Average weighted trapping time of the node- and edge-weighted fractal networks

摘要

In this paper, we study the trapping problem in the node- and edge- weighted fractal networks with the underlying geometries, focusing on a particular case with a perfect trap located at the central node. We derive the exact analytic formulas of the average weighted trapping time (AWTT), the average of node-to-trap mean weighted first-passage time over the whole networks, in terms of the network size N-g, the number of copies s, the node-weight factor w and the edge-weight factor r. The obtained result displays that in the large network, the AWTT grows as a power-law function of the network size N-g with the exponent, represented by theta(s, r, w) = log(s) (srw(2)) when srw(2) not equal 1. Especially when srw(2) = 1, AWTT grows with increasing order N-g as log N-g. This also means that the efficiency of the trapping process depend on three main parameters: the number of copies s > 1, node-weight factor 0 < w <= 1, and edge-weight factor 0 < r <= 1. The smaller the value of srw(2) is, the more efficient the trapping process is. (C) 2016 Elsevier B.V. All rights reserved.