带权图的多重分形研究

刘胜久,李天瑞,珠杰,刘佳

Research on multi⁃fractals of weighted graphs

Shengjiu Liu,Tianrui Li,Jie Zhu,Jia Liu

表1 节点权重为正实数的四种不同类型带权图分形维数统计表

Table 1 Statistics of fractal dimensions of four weighted graphs with node weight being positive real numbers

编号	节点权重	边权重	分形维数
1	正实数 $f (v)$	正实数 $f (e)$	$\frac{1}{l g \sum_{v \in V} f (v)} l g \sum_{e \in E} f (e)$ (6)
2		负实数 $- f (e)$	$\frac{1}{l g \sum_{v \in V} f (v)} l g e^{i π} \sum_{e \in E} f (e)$ (7)
3		纯虚数 $i f (e)$	$\frac{1}{l g \sum_{v \in V} f (v)} l g e^{\frac{i π}{2}} \sum_{e \in E} f (e)$ (8)
4		复数 $(a + b i) f (e)$	$\frac{1}{l g \sum_{v \in V} f (v)} l g \sqrt[]{a^{2} + b^{2}} e^{i t a n^{- 1} \frac{b}{a}} \sum_{e \in E} f (e)$ (9)