Fast Generation of Spatially Embedded Random Networks

TL;DR

This paper introduces a highly efficient algorithm for generating spatially embedded random networks, significantly reducing the computational complexity from quadratic to linear in the number of nodes and edges.

Contribution

The paper presents a novel $O(n + e)$ algorithm for fast generation of spatially embedded random networks, improving over previous $O(n^2)$ methods.

Findings

The new algorithm is significantly faster for large networks.

It maintains the statistical properties of the original models.

The approach is applicable to various spatially embedded network types.

Abstract

Spatially Embedded Random Networks such as the Waxman random graph have been used in a variety of settings for synthesizing networks. However, little thought has been put into fast generation of these networks. Existing techniques are $O(n^2)$ where $n$ is the number of nodes in the graph. In this paper we present an $O(n + e)$ algorithm, where $e$ is the number of edges.