Average Trapping time on the 3-dimensional 3-level Sierpinski gasket network with a set of trap nodes

TL;DR

This paper derives analytical expressions for the mean global first passage time and average trapping time on a 3D Sierpinski gasket network, revealing how trap node sets influence trapping efficiency.

Contribution

It provides the first analytical formulas for ATT on the 3D Sierpinski gasket with multiple trap nodes, based on the network's self-similarity.

Findings

ATT varies significantly with different trap node sets.

The super-linear relationship between ATT and iteration number remains consistent.

Analytical results are validated through examples and numerical simulations.

Abstract

As a basic dynamic feature on complex networks, the property of random walk has received a lot of attention in recent years. In this paper, we first studied the analytical expression of the mean global first passage time (MGFPT) on the 3-dimensional 3-level Sierpinski gasket network. Based on the self-similar structure of the network, the correlation between the MGFPT and the average trapping time (ATT) is found, and then the analytical expression of the ATT is obtained. Finally, by establishing a joint network model, we further give the standard process of solving the analytical expression of the ATT when there is a set of trap nodes in the network. By illustrating examples and numerical simulations, it can be proved that when the trap node sets are different, the ATT will be quite different, but the the super-linear relationship with the number of iterations will not be changed.