Modeling the Small-World Phenomenon with Road Networks

TL;DR

This paper introduces a new model for the small-world phenomenon on road networks, demonstrating improved routing efficiency and scale-free properties that better reflect real-world social connections.

Contribution

The Neighborhood Preferential Attachment model combines existing models to better explain small-world navigability in road networks, outperforming previous models in routing efficiency.

Findings

Our model achieves shorter average hop lengths in routing.

Networks generated are scale-free, similar to real social networks.

The model outperforms Kleinberg's and Barabási-Albert models in empirical tests.

Abstract

Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages. Many subsequent papers have attempted to model this phenomenon, with most concentrating on the "short chain" of acquaintances rather than their ability to efficiently route messages. In this paper, we study the small-world navigability of the U.S. road network, with the goal of providing a model that explains how messages in the original small-world experiments could be routed along short paths using U.S. roads. To this end, we introduce the Neighborhood Preferential Attachment model, which combines elements from Kleinberg's model and the Barab\'asi-Albert model, such that long-range links are chosen according to both the degrees and (road-network) distances of vertices in the network. We empirically evaluate all three models by running a decentralized routing algorithm, where each vertex only has knowledge of its own neighbors, and find that our model outperforms both of these models in terms of the average hop length. Moreover, our experiments indicate that similar to the Barab\'asi-Albert model, networks generated by our model are scale-free, which could be a more realistic representation of acquaintanceship links in the original small-world experiment.