A simple model clarifies the complicated relationships of complex networks

TL;DR

This paper introduces a simple optimization-based model that can generate a wide variety of complex network traits, offering a unified understanding of their relationships.

Contribution

It presents a universal, optimization-driven model capable of reproducing diverse network properties and structures, simplifying the understanding of complex network relationships.

Findings

Model reproduces scale-free, small-world, and fractal networks.

Revised model generates community-structure networks.

Provides a universal perspective on complex network modeling.

Abstract

Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it is widely believed that these traits origin from different causes. However, we find that a simple model based on optimisation can produce many traits, including scale-free, small-world, ultra small-world, Delta-distribution, compact, fractal, regular and random networks. Moreover, by revising the proposed model, the community-structure networks are generated. By this model and the revised versions, the complicated relationships of complex networks are illustrated. The model brings a new universal perspective to the understanding of complex networks and provide a universal method to model complex networks from the viewpoint of optimisation.