Binary Apollonian networks

TL;DR

This paper introduces binary Apollonian networks, which exhibit small-world and scale-free properties without clustering, and explores their potential for modeling complex real-world systems.

Contribution

It defines a new class of networks inspired by Pascal's triangle and Sierpinski triangle, revealing their structural properties and potential applications.

Findings

Inherits small-world and scale-free properties

Displays no clustering

Potential for modeling real-world systems

Abstract

There is a well-known relationship between the binary Pascal's triangle and Sierpinski triangle in which the latter obtained from the former by successive modulo 2 additions on one of its corners. Inspired by that, we define a binary Apollonian network and obtain two structures featuring a kind of dendritic growth. They are found to inherit the small-world and scale-free property from the original network but display no clustering. Other key network properties are explored as well. Our results reveal that the structure contained in the Apollonian network may be employed to model an even wider class of real-world systems.