The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks (Analysis in Theory and Applications, 2024)
The random walk is one of the most basic dynamic properties of complexnetworks, which has gradually become a research hotspot in recent years due to itsmany applications in actual networks. An important characteristic of the random walkis the mean time to absorption, which plays an extremely important role in the studyof topology, dynamics and practical application of complex networks. Analyzing themean 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 randomwalks on the network. The existing literatures have proved that even local self-similarstructures 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 theseself-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 expressionsand approximate expressions of the mean time to absorption on the network modelare obtained, which prove that the size of the self-similar structure in the network willdirectly restrict the influence of the self-similar structure on the properties of randomwalks 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 highestabsorption efficiency.
Keywords: Mean time to absorption; self-similar network; Sierpinski Gasket.