A deterministic small-world network created by edge iterations

TL;DR

This paper introduces a simple deterministic model for small-world networks with a discrete exponential degree distribution, facilitating better understanding of node interactions in fixed-connection systems.

Contribution

It presents a novel deterministic method for generating small-world networks, contrasting with traditional stochastic models, and analyzes its main properties.

Findings

The model produces small-world networks with exponential degree distribution.

Main characteristics of the network are analytically derived.

The approach aids visualization of node interactions in fixed interconnection systems.

Abstract

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.