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

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 three dimensional Sierpinski gasket network is constructed, whose main feature is that it contains the locally self-similar structures of the two dimensional Sierpinski gasket network and the three 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 of a random walker by a particular site 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.