Analysis of diffusion and trapping efficiency for random walks on non-fractal scale-free trees

Abstract

We study discrete random walks on the NFSFT and provide new methods to calculate the analytic solutions of the MFPT for any pair of nodes, the MTT for any target node and MDT for any source node. Further more, using the MTT and the MDT as the measures of trapping efficiency and diffusion efficiency respectively, we compare the trapping efficiency and diffusion efficiency for any two nodes of NFSFT and find the best (or worst) trapping sites and the best (or worst) diffusion sites. Our results show that: the two hubs of NFSFT is the best trapping site, but it is also the worst diffusion site, the nodes which are the farthest nodes from the two hubs are the worst trapping sites, but they are also the best diffusion sites. Comparing the maximum and minimum of MTT and MDT, we found that the ratio between the maximum and minimum of MTT grows logarithmically with network order, but the ratio between the maximum and minimum of MTT is almost equal to $1$. These results implie that the trap's position has great effect on the trapping efficiency, but the position of source node almost has no effect on diffusion efficiency. We also conducted numerical simulation to test the results we have derived, the results we derived are consistent with those obtained by numerical simulation.

23 pages, 4 figures

References in corpus (10)

• Fractal and Transfractal Recursive Scale-Free Nets
• First passage time statistics of Brownian motion with purely time dependent drift and diffusion
• Exact mean first-passage time on the T-graph
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Determining mean first-passage time on a class of treelike regular fractals
• Random walks on the Apollonian network with a single trap
• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Mean first-passage time for random walks on the T-graph
• Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks
• From regular to growing small-world networks

Cited by in corpus (4)

• Exact calculations of first-passage properties on the pseudofractal scale-free web
• Mean trapping time for an arbitrary node on regular hyperbranched polymers
• Analysis of fluctuations in the first return times of random walks on regular branched networks
• Volatilities analysis of first-passage time and first-return time on a small-world scale-free network