The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton ...networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.
•The asymptotic formula of average distance for tetrahedron networks are obtained.•The average geodesic distance of the Sierpinski tetrahedron is described as an integral.•The finite patterns for integrals of geodesic distance are observed.
•The average distance on stretched Sierspinski gasket is calculated.•The integral of geodesic distances in terms of a local-self-similar measure is established.•The finite patterns of integrals are ...used.
The stretched Sierpiński gasket is a local self-similar set, but not strictly self-similar. By the local self-similarity of scale and measure, we calculate its average geodesic distance within the gasket by the method of finite pattern.
