The evolution of navigable small-world networks

TL;DR

This paper introduces and analyzes a dynamic model for small-world networks where the graph evolves through successive rewiring, enabling efficient navigation similar to Kleinberg's static model.

Contribution

It presents a novel dynamic rewiring algorithm for small-world networks, extending Kleinberg's static model to an evolving network context.

Findings

The rewiring process produces networks with navigability properties similar to Kleinberg's model.

The algorithm demonstrates effective navigation with minimal prior knowledge.

The model captures the evolution of small-world networks over time.

Abstract

Small-world networks, which combine randomized and structured elements, are seen as prevalent in nature. Several random graph models have been given for small-world networks, with one of the most fruitful, introduced by Jon Kleinberg, showing in which type of graphs it is possible to route, or navigate, between vertices with very little knowledge of the graph itself. Kleinberg's model is static, with random edges added to a fixed grid. In this paper we introduce, analyze and test a randomized algorithm which successively rewires a graph with every application. The resulting process gives a model for the evolution of small-world networks with properties similar to those studied by Kleinberg.