盆栽分形网络两点间的电阻距离

Resistance Distance between Two Points of Potting Fractal Network

图中两顶点间的电阻距离是指将图中每条边用单位电阻替换后得到的电网络中对应节点间的有效电阻。分形是跨度不同尺度自相似的无限复杂模式,它是通过不断重复一个简单的过程而重复出来的结构。本文研究盆栽分形网络这类自相似网络。利用消除原理、替换原理以及局部和规则,给出了任意两个节点间电阻距离的递推公式。

The resistance distance between two vertices in the graph refers to the effective resistance between corresponding nodes in the electrical network obtained by replacing each edge in the graph with a unit resistor.Fractal is an infinite complex model with self-similarity across different scales,which is obtained by repeating a simple process.In this paper,for a class of self-similar networks named potting networks,we obtain a recursive formula for computing resistance distance between any two nodes by using elimination principle,substitution principle and local sum rules.