Small-Worlds, Mazes and Random Walks

TL;DR

This paper explores the connection between Small-World phenomena in complex networks and Random Walks through maze representations, revealing a power-law scaling instead of the typical logarithmic behavior.

Contribution

It introduces a novel approach linking maze iconography to Small-World networks via Random Walks, providing insights into their scaling properties.

Findings

Small-World behavior exhibits power-law scaling in this model

Mazes can be generated using Random Walks and interpreted as graphs

Loops in mazes act as shortcuts, influencing network properties

Abstract

We establish a relationship between the Small-World behavior found in complex networks and a family of Random Walks trajectories using, as a linking bridge, a maze iconography. Simple methods to generate mazes using Random Walks are discussed along with related issues and it is explained how to interpret mazes as graphs and loops as shortcuts. Small-World behavior was found to be non-logarithmic but power-law in this model, we discuss the reason for this peculiar scaling