A geometric growth model interpolating between regular and small-world networks

TL;DR

This paper introduces a geometric growth model that smoothly transitions between regular linear graphs and small-world networks, providing insights into their topological properties through theoretical and simulation analyses.

Contribution

It presents a novel geometric growth model that interpolates between regular and small-world networks, complementing existing static models.

Findings

Model exhibits a transition from large to small world properties.

Theoretical predictions align well with numerical simulations.

Provides a new framework for understanding network topology evolution.

Abstract

We propose a geometric growth model which interpolates between one-dimensional linear graphs and small-world networks. The model undergoes a transition from large to small worlds. We study the topological characteristics by both theoretical predictions and numerical simulations, which are in good accordance with each other. Our geometrically growing model is a complementarity for the static WS model.