Scaling of average receiving time on weighted polymer networks with some topological properties

Abstract

Abstract In this paper, a family of the weighted polymer networks is introduced depending on the number of copies f and a weight factor r. The topological properties of weighted polymer networks can be completely analytically characterized in terms of the involved parameters and/or of the fractal dimension. Moreover, assuming that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the weight of edge linking them, namely weight-dependent walk. Then, we calculate the average receiving time (ART) with weighted-dependent walks, which is the sum of mean first-passage times (MFPTs) for all nodes absorpt at the trap located at the central node as a recursive relation. The obtained remarkable results display that when $$\frac{1}{f+1} < r < 1$$ 1 f + 1 < r < 1 , the ART grows sublinearly with the network size; when $$r=\frac{1}{f+1}$$ r = 1 f + 1 , ART grows with increasing size N g as $${\mathrm{ln}}^{2}{N}_{g}$$ ln 2 N g ; when $$0 < r < \frac{1}{f+1}$$ 0 < r < 1 f + 1 , ART grows with increasing size N g as ln N g . In the treelike polymer networks, ART grows with linearly with the network size N g when r = 1. Thus, the weighted polymer networks are more efficient than treelike polymer networks in receiving information.