Evolving small-world networks with geographical attachment preference

TL;DR

This paper presents a minimal evolving model for small-world networks that emphasizes geographical proximity in node attachment, capturing key real-world network features like small-world effect and high clustering.

Contribution

The model introduces a parameter-controlled mechanism for network growth based on geographical attachment, combining analytical and numerical analysis.

Findings

Network exhibits small-world properties.

High clustering coefficient observed.

Model aligns with real-world network characteristics.

Abstract

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.