A Small-World and Scale-Free Network Generated by Sierpinski Tetrahedron

The Sierpinski tetrahedron is used to construct evolving networks, whose vertexes are all solid regular tetrahedra in the construction of the Sierpinski tetrahedron up to the stage [Formula: see text] and any two vertexes are neighbors if and only if the corresponding tetrahedra are in contact with each other on boundary. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.