Random Sierpinski network with scale-free small-world and modular structure

TL;DR

This paper introduces a stochastic Sierpinski gasket-based network called RSN, which exhibits multiple complex features like scale-free, small-world, modularity, and planarity, with analytical and numerical validation.

Contribution

It presents a novel stochastic Sierpinski gasket model for networks, demonstrating its rich structural properties and potential applications in biological and information systems.

Findings

RSN is scale-free and small-world

RSN is modular and maximal planar

Analytical results match numerical simulations

Abstract

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our network representation method could be applied to study the complexity of some real systems in biological and information fields.