Average trapping time on a type of horizontally segmented 3 dimensional Sierpinski gasket network with two types of locally self-similar structures

TL;DR

This paper constructs a novel 3D Sierpinski gasket network with two types of self-similar structures and analyzes how these structures influence the average trapping time of random walks.

Contribution

It introduces a horizontally segmented 3D Sierpinski gasket network with controllable self-similar structures and derives the analytical expression for average trapping time.

Findings

The dominant self-similar structure significantly affects the random walk process.

The scale transformation between structures can be controlled by a crosscutting coefficient.

Analytical expression for average trapping time is obtained.

Abstract

As a classic self-similar network model, Sierpinski gasket network has been used many times to study the characteristics of self-similar structure and its influence on the dynamic properties of the network. However, the network models studied in these problems only contain a single self-similar structure, which is inconsistent with the structural characteristics of the actual network models. In this paper, a type of horizontally segmented 3 dimensional Sierpinski gasket network is constructed, whose main feature is that it contains the locally self-similar structures of the 2 dimensional Sierpinski gasket network and the 3 dimensional Sierpinski gasket network at the same time, and the scale transformation between the two kinds of self-similar structures can be controlled by adjusting the crosscutting coefficient. The analytical expression of the average trapping time on the network model is solved, which used to analyze the effect of two types of self-similar structures on the properties of random walks. Finally, we conclude that the dominant self-similar structure will exert a greater influence on the random walk process on the network.