The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

TL;DR

This paper investigates how the scale of local self-similar structures in a Horizontal Partitioned Sierpinski Gasket network influences the mean time to absorption of random walks, providing analytical expressions and insights into node absorption efficiency.

Contribution

It introduces a new class of self-similar network models with controllable structure scale and derives analytical formulas for mean absorption time, linking structure size to random walk properties.

Findings

Size of self-similar structures directly affects absorption time.

Analytical expressions for mean time to absorption are derived.

Identified nodes with highest absorption efficiency.

Abstract

The random walk is one of the most basic dynamic properties of complex networks, which has gradually become a research hotspot in recent years due to its many applications in actual networks. An important characteristic of the random walk is the mean time to absorption, which plays an extremely important role in the study of topology, dynamics and practical application of complex networks. Analyzing the mean time to absorption on the regular iterative self-similar network models is an important way to explore the influence of self-similarity on the properties of random walks on the network. The existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network, but they have failed to prove whether these effects are related to the scale of these self-similar structures. In this article, we construct and study a class of Horizontal Partitioned Sierpinski Gasket network model based on the classic Sierpinski gasket network, which is composed of local self-similar structures, and the scale of these structures will be controlled by the partition coefficient $k$. Then, the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained, which prove that the size of the self-similar structure in the network will directly restrict the influence of the self-similar structure on the properties of random walks on the network. Finally, we also analyzed the mean time to absorption of different absorption nodes on the network to find the location of the node with the highest absorption efficiency.