TY - JOUR
T1 - The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks
AU - Zhang , Zhizhuo
AU - Wu , Bo
AU - Yu , Zuguo
JO - Analysis in Theory and Applications
VL - 1
SP - 1
EP - 21
PY - 2024
DA - 2024/04
SN - 40
DO - http://doi.org/10.4208/ata.OA-2021-0014
UR - https://global-sci.org/intro/article_detail/ata/23017.html
KW - Mean time to absorption, self-similar network, Sierpinski Gasket.
AB - <p style="text-align: justify;">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.</p>