Scale-free Network on Euclidean Space Optimized by Rewiring of Links

TL;DR

This paper constructs a scale-free network on Euclidean space, optimizing total wiring length through rewiring while maintaining node degrees, resulting in a network with small diameter, high clustering, and a stretched exponential link length distribution.

Contribution

It introduces a method to optimize a scale-free network on a plane by rewiring links to minimize total length without altering node degrees, combining spatial constraints with scale-free properties.

Findings

Optimized network has small diameter and high clustering.

Link length distribution exhibits a stretched exponential tail.

Total wiring length is minimized while preserving degree distribution.

Abstract

A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring length associated with a such a network defined on a two dimensional plane is optimized. The optimization process consists of random selection of a pair of links and rewiring them to reduce the total length of the pair but with the constraint that the degree as well as the out-degree and in-degree of each node are precisely maintained. The resulting optimized network has a small diameter as well as high clustering and the link length distribution has a stretched exponential tail.