The rigorous solution for the average distance of a Sierpinski network

TL;DR

This paper derives an exact, closed-form solution for the average distance in a deterministic Sierpinski network, confirming that it grows logarithmically with network size, contrasting with random network behavior.

Contribution

The paper provides the first rigorous analytical formula for the average distance in a Sierpinski network, using recursion relations based on its self-similar structure.

Findings

Average distance grows logarithmically with network size

The analytical solution confirms previous numerical results

Contrasts with average distance behavior in random networks

Abstract

The closed-form solution for the average distance of a deterministic network--Sierpinski network--is found. This important quantity is calculated exactly with the help of recursion relations, which are based on the self-similar network structure and enable one to derive the precise formula analytically. The obtained rigorous solution confirms our previous numerical result, which shows that the average distance grows logarithmically with the number of network nodes. The result is at variance with that derived from random networks.