Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

TL;DR

This paper introduces deterministic Sierpinski networks that exhibit scale-free, small-world, and power-law strength-degree correlation properties, aligning well with real-world network characteristics.

Contribution

It presents a new class of maximal planar, scale-free, small-world networks based on Sierpinski fractals with analytical characterizations.

Findings

Degree and strength distributions follow power laws.

Networks exhibit high clustering coefficients.

Strength-degree correlation is analytically derived.

Abstract

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.