Geographical Embedding of Scale-Free Networks

TL;DR

This paper introduces a new method for embedding scale-free networks into Euclidean space, emphasizing geographic proximity and link length minimization, revealing significant differences from traditional off-lattice models.

Contribution

It proposes a novel embedding algorithm for scale-free networks that considers geographic closeness and analyzes its impact on network properties.

Findings

Embedded networks show dramatic topological and geometrical changes.

The results challenge the applicability of off-lattice scale-free models to real-world networks.

The method provides insights into the physical constraints of spatially embedded networks.

Abstract

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scale-free networks embedded by the suggested algorithm are studied both analytically and through simulations. Our findings indicate dramatic changes in the embedded networks, in comparison to their off-lattice counterparts, and call into question the applicability of off-lattice scale-free models to realistic, everyday-life networks.