Complex networks modeled on the Sierpinski gasket

• Evolving networks modeled on the Sierpinski gasket are constructed and analyzed.
• The evolving networks are scale-free.
• The evolving networks have the small-world effect.

In this paper, we use the Sierpinski gasket to construct evolving networks GtGt whose node set is the solid regular triangles in the construction of the Sierpinski gasket up to the stage tt and any two nodes are neighbors if and only if the corresponding solid triangles are in contact with each other on boundary. Using the encoding method, we show that our evolving networks are scale-free (power-law degree distribution) and have the small-world effect (small average path length and high clustering coefficient).