论文标题
在水平分区的Sierpinski垫圈网络上吸收的平均吸收时间
The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks
论文作者
论文摘要
随机步行是复杂网络的最基本动态属性之一，由于其在实际网络中的许多应用，近年来它逐渐成为研究热点。随机步行的一个重要特征是平均吸收时间，这在拓扑，动力学和复杂网络的实际应用中起着极为重要的作用。分析在常规迭代自相似网络模型上吸收吸收的平均时间是探索自相似性对网络随机步行属性的影响的重要方法。现有文献证明，即使是局部自相似结构也可以极大地影响全球网络上随机步行的特性，但是它们未能证明这些影响是否与这些自相似结构的规模有关。在本文中，我们基于经典的Sierpinski垫圈网络构建和研究一类水平分区的Sierpinski垫片网络模型，该网络由局部自相似结构组成，这些结构的规模将由分区系数$ k $控制。然后，获得了在网络模型上吸收的平均吸收时间的分析表达式和近似表达式，这证明网络中的自相似结构的大小将直接限制自相似结构对网络随机步行属性的影响。最后，我们还分析了在网络上吸收不同吸收节点的平均时间，以找到具有最高吸收效率的节点的位置。
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.
