Asymptotic formula on average path length of fractal networks modelled on Sierpinski Gasket

TL;DR

This paper presents a new method for constructing evolving networks based on the Sierpinski gasket, deriving an asymptotic formula for their average path length using self-similarity and renewal theory.

Contribution

It introduces a novel network model inspired by fractal geometry and provides an analytical asymptotic formula for average path length.

Findings

Asymptotic formula for average path length derived

Network model based on Sierpinski gasket constructed

Utilizes self-similarity and renewal theorem techniques

Abstract

In this paper, we introduce a new method to construct evolving networks based on the construction of the Sierpinski gasket. Using self-similarity and renewal theorem, we obtain the asymptotic formula for average path length of our evolving networks.