Topological Properties And Fractal Dimension Of The Sierpinski And Generalized Sierpinski Networks

We first construct two kinds of networks based on the procedure to constructSierpinski gasket and generalized Sierpinski gasket which are basic examples ofself-similar sets in fractal theory. Then some of their topological properties arediscussed. The degree distributions of nodes show that these networks are notscale-free. A mixture of two normal distributions is used to fit the distributionof shortest path lengths of these networks (n≥5). The analytical formulas ofclustering coefficient and edge clustering coefficient of these networks are given.Finally the fractal dimensions of these networks are calculated and comparedwith those of the n-level basic sets of Sierpinski gasket and generalized Sieroinskigasket. It is found that di?erent metrics can induce di?erent fractal dimensions.