted networks is proposed for the first time in the literatures. The dominating terms of the EMWFPT obtained by the following two methods are coincident. 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. The obtained results show that the effective resistance is equal to the weighted shortest path between two nodes. And the dominating term of the EMWFPT scales linearly with network size in large network.
authors.affiliation: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University Zhenjiang, Jiangsu, 212013, P.R. China.
authors.forename: Meifeng
authors.initials: M
authors.lastname: Dai
authors.affiliation: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University Zhenjiang, Jiangsu, 212013, P.R. China.
authors.forename: Yanqiu
authors.initials: Y
authors.lastname: Sun
authors.affiliation: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University Zhenjiang, Jiangsu, 212013, P.R. China.
authors.forename: Yu
authors.initials: Y
authors.lastname: Sun
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo, 315211, P.R. China.
authors.forename: Lifeng
authors.initials: L
authors.lastname: Xi
authors.affiliation: Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University Zhenjiang, Jiangsu, 212013, P.R. China.
authors.forename: Shuxiang
authors.initials: S
authors.lastname: Shao