A small-world and scale-free network generated by Sierpinski Pentagon

• Evolving networks generated by the Sierpinski Pentagon are constructed and analyzed.
• The evolving networks are scale-free.
• The evolving networks have the small-world effect.
• The evolving networks are not fractal scaling.

The Sierpinski Pentagon is used to construct evolving networks, whose nodes are all solid regular pentagons in the construction of the Sierpinski Pentagon up to the stage tt and any two nodes are neighbors if and only if the intersection of corresponding pentagons is non-empty and non-singleton. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.