Spatially embedded growing small-world networks

TL;DR

This paper introduces spatially-based growing network models that develop small-world properties, demonstrating how the embedding space's dimension influences network characteristics like path length and clustering.

Contribution

It presents a novel class of spatially embedded growth models and analyzes how space dimension affects network properties such as small-world features.

Findings

Higher-dimensional spaces lead to shorter path lengths.

Clustering decreases as space dimension increases.

Small-world features emerge naturally in the models.

Abstract

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the resulting statistical network properties and the dimension and topology of the space in which the networks are embedded. In particular, we consider models in which nodes are placed one by one in random locations in space, with each such placement followed by configuration relaxation toward uniform node density, and connection of the new node with spatially nearby nodes. We find that such growth processes naturally result in networks with small-world features, including a short characteristic path length and nonzero clustering. These properties do not appear to depend strongly on the topology of the embedding space, but do depend strongly on its dimension; higher-dimensional spaces result in shorter path lengths but less clustering.